Breaking Math Podcast

The Fluid Dynamics of Sheep Oct 29, 2024

In this episode of Breaking Math, we explore the unexpected link between sheep herding and fluid dynamics! Did you know that the way sheep move in a herd is governed by the same mathematical principles as water flowing in a river? By following simple rules of alignment, cohesion, and separation, sheep create a coordinated, fluid-like movement that scientists can model to predict behavior.

Join us as we break down how these principles apply not only to animal herds but also to real-world applications like robotics, autonomous vehicles, and crowd management. Whether you're a math lover, curious about animal behavior, or fascinated by the science behind traffic flow, this episode reveals the incredible power of mathematics in nature. Don’t forget to subscribe for more insights into the surprising connections between math and the world around us!

Timestamps:
00:00 - Introduction to Sheep Herding and Fluid Dynamics
02:15 - What is Fluid Dynamics?
06:30 - How Sheep Behave Like Particles in a Fluid
10:45 - Mathematical Models of Herding Behavior
16:20 - Real-world Applications: From Farming to Robotics
20:55 - Conclusion & Key Takeaways

Tags: #BreakingMath #FluidDynamics #AnimalBehavior #MathInNature #SheepHerding #Robotics #ScienceExplained #EmergentBehavior
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The Discovery of the Largest Prime Number: M136279841 Oct 22, 2024

In this exciting episode of Breaking Math, we explore the groundbreaking discovery of the largest prime number ever found—M136279841, a Mersenne prime with over 41 million digits! Join us as we dive deep into the story behind this astonishing mathematical achievement, led by Luke Durant, a volunteer from the Great Internet Mersenne Prime Search (GIMPS) project.

Discover how Mersenne primes work, why they’re so important to the world of mathematics, and how cutting-edge technology like GPUs has revolutionized the search for these massive numbers. We also discuss the critical role that prime numbers play in cryptography and online security, making this discovery relevant far beyond just the realm of theoretical mathematics.

Learn about the global collaborative effort that made this record-breaking discovery possible, and find out how you can join the hunt for the next giant prime! Whether you're a math enthusiast, a tech geek, or just curious about the wonders of numbers, this episode is packed with insights that will inspire you to think about prime numbers in a whole new way.

Key Takeaways:

The discovery of M136279841, a prime number with 41,024,320 digits.
The role of Luke Durant and the GIMPS project in pushing the boundaries of prime number research.
How GPUs are transforming the way we discover massive primes.
The importance of prime numbers in modern cryptography and technology.
The connection between Mersenne primes and perfect numbers.

Links Mentioned:

Join the GIMPS project and search for the next prime: www.mersenne.org/download
Learn more about Mersenne primes: Mersenne Prime History

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Exploring GFlowNets and AI-Driven Material Discovery for Carbon Capture Oct 22, 2024

In this episode of Breaking Math, hosts Gabriel Hesch and Autumn Phaneuf dive into the cutting-edge world of Generative Flow Networks (GFlowNets) and their role in artificial intelligence and material science. The discussion centers on how GFlowNets are revolutionizing the discovery of new materials for carbon capture, offering a powerful alternative to traditional AI models. Learn about the mechanics of GFlowNets, their advantages, and the groundbreaking results in developing materials with enhanced CO2 absorption capabilities. The episode also explores the future potential of GFlowNets in AI-driven material discovery and beyond, emphasizing their transformative impact on carbon capture technology and sustainable innovation.

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You can find the paper “Discovery of novel reticular materials for carbon dioxide capture using GFlowNets” by Cipcigan et al in Digital Discovery Journal by the Royal Society of Chemistry.

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Victorian Era Spooky Scientists & Paranormal Activity Oct 15, 2024

Explore the intriguing intersection of science and spiritualism in the Victorian era. This episode uncovers how prominent scientists like Michael Faraday, William James, and Marie & Pierre Curie engaged with supernatural phenomena and the rise of spiritualism. Discover the scientific efforts to debunk or understand paranormal activities, and how these investigations shaped modern science. Dive into the fascinating legacy of this 19th-century movement and its lasting impact on today's scientific inquiries into the unknown. Perfect for fans of history, science, and the supernatural.

Keywords: Victorian era, spiritualism, science, supernatural, Michael Faraday, William James, Alfred Russell Wallace, Curies, Eleanor Sidgwick, idiomotor effect
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Is AI Conscious? Oct 08, 2024

AI & Consciousness: Philosophical Debates, Ethical Implications & the Future of Conscious Machines
In this episode of Breaking Math, hosts Autumn and Gabriel explore the intricate relationship between artificial intelligence (AI) and consciousness. Delve into historical perspectives, philosophical debates, and the ethical questions surrounding the creation of conscious machines. Key topics include the evolution of AI, challenges in defining and testing consciousness, and the potential rights of AI beings. We also examine the Turing Test, the debate between strong AI vs. weak AI, and concepts like personhood and integrated information theory. Perfect for anyone interested in AI ethics, the nature of consciousness, and the responsibilities of advanced AI technology.
Keywords: AI, consciousness, Turing test, strong AI, weak AI, ethics, philosophy, personhood, integrated information theory, neural networks
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Molecular dynamics simulation with GFlowNets: machine learning the importance of energy estimators in computational chemistry and drug discovery Oct 01, 2024

In this episode of Breaking Math, hosts Autumn and Gabriel take a deep dive into the paper “Towards Equilibrium Molecular Conformation Generation with GFlowNets” by Volokova et al., published in the Digital Discovery Journal by the Royal Society of Chemistry. They explore the cutting-edge intersection of molecular conformations and machine learning, comparing traditional methods like molecular dynamics and cheminformatics with the innovative approach of Generative Flow Networks (GFlowNets) for molecular conformation generation.

The episode covers empirical results that showcase the effectiveness of GFlowNets in computational chemistry, their scalability, and the role of energy estimators in advancing fields like drug discovery. Tune in to learn how machine learning is transforming the way we understand molecular structures and driving breakthroughs in chemistry and pharmaceuticals.

Keywords: molecular conformations, machine learning, GFlowNets, computational chemistry, drug discovery, molecular dynamics, cheminformatics, energy estimators, empirical results, scalability, math, mathematics, physics, AI

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Do Plants Know Math? Sep 24, 2024

Mathematical Patterns in Plants: Fibonacci, Golden Ratio & Nature's Hidden Math with Christophe Gole & Nancy Pick
In this episode of Breaking Math, host Autumn interviews authors Christophe Gole and Nancy Pick about the captivating world of mathematical patterns in plants, inspired by their book Do Plants Know Math?. Explore the intersection of mathematics and biology as they discuss the Fibonacci sequence, the golden ratio, and spiral formations that reveal nature's mathematical beauty. Learn about the optimization of plant structures, the role of women in mathematics, and get recommendations for further reading. Topics include phyllotaxis, fractals, and their connections to AI, physics, and topology.
Keywords: mathematics, biology, plant math, Fibonacci, phylotaxis, spirals, golden ratio, fractals, nature, science, women in math,topology, ai, physics, math, plants, gardening
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Mapmatics: A Mathematician's Guide to Navigating the World with Maps with Paulina Rowinska Sep 17, 2024

Math & Cartography: Dr. Paula Rowinska on Map Projections, Gerrymandering & Real-World Math
In this episode of Breaking Math, host Autumn interviews Dr. Paula Rowinska about her unique journey from earning a PhD in mathematics to writing about math and cartography. They discuss the fascinating connection between map-making and mathematics, debunking misconceptions about map projections and exploring key topics like the coastline paradox, gerrymandering, and the traveling salesman problem. Learn how these mathematical concepts play a crucial role in areas like crime analysis, geopolitics, and more. Perfect for enthusiasts of math, cartography, and real-world problem-solving.

The conversation also celebrates the contributions of underrepresented women in mathematics and underscores the importance of math in everyday life. Tune in to discover how mathematics shapes our understanding of the world through cartography, topology, and even AI.
Keywords: mathematics, cartography, map projections, coastline paradox, gerrymandering, women in math, traveling salesman problem, crime analysis, topology, metric map, ai, physics, math
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The Intentional Engineer (with Jeff Perry) Sep 10, 2024

In this conversation, Gabriel and Autumn interview Jeff Perry, a career coach and author of the book 'The Intentional Engineer'. They discuss the importance of being intentional in one's career, understanding one's passions and skills, and building a strong professional network. Jeff shares his journey from being an engineer to becoming an engineer coach and offers advice on how to navigate career transitions. They also explore the concept of 'genius zones' and how to identify and leverage one's unique strengths and talents. In this conversation, Jeff discusses the concept of the zone of incompetence, competence, excellence, and genius. They share personal anecdotes and examples to illustrate these zones and emphasize the importance of self-awareness and collaboration. They also touch on the role of mindset in driving behavior and results, particularly in the context of engineering and tech careers. Jeff offers coaching and resources for individuals looking to make intentional career shifts or upgrades.

Keywords: career, intentionality, engineering, skills, passions, network, genius zones, strengths, talents, zone of incompetence, zone of competence, zone of excellence, zone of genius, self-awareness, collaboration, mindset, engineering, tech careers, intentional career shifts

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Math for English Majors with Ben Orlin Sep 03, 2024

Math & Language: Creativity, Quantification, and Making Math Accessible with Ben Orlin
In this episode of Breaking Math, hosts sit down with Ben Orlin, author of Math for English Majors and Math with Bad Drawings, to explore the intersection of math and language. Discover the unique skill sets required for mathematics and creativity, how math education can be made more accessible, and the role of quantification in empowering individuals across various fields, including literature and the arts. The conversation highlights the historical contributions of women in math, including the impact of Einstein’s wife on his work. Ben also shares insights into his writing process and the challenges of making math relatable to a broad audience. Learn how mathematical thinking can enhance one's appreciation for literature and the world.

Keywords: math, language, skill sets, math education, accessibility, quantification, power of math, women in math, Einstein's wife, math, literature, book, writing, perspective, abstraction, relationships

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What is Data Visualization? From the Expert Behind PolicyViz Aug 27, 2024

In this episode Autumn and Dr. Jonathan Schwabish discuss the importance of strategic thinking in data visualization and the key elements of good data. He emphasizes the need to understand the data and how it was collected, as well as the importance of starting bar charts at zero. He also highlights common mistakes in data visualization, such as distorting or lying with visuals, and the potential impact of data visualization on policy decisions. Looking to the future, he discusses the role of AI in data visualization, the integration of AI into visualization tools, and the potential of augmented reality and virtual reality in data visualization. Jon Schwabish discusses the different data visualization tools he uses, including Excel, R, Tableau, Datawrapper, and Flourish. He emphasizes the importance of choosing the right tool for the specific use case and audience. He also highlights the need for policymakers and individuals to be trained in interpreting and using data visualizations effectively. Schwabish discusses the ethical considerations in data visualization, such as using inclusive language and considering accessibility.

Keywords: data visualization, strategic thinking, good data, common mistakes, impact on policy decisions, AI, augmented reality, virtual reality, data visualization tools, Excel, R, Tableau, Datawrapper, Flourish, policymakers, data interpretation, ethical considerations, inclusive language, accessibility

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Love Triangle and Other Maths (with Matt Parker) Aug 20, 2024

In this episode, Gabriel and Autumn interview mathematician, comedian, and author Matt Parker about his latest book, "Love Triangle." They discuss the unique page numbering system in the book, which is based on the sine function, and how it adds an extra layer of discovery for readers. They also explore the use of triangles and quads in 3D modeling, the concept of Perlin noise, and the perception of randomness. The conversation touches on the intersection of mathematics and creativity, as well as the practical applications of mathematical concepts in various fields. The conversation explores various topics related to mathematics, including the analysis of the Mona Lisa, the use of math in playing pool, the discovery of new shapes, and the application of math in various fields. The speakers discuss the motivation behind exploring these topics and the interplay between math and art. They also provide advice for science and math content creators on YouTube.

Keywords: mathematics, book, Love Triangle, page numbering, sine function, triangles, quads, 3D modeling, Perlin noise, randomness, creativity, practical applications, mathematics, Mona Lisa, parallax, pool, shapes, Fourier analysis, YouTube, physics, AI, machine learning
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The Black Hole Heist Aug 16, 2024

Surprise! It's a Friday episode for you! Yes, yes it is a rerun, but we wanted to share it anyways. We can't wait for our fall lineup because it's packed with surprises. See you back on Tuesday.

Keywords: Black holes, gravity, universe, physics, ai, machine learning, education, statistics, engineering, humanity

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Black Holes: The Abyss Part 3 Aug 13, 2024

It's the last week of our summer break and we have 2 episodes this week for you as a little treat. So check out our show on Friday too for a little bit more fun. We can't wait for our fall lineup because it's packed with surprises. If you have not listened to the last two episodes, then we'd highly recommend going back and listening to those. We're choosing to present this information this way because otherwise we'd waste most of your time re-explaining concepts we've already covered.

Black holes are so bizarre when we measured against the yardstick of the mundanity of our day to day lives that they inspire fear, awe, and controversy. In this last episode of the Abyss series, we will look at some more cutting-edge problems and paradoxes surrounding black holes. So how are black holes and entanglement related? What is the holographic principle? And what is the future of black holes?

Keywords: Black holes, gravity, universe, physics, ai, machine learning, education, statistics, engineering, humanity

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Black Holes: The Abyss Part 2 Aug 06, 2024

Happy Summer! We have another week of our summer break after this episode from 2018. We will be back shortly with more content and surprises!
Black holes are objects that seem exotic to us because they have properties that boggle our comparatively mild-mannered minds. These are objects that light cannot escape from, yet glow with the energy they have captured until they evaporate out all of their mass. They thus have temperature, but Einstein's general theory of relativity predicts a paradoxically smooth form. And perhaps most mind-boggling of all, it seems at first glance that they have the ability to erase information. So what is black hole thermodynamics? How does it interact with the fabric of space? And what are virtual particles?
Keywords: Black holes, gravity, universe, physics, ai, machine learning, education, statistics, engineering, humanity

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Black Holes: The Abyss Part 1 Jul 30, 2024

Happy Summer! Check out part one of our three part series on black holes from 2018. Enjoy!
The idea of something that is inescapable, at first glance, seems to violate our sense of freedom. This sense of freedom, for many, seems so intrinsic to our way of seeing the universe that it seems as though such an idea would only beget horror in the human mind. And black holes, being objects from which not even light can escape, for many do beget that same existential horror. But these objects are not exotic: they form regularly in our universe, and their role in the intricate web of existence that is our universe is as valid as the laws that result in our own humanity. So what are black holes? How can they have information? And how does this relate to the edge of the universe?
Keywords: Black holes, gravity, universe, physics, ai, machine learning, education, statistics, engineering, humanity

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What are Journal Rankings? The basics: a minisode. Jul 23, 2024

In this minisode, Autumn explores the basics in the world of journal rankings and metrics. She discusses the importance of journal rankings and how they are determined, focusing on metrics like impact factor, mathematical citation quotient (MCQ), and publication power approach (PPA). She explains how these metrics provide insights into a journal's influence and performance, but also emphasizes the need for a comprehensive evaluation of research beyond just metrics.

Keywords: journal rankings, journal metrics, impact factor, mathematical citation quotient, publication power approach, research evaluation, math, physics, ai, machine learning, education, publishing, academic journals

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103: Why Machines Learn: The Math Behind AI Jul 16, 2024

In this episode Autumn and Anil Ananthaswamy discuss the inspiration behind his book “Why Machines Learn” and the importance of understanding the math behind machine learning. He explains that the book aims to convey the beauty and essential concepts of machine learning through storytelling, history, sociology, and mathematics. Anil emphasizes the need for society to become gatekeepers of AI by understanding the mathematical basis of machine learning. He also explores the history of machine learning, including the development of neural networks, support vector machines, and kernel methods. Anil highlights the significance of the backpropagation algorithm and the universal approximation theorem in the resurgence of neural networks.

Keywords: machine learning, math, inspiration, storytelling, history, sociology, gatekeepers, neural networks, support vector machines, kernel methods, backpropagation algorithm, universal approximation theorem, AI, ML, physics, mathematics, science

You can find Anil Ananthaswamy on Twitter @anilananth and his new book “Why Machines Learn”
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102: The Intersection of Mathematics and Democracy Jul 09, 2024

This discussion Autumn and Gabe delves into Ismar Volic's personal background and inspiration for writing the book, “Making Democracy Count” as well as the practical and theoretical aspects of voting systems. Additionally, the conversation explores the application of voting systems to everyday decision-making and the use of topological data analysis in understanding societal polarization. The conversation covers a wide range of topics, including data visualization, gerrymandering, electoral systems, and the intersection of mathematics and democracy. Volic, shares insights on the practical implications of implementing mathematical improvements in electoral systems and the legal and constitutional hurdles that may arise. He also discusses the importance of educating oneself about the quantitative underpinnings of democracy and the need for interdisciplinary discussions that bridge mathematics and politics.

Keywords: math podcast, creativity, mascot, background, Matlab, ranked choice voting, elections, author's background, inspiration, voting systems, topological data analysis, societal polarization, mathematics, democracy, data visualization, gerrymandering, electoral systems, interdisciplinary discussions, practical implications, legal hurdles, constitutional considerations

You can find Ismar Volic on Twitter and LinkedIn @ismarvolic. Please go check out the Institute for Mathematics and Democracy and Volic’s new book “Making Democracy Count”
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Math Lounge: Celebrating 101 Episodes Jul 02, 2024

In this conversation, Gabe and Autumn celebrate the 101st episode of Breaking Math and discuss the evolution of the podcast. They highlight the importance of creativity in teaching mathematics and share their plans to expand Breaking Math into Breaking Math Media. They also discuss the history of physics and the big questions that inform the podcast. The hosts express their desire to collaborate with listeners and explore practical applications of math in different fields. They also mention books like 'A Quantum Story' and 'Incomplete Nature' that delve into the mysteries of quantum mechanics and consciousness. The hosts highlight the unique and creative nature of their podcast, inviting listeners to join them in the Math Lounge, a metaphorical nightclub where math and creativity intersect.
Keywords: Breaking Math, podcast, creativity, mathematics, Breaking Math Media, physics, history, quantum mechanics, book discussion, double-slit experiment, quantum mechanics, interdisciplinary discussions, machine learning, neuroscience, gamification of math, collaboration, practical applications, consciousness, Math Lounge

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100: Creating Inclusive Spaces for LGBTQIA+ in STEM Jun 25, 2024

In this episode Autumn is joined by Erika Lynn Dawson Head, the Executive Director of Diversity and Inclusive Community Development for the Manning College of Information and Computer Sciences, discusses her role in STEM, mentorship, and community building. The conversation dives into allyship, LGBTQ+ support, and the challenges of creating safe and inclusive spaces in STEM and higher education. The discussion also explores the intersectionality of identities and the importance of recognizing and addressing biases in professional and educational environments. The conversation covers a range of topics related to diversity, inclusion, and the challenges faced by marginalized communities. It delves into the importance of creating safe spaces, addressing biases, and the need for education and awareness. The discussion also explores the concept of calling people in, the impact of cultural shifts in professional settings, and the significance of building a diverse network of support. Here we cover the importance of role models and support for LGBTQIA+ individuals in STEM fields, the impact of coming out, the need for inclusive spaces, and the significance of kindness and understanding in navigating difficult conversations.

Keywords: diversity, equity, inclusion, STEM, mentorship, LGBTQ+, allyship, safe spaces, intersectionality, biases, professional conduct, higher education, diversity, inclusion, safe spaces, biases, education, awareness, calling people in, cultural shifts, professional settings, network of support, LGBTQIA+, role models, STEM, coming out, inclusive spaces, kindness, understanding, difficult conversations

You can connect with Erika for more opportunities and speaking engagements on LinkedIn.

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Minisode: Absolutely Nothing Jun 18, 2024

In this episode of Breaking Math, Autumn and Gabe explore the concept of nothingness and its significance in various fields. They discuss the philosophical, scientific, mathematical, and literary aspects of nothingness, highlighting its role in understanding reality and existence. They mention books like 'Incomplete Nature' by Terence Deacon and 'Zero: The Biography of a Dangerous Idea' by Charles Seife, which delve into the concept of absence and zero. The episode concludes by emphasizing the complexity and versatility of nothingness, inviting listeners to think deeper about its implications.
Keywords: nothingness, philosophy, science, mathematics, literature, reality, existence, absence, zero
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99 (Part II) Math in Drag: Interview with OnlineKyne Jun 11, 2024

Summary

This episode is an interview with OnlineKyne, the author of the book Math in Drag. The conversation focuses on how to be an effective online educator and covers various topics in mathematics, including Cantor's infinite sets, probability, and statistics. The interview also delves into the process of writing the book and highlights the connection between math and drag. The chapters in the conversation cover the journey of a content creator, tips for science content creators, the concept of infinity, the significance of celebrity numbers, game theory, probability, statistics, and the ethical implications of math and drag.

Takeaways

Being an effective online educator involves distilling complex concepts into concise and valuable content.
Math and drag share similarities in breaking rules and defying authority.
Mathematics has a rich history and is influenced by various cultures and individuals.
Statistics can be used to manipulate and deceive, so it is important to be critical of data and its interpretation.

Chapters

00:00 Introduction

00:54 Journey as a Content Creator

03:50 Tips and Tricks for Science Content Creators

04:15 Writing the Book

05:12 Math and Drag

06:40 Infinite Possibilities

07:35 Celebrity Numbers

08:59 How to Cut a Cake and Eat It

09:57 Luck Be a Ladyboy

12:44 Illegal Math

16:02 The Average Queen

25:03 Math and Drag Breaking the Rules

27:22 Conclusion

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98. Math in Drag: An Episode with Math Educator Kyne Santos Jun 04, 2024

Summary

In this conversation, Gabriel Hesch interviews Kyne Santos, an online creator who combines art, music, and performance in math education. They discuss the intersection of math and music, the controversy surrounding math and drag, and the creative side of math. They also explore topics such as topology, mathematical shapes, and influential books in math. The conversation highlights the importance of challenging traditional definitions and finding new and innovative ways to engage with math education.

Takeaways

Math and music have a strong connection, and math can be used to analyze, manipulate, and create music.
Combining art and math education can make learning math more engaging and fun.
Topology is a branch of mathematics that relaxes the rigid terms used in geometry and focuses on the similarities and differences between shapes.
Mathematical discoveries can come from playing around and exploring different possibilities.
Challenging traditional definitions and thinking creatively are important aspects of math education.

Chapters

00:00 Introduction: Best Song Ever Created

02:03 Introduction of Guest: Kyne Santos

03:00 Math and Drag: Combining Art and Math Education

07:45 Addressing Controversy: Math and Drag

08:15 Music and Math: The Intersection

09:14 Mathematical Shapes: Mobius Strip

10:10 Topology vs Geometry

13:01 Holes and Topology

15:14 Topology and Thought Experiments

21:13 Aperiodic Monotiles: New Math Discovery

23:02 New Shapes and Descriptive Rules

25:26 Influential Books: The Quantum Story and Incomplete Nature

27:01 Conclusion and Next Episode Preview

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97: (Part 2) Can We Survive on Mars? Hot Tips with Zach Weinersmith May 28, 2024

In this conversation, Autumn Phaneuf interviews Zach Weinersmith, a cartoonist and writer, about the feasibility and implications of space settlement. They discuss the challenges and misconceptions surrounding space colonization, including the idea that it will make us rich, mitigate war, and make us wiser. They explore the potential of the moon and Mars as settlement options, as well as the concept of rotating space stations. They also touch on the physiological effects of space travel and the need for further research in areas such as reproduction and ecosystem design. The conversation explores the challenges and implications of human settlement in space. It discusses the lack of data on the long-term effects of space travel on the human body, particularly for women. The conversation also delves into the need for a closed-loop ecosystem for sustainable space settlement and the legal framework surrounding space exploration and resource extraction. The main takeaways include the importance of addressing reproductive and medical challenges, the need for a better legal regime, and the debunking of misconceptions about space settlement.

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A City on Mars, Keywords space settlement, feasibility, challenges, misconceptions, moon, Mars, rotating space stations, reproduction, ecosystem design, space settlement, human reproduction, closed-loop ecosystem, space law, resource extraction, logistics, math.

96: Can We Survive on Mars? Hot Tips with Zach Weinersmith May 21, 2024

In this conversation, Autumn Phaneuf and Zach Weinersmith discusses his new book, A City on Mars, which takes a humorous look at the challenges of building a Martian society. He explores the misconceptions and myths surrounding space settlement and the feasibility of colonizing Mars. He argues that space is unlikely to make anyone rich and that the idea that space will mitigate war is unsupported. He also discusses the potential benefits and limitations of settling on the Moon and Mars, as well as the technical challenges involved.

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A City on Mars, space settlement, Mars colonization, misconceptions, myths, feasibility, space myths, space economics, war, Moon settlement, technical challenges, logistics, math.

What's the Use? Interview with Professor Ian Stewart May 14, 2024

Welcome to another engaging episode of the Breaking Math Podcast! Today's episode, titled "What is the Use?," features a fascinating conversation with the renowned mathematician and author, Professor Ian Stewart. As Professor Stewart discusses his latest book "What's the Use? How Mathematics Shapes Everyday Life," we dive deep into the real-world applications of mathematics that often go unnoticed in our daily technologies, like smartphones, and their unpredictable implications in various fields.

We'll explore the history of quaternions, invented by William Rowan Hamilton, which now play a critical role in computer graphics, gaming, and particle physics. Professor Stewart will also shed light on the non-commutative nature of quaternions, mirroring the complexities of spatial rotations, and how these mathematical principles find their correspondence in the natural world.

Furthermore, our discussion will encompass the interconnectivity within mathematics, touching upon how algebra, geometry, and trigonometry converge to paint a broader picture of this unified field. We also discuss the intriguing concept of "Fearful Symmetry" and how symmetrical and asymmetrical patterns govern everything from tiger stripes to sand dunes.

With references to his other works, including "Professor Stewart's Cabinet of Mathematical Curiosities" and "The Science of Discworld," Professor Stewart brings an element of surprise and entertainment to the profound impact of mathematics on our understanding of the world.

So stay tuned as we unlock the mysteries and the omnipresent nature of math in this thought-provoking episode with Professor Ian Stewart!

95: Bayes' Theorem Explains It All: An Interview with Tom Chivers May 07, 2024

Summary

Tom Chivers discusses his book 'Everything is Predictable: How Bayesian Statistics Explain Our World' and the applications of Bayesian statistics in various fields. He explains how Bayesian reasoning can be used to make predictions and evaluate the likelihood of hypotheses. Chivers also touches on the intersection of AI and ethics, particularly in relation to AI-generated art. The conversation explores the history of Bayes' theorem and its role in science, law, and medicine. Overall, the discussion highlights the power and implications of Bayesian statistics in understanding and navigating the world.

The conversation explores the role of AI in prediction and the importance of Bayesian thinking. It discusses the progress of AI in image classification and the challenges it still faces, such as accurately depicting fine details like hands. The conversation also delves into the topic of predictions going wrong, particularly in the context of conspiracy theories. It highlights the Bayesian nature of human beliefs and the influence of prior probabilities on updating beliefs with new evidence. The conversation concludes with a discussion on the relevance of Bayesian statistics in various fields and the need for beliefs to have probabilities and predictions attached to them.

Takeaways
Bayesian statistics can be used to make predictions and evaluate the likelihood of hypotheses.
Bayes' theorem has applications in various fields, including science, law, and medicine.
The intersection of AI and ethics raises complex questions about AI-generated art and the predictability of human behavior.
Understanding Bayesian reasoning can enhance decision-making and critical thinking skills. AI has made significant progress in image classification, but still faces challenges in accurately depicting fine details.
Predictions can go wrong due to the influence of prior beliefs and the interpretation of new evidence.
Beliefs should have probabilities and predictions attached to them, allowing for updates with new information.
Bayesian thinking is crucial in various fields, including AI, pharmaceuticals, and decision-making.
The importance of defining predictions and probabilities when engaging in debates and discussions.

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94. Interview with Steve Nadis, Co-author of 'Gravity of Math' Apr 30, 2024

Summary

**Tensor Poster - If you are interested in the Breaking Math Tensor Poster on the mathematics of General Relativity, email us at BreakingMathPodcast@gmail.com

In this episode, Gabriel Hesch and Autumn Phaneuf interview Steve Nadis, the author of the book 'The Gravity of Math.' They discuss the mathematics of gravity, including the work of Isaac Newton and Albert Einstein, gravitational waves, black holes, and recent developments in the field. Nadis shares his collaboration with Shing-Tung Yau and their journey in writing the book. They also talk about their shared experience at Hampshire College and the importance of independent thinking in education. In this conversation, Steve Nadis discusses the mathematical foundations of general relativity and the contributions of mathematicians to the theory. He explains how Einstein was introduced to the concept of gravity by Bernhard Riemann and learned about tensor calculus from Gregorio Ricci and Tullio Levi-Civita. Nadis also explores Einstein's discovery of the equivalence principle and his realization that a theory of gravity would require accelerated motion. He describes the development of the equations of general relativity and their significance in understanding the curvature of spacetime. Nadis highlights the ongoing research in general relativity, including the detection of gravitational waves and the exploration of higher dimensions and black holes. He also discusses the contributions of mathematician Emmy Noether to the conservation laws in physics. Finally, Nadis explains Einstein's cosmological constant and its connection to dark energy.

Chapters

00:00 Introduction and Book Overview

08:09 Collaboration and Writing Process

25:48 Interest in Black Holes and Recent Developments

35:30 The Mathematical Foundations of General Relativity

44:55 The Curvature of Spacetime and the Equations of General Relativity

56:06 Recent Discoveries in General Relativity

01:06:46 Emmy Noether's Contributions to Conservation Laws

01:13:48 Einstein's Cosmological Constant and Dark Energy

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93. The 10,000 Year Problem (feat. David Gibson of Ray Kitty Creation Workship) Apr 23, 2024

Summary: The episode discusses the 10,000 year dilemma, which is a thought experiment on how to deal with nuclear waste in the future. Today's episode is hosted by guest host David Gibson, who is the founder of the Ray Kitty Creation Workshop. (Find out more about the Ray Kitty Creation Workshop by clicking here).

Gabriel and Autumn are out this week, but will be returning in short order with 3 separate interviews with authors of some fantastic popular science and math books including:

The Gravity of Math: How Geometry Rules the Universe by Dr. Shing-Tung Yau and Steve Nadis. This book is all about the history of our understanding of gravity from the theories of Isaac Newton to Albert Einstein and beyond, including gravitational waves, black holes, as well as some of the current uncertainties regarding a precise definition of mass. On sale now!
EVERYTHING IS PREDICTABLE: How Bayesian Statistics Explain Our World by Tom Chivers. Published by Simon and Schuster. This book explains the importance of Baye's Theorem in helping us to understand why highly accurate screening tests can lead to false positives, a phenomenon we saw during the Covid-19 pandemic; How a failure to account for Bayes’ Theorem has put innocent people in jail; How military strategists using the theorem can predict where an enemy will strike next, and how Baye's Theorem is helping us to understang machine learning processes - a critical skillset to have in the 21st century.
Available 05/07/2024
A CITY ON MARS: Can we settle space, should we settle space, and have we really thought this through? by authors Dr. Kelly and Zach Weinersmith. Zach Weinersmith is the artist and creator of the famous cartoon strip Saturday Morning Breaking Cereal!
We've got a lot of great episodes coming up! Stay tuned.

92. The Mathematical Heart of Games Explored with Prof. du Sautoy Apr 16, 2024

An interview with Prof. Marcus du Sautoy about his book Around the Wold in Eighty Games . . . .a Mathematician Unlocks the Secrets of the World's Greatest Games.
Topics covered in Today's Episode:

1. Introduction to Professor Marcus du Sautoy and the Role of Games

- Impact of games on culture, strategy, and learning

- The educational importance of games throughout history

2. Differences in gaming cultures across regions like India and China

3. Creative Aspects of Mathematics

4. The surprising historical elements and banned games by Buddha

5. Historical and geographical narratives of games rather than rules

6. Game Theory and Education

7. Unknowable questions like thermodynamics and universe's infinity

8. Professor du Sautoy's Former Books and Collections

9. A preview of his previous books and their themes

10. Gaming Cultures and NFTs in Blockchain

11. Gamification in Education

12. The Role of AI in Gaming

13. Testing machine learning in mastering games like Go

14. Alphago's surprising move and its impact on Go strategies

15 . The future of AI in developing video game characters, plots, and environments

16. Conclusion and Giveaway Announcement

*Free Book Giveaway of Around The World in 88 Games . . . by Professor Marcus Du Sautory! Follow us on our socials for details:
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91. Brain Organelles, AI, and Other Scary Science - An Interview with GT (Part 2) Apr 04, 2024

Summary

Brain Organelles, A.I. and Defining Intelligence in Nature-

In this episode, we continue our fascinating interview with GT, a science content creator on TikTok and YouTube known for their captivating - and sometimes disturbing science content.
GT can be found on the handle ‘@bearBaitOfficial’ on most social media channels.
In this episode, we resume our discussion on Brain Organelles - which are grown from human stem cells - how they are being used to learn about disease, how they may be integrated in A.I. as well as eithical concerns with them.
We also ponder what constitutes intelligence in nature, and even touch on the potential risks of AI behaving nefariously.
You won't want to miss this thought-provoking and engaging discussion.
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90. LEAN Theorem Provers used to model Physics and Chemistry Mar 16, 2024

This episode is inspired by a correspondence the Breaking Math Podcast had with the editors of Digital Discovery, a journal by the Royal Society of Chemistry. In this episode the hosts review a paper about how the Lean Interactive Theorem Prover, which is usually used as a tool in creating mathemtics proofs, can be used to create rigorous and robust models in physics and chemistry.

Also - we have a brand new member of the Breaking Math Team! This episode is the debut episode for Autumn, CEO of Cosmo Labs, occasional co-host / host of the Breaking Math Podcast, and overall contributor who has been working behind the scenes on the podcast on branding and content for the last several months. Welcome Autumn!

Autumn and Gabe discuss how the paper explores the use of interactive theorem provers to ensure the accuracy of scientific theories and make them machine-readable. The episode discusses the limitations and potential of interactive theorem provers and highlights the themes of precision and formal verification in scientific knowledge. This episode also provide resources (listed below) for listeners interested in learning more about working with the LEAN interactive theorem prover.

Takeaways

Interactive theorem provers can revolutionize the way scientific theories are formulated and verified, ensuring mathematical certainty and minimizing errors.
Interactive theorem provers require a high level of mathematical knowledge and may not be accessible to all scientists and engineers.
Formal verification using interactive theorem provers can eliminate human error and hidden assumptions, leading to more confident and reliable scientific findings.
Interactive theorem provers promote clear communication and collaboration across disciplines by forcing explicit definitions and minimizing ambiguities in scientific language. Lean Theorem Provers enable scientists to construct modular and reusable proofs, accelerating the pace of knowledge acquisition.
Formal verification presents challenges in terms of transforming informal proofs into a formal language and bridging the reality gap.
Integration of theorem provers and machine learning has the potential to enhance creativity, verification, and usefulness of machine learning models.
The limitations and variables in formal verification require rigorous validation against experimental data to ensure real-world accuracy.
Lean Theorem Provers have the potential to provide unwavering trust, accelerate innovation, and increase accessibility in scientific research.
AI as a scientific partner can automate the formalization of informal theories and suggest new conjectures, revolutionizing scientific exploration.
The impact of Lean Theorem Provers on humanity includes a shift in scientific validity, rapid scientific breakthroughs, and democratization of science.

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89. Brain Organelles, AI, and the Other Scary Science - An Interview with GT (Part I) Mar 05, 2024

This conversation explores the topic of brain organoids and their integration with robots. The discussion covers the development and capabilities of brain organoids, the ethical implications of their use, and the differences between sentience and consciousness. The conversation also delves into the efficiency of human neural networks compared to artificial neural networks, the presence of sleep in brain organoids, and the potential for genetic memories in these structures. The episode concludes with an invitation to part two of the interview and a mention of the podcast's Patreon offering a commercial-free version of the episode.

Takeaways

Brain organoids are capable of firing neural signals and forming structures similar to those in the human brain during development.
The ethical implications of using brain organoids in research and integrating them with robots raise important questions about sentience and consciousness.
Human neural networks are more efficient than artificial neural networks, but the reasons for this efficiency are still unknown.
Brain organoids exhibit sleep-like patterns and can undergo dendrite growth, potentially indicating learning capabilities.
Collaboration between scientists with different thinking skill sets is crucial for advancing research in brain organoids and related fields.

Chapters

00:00 Introduction: Brain Organoids and Robots
00:39 Brain Organoids and Development
01:21 Ethical Implications of Brain Organoids
03:14 Summary and Introduction to Guest
03:41 Sentience and Consciousness in Brain Organoids
04:10 Neuron Count and Pain Receptors in Brain Organoids
05:00 Unanswered Questions and Discomfort
05:25 Psychological Discomfort in Brain Organoids
06:21 Early Videos and Brain Organoid Learning
07:20 Efficiency of Human Neural Networks
08:12 Sleep in Brain Organoids
09:13 Delta Brainwaves and Brain Organoids
10:11 Creating Brain Organoids with Specific Components
11:10 Genetic Memories in Brain Organoids
12:07 Efficiency and Learning in Human Brains
13:00 Sequential Memory and Chimpanzees
14:18 Different Thinking Skill Sets and Collaboration
16:13 ADHD and Hyperfocusing
18:01 Ethical Considerations in Brain Research
19:23 Understanding Genetic Mutations
20:51 Brain Organoids in Rat Bodies
22:14 Dendrite Growth in Brain Organoids
23:11 Duration of Dendrite Growth
24:26 Genetic Memory Transfer in Brain Organoids
25:19 Social Media Presence of Brain Organoid Companies
26:15 Brain Organoids Controlling Robot Spiders
27:14 Conclusion and Invitation to Part 2

References:

Muotri Labs (Brain Organelle piloting Spider Robot)

Cortical Labs (Brain Organelle's trained to play Pong)

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Summary:

88. Can OpenAi's SORA learn and model real-world physics? (Part 1 of n) Feb 27, 2024

This is a follow up on our previous episode on OpenAi's SORA. We attempt to answer the question, "Can OpenAi's SORA model real-world physics?"

We go over the details of the technical report, we discuss some controversial opinoins by experts in the field at Nvdia and Google's Deep Mind.

The transcript for episode is avialable below upon request.

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87. OpenAi SORA, Physics-Informed ML, and a.i. Fraud- Oh My! Feb 20, 2024

OpenAI's Sora, a text-to-video model, has the ability to generate realistic and imaginative scenes based on text prompts. This conversation explores the capabilities, limitations, and safety concerns of Sora. It showcases various examples of videos generated by Sora, including pirate ships battling in a cup of coffee, woolly mammoths in a snowy meadow, and golden retriever puppies playing in the snow. The conversation also discusses the technical details of Sora, such as its use of diffusion and transformer models. Additionally, it highlights the potential risks of AI fraud and impersonation. The episode concludes with a look at the future of physics-informed modeling and a call to action for listeners to engage with Breaking Math content.

Takeaways

OpenAI's Sora is a groundbreaking text-to-video model that can generate realistic and imaginative scenes based on text prompts.
Sora has the potential to revolutionize various industries, including entertainment, advertising, and education.
While Sora's capabilities are impressive, there are limitations and safety concerns, such as the potential for misuse and the need for robust verification methods.
The conversation highlights the importance of understanding the ethical implications of AI and the need for ongoing research and development in the field.

Chapters

00:00 Introduction to OpenAI's Sora

04:22 Overview of Sora's Capabilities

07:08 Exploring Prompts and Generated Videos

12:20 Technical Details of Sora

16:33 Limitations and Safety Concerns

23:10 Examples of Glitches in Generated Videos

26:04 Impressive Videos Generated by Sora

29:09 AI Fraud and Impersonation

35:41 Future of Physics-Informed Modeling

36:25 Conclusion and Call to Action

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Summary

#OpenAiSora #

86. Math, Music, and Artificial Intelligence - Levi McClain Interview (Final Part) Feb 18, 2024

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Transcripts are available upon request. Email us at BreakingMathPodcast@gmail.com

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Visit our guest Levi McClain's Pages:

youtube.com/@LeviMcClain

levimcclain.com/

Summary

Levi McClean discusses various topics related to music, sound, and artificial intelligence. He explores what makes a sound scary, the intersection of art and technology, sonifying data, microtonal tuning, and the impact of using 31 notes per octave. Levi also talks about creating instruments for microtonal music and using unconventional techniques to make music. The conversation concludes with a discussion on understanding consonance and dissonance and the challenges of programming artificial intelligence to perceive sound like humans do.

Takeaways:

The perception of scary sounds can be analyzed from different perspectives, including composition techniques, acoustic properties, neuroscience, and psychology.
Approaching art and music with a technical mind can lead to unique and innovative creations.
Sonifying data allows for the exploration of different ways to express information through sound.
Microtonal tuning expands the possibilities of harmony and offers new avenues for musical expression.
Creating instruments and using unconventional techniques can push the boundaries of traditional music-making.
Understanding consonance and dissonance is a complex topic that varies across cultures and musical traditions.
Programming artificial intelligence to understand consonance and dissonance requires a deeper understanding of human perception and cultural context.

Chapters

00:00 What Makes a Sound Scary

03:00 Approaching Art and Music with a Technical Mind

05:19 Sonifying Data and Turning it into Sound

08:39 Exploring Music with Microtonal Tuning

15:44 The Impact of Using 31 Notes per Octave

17:37 Why 31 Notes Instead of Any Other Arbitrary Number

19:53 Creating Instruments for Microtonal Music

21:25 Using Unconventional Techniques to Make Music

23:06 Closing Remarks and Questions

24:03 Understanding Consonance and Dissonance

25:25 Programming Artificial Intelligence to Understand Consonance and Dissonance

85. Math, Music, Neuroscience, and Fear - an Interview with Musician Levi McClain Feb 13, 2024

We are joined today by content creator Levi McClain to discuss the mathematics behind music theory, neuroscience, and human experiences such as fear as they relate to audio processing.

For a copy of the episode transcript, email us at BreakingMathPodcast@gmail.com.

For more in depth discussions on these topics and more, check out Levi's channels at:

Patreon.com/LeviMcClain

youtube.com/@LeviMcClain

Tiktok.com/@levimcclain

Instagram.com/levimcclainmusic

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84. (Part 2) Intelligence in Nature v. Machine Learning - an Interview with Brit Cruise Feb 06, 2024

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Part 2/2 of the interview with Brit Cruise, creator of the YouTube channel "Art of the Problem," about interesting mathematics,, electrical and computer engineering problems.

In Part 1, we explored what 'intelligence' may be defined as by looking for examples of brains and proto-brains found in nature (including mold, bacteria, fungus, insects, fish, reptiles, and mammals).

In Part 2, we discuss aritifical neural nets and how they are both similar different from human brains, as well as the ever decreasing gap between the two.

Brit's YoutTube Channel can be found here: Art of the Problem - Brit Cruise

Transcript will be made available soon! Stay tuned. You may receive a transcript by emailing us at breakingmathpodcast@gmail.com.

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83. Intelligence in Nature v. Machine Learning-An Interview with Brit Cruise - Part 1 of 2 Jan 30, 2024

In this episode (part 1 of 2), I interview Brit Cruise, creator of the YouTube channel 'Art of the Problem.' On his channel, he recently released the video "ChatGPT: 30 Year History | How AI learned to talk." We discuss examples of intelligence in nature and what is required in order for a brain to evolve at the most basic level. We use these concepts to discuss what artificial intelligence - such as Chat GPT - both is and is not.

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82. A.I. and Materials Discovery - an Interview with Taylor Sparks Jan 21, 2024

Transcripts of this episode are avialable upon request. Email us at BreakingMathPodcast@gmail.com.

In this episode Gabriel Hesch interviews Taylor Sparks, a professor of material science and engineering, about his recent paper on the use of generative modeling a.i. for material disovery. The paper is published in the journal Digital Discovery and is titled 'Generative Adversarial Networks and Diffusion MOdels in Material Discovery. They discuss the purpose of the call, the process of generative modeling, creating a representation for materials, using image-based generative models, and a comparison with Google's approach. They also touch on the concept of conditional generation of materials, the importance of open-source resources and collaboration, and the exciting developments in materials and AI. The conversation concludes with a discussion on future collaboration opportunities.

Takeaways

Generative modeling is an exciting approach in materials science that allows for the prediction and creation of new materials.
Creating a representation for materials, such as using the crystallographic information file, enables the application of image-based generative models.
Google's approach to generative modeling received attention but also criticism for its lack of novelty and unconditioned generation of materials.
Open-source resources and collaboration are crucial in advancing materials informatics and machine learning in the field of materials science.

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How is Machine Learning being used to further original scientific discoveries?

In Memory of Sofia Baca, Cofounder and cohost of Breaking Math Jan 11, 2024

In October of 2023, Sofia Baca passed away unexpectedly from natural causes. Sofia was one of the founders and cohosts of the Breaking Math Podcast. In this episode, host Gabriel Hesch interviews Diane Baca, mother of Sofia Baca as we talk about her passions for creativity, mathematics, science, and discovering what it means to be human.
Sofia lived an exceptional life with explosive creativity, a voracious passion for mathematics, physics, computer science, and creativity. Sofia also struggled immensely with mental health issues which included substance abuse as well as struggling for a very long time understand the source of their discontent. Sofia found great happiness in connecting with other people through teaching, tutoring, and creative expression. The podcast will continue in honor of Sofia. There are many folders of ideas that Sofia left with ideas for the show or for other projects. We will continue this show with sharing some of these ideas, but also with sharing stories of Sofia - including her ideas and her struggles in hopes that others may find solace in that they are not alone in their struggles. But also in hopes that others may find inspiration in what Sofia had to offer.
We miss you dearly, Sofia.

81: Correct. Now Try Again (Multiple Approaches to the Same Problem) Jul 24, 2023

Join Sofía Baca and her guests, the host and co-host of the Nerd Forensics podcast, Millicent Oriana and Jacob Urban, as they explore what it means to be able to solve one problem in multiple ways.

This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For full text, visit: https://creativecommons.org/licenses/by-sa/4.0/

[Featuring: Sofía Baca; Millicent Oriana, Jacob Urban[

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80: Physical Dimension (Dimensional Analysis) Jun 26, 2023

The history of mathematics, in many ways, begins with counting. Things that needed, initially, to be counted were, and often still are, just that; things. We can say we have twelve tomatoes, or five friends, or that eleven days have passed. As society got more complex, tools that had been used since time immemorial, such as string and scales, became essential tools for counting not only concrete things, like sheep and bison, but more abstract things, such as distance and weight based on agreed-upon multiples of physical artifacts that were copied. This development could not have taken place without the idea of a unit: a standard of measuring something that defines what it means to have one of something. These units can be treated not only as counting numbers, but can be manipulated using fractions, and divided into arbitrarily small divisions. They can even be multiplied and divided together to form new units. So where does the idea of a unit come from? What's the difference between a unit, a dimension, and a physical variable? And how does the idea of physical dimension allow us to simplify complex problems? All of this and more on this episode of Breaking Math.

Distributed under a CC BY-SA 4.0 International License. For full text, visit: https://creativecommons.org/licenses/by-sa/4.0/

[Featuring: Sofía Baca; Millicent Oriana, Jacob Urban]

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79: 1 2 3 (Counting) Jun 08, 2023

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Join Sofia Baca and Nerd Forensics co-host Jacob Urban as they discuss all things counting!

Counting is the first arithmetic concept we learn, and we typically learn to do so during early childhood. Counting is the basis of arithmetic. Before people could manipulate numbers, numbers had to exist. Counting was first done on the body, before it was done on apparatuses outside the body such as clay tablets and hard drives. However, counting has become an invaluable tool in mathematics itself, as became apparent when counting started to be examined analytically. How did counting begin? What is the study of combinatorics? And what can be counted? All of this and more, on this episode of Breaking Math.

This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License (full text: https://creativecommons.org/licenses/by-sa/4.0/)

[Featuring: Sofia Baca; Jacob Urban]

78: Perpetual Notion (Entropy and Thermodynamics) May 09, 2023

As you listen to this episode, you'll be exerting mental effort, as well as maybe exerting effort doing other things. The energy allowing your neurons to continually charge and discharge, as well as exert mechanical energy in your muscles and chemical energy in places like your liver and kidneys, came from the food you ate. Specifically, it came from food you chewed, and then digested with acid and with the help of symbiotic bacteria. And even if that food you're eating is meat, you can trace its energy back to the sun and the formation of the earth. Much of this was established in the previous episode, but this time we're going to explore a fundamental property of all systems in which heat can be defined. All of these structures had a certain order to them; the cow that might have made your hamburger had all the same parts that you do: stomach, lips, teeth, and brain. The plants, such as the tomatoes and wheat, were also complex structures, complete with signaling mechanisms. As you chewed that food, you mixed it, and later, as the food digested, it became more and more disordered; that is to say, it became more and more "shuffled", so to speak, and at a certain point, it became so shuffled that you'd need all the original information to reconstruct it: reversing the flow of entropy would mean converting vomit back into the original food; you'd need all the pieces. The electrical energy bonding molecules were thus broken apart and made available to you. And, if you're cleaning your room while listening to this, you are creating order only at the cost of destroying order elsewhere, since you are using energy from the food you ate. Even in industrial agriculture where from 350 megajoules of human and machine energy, often 140 gigajoules of corn can be derived per acre, a ratio of more than 400:1, the order that the seeds seem to produce from nowhere is constructed from the energy of the chaotic explosion from a nearby star. So why are the concepts of heat, energy, and disorder so closely linked? Is there a general law of disorder? And why does the second law mean you can't freeze eggs in a hot pan? All of this and more on this episode of Breaking Math.

Distributed under a CC BY-SA 4.0 License (https://creativecommons.org/licenses/by-sa/4.0/)

[Featuring: Sofia Baca; Millicent Oriana, Jacob Urban]

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77: An Interview with Christopher Roblesz of MathNMore Feb 28, 2023

Christopher Roblesz is a math educator who, until the pandemic, worked as a teacher. It was his experiences during the pandemic, and his unwavering passion for preparing disadvantaged youth for STEM careers, that eventually led him to developing mathnmore, a company focused on providing an enriched educational experience for sstudents who are preparing for these careers.More on energy and entropy next time!All of this and more on this interview episode of Breaking Math!

[Featuring: Sofia Baca; Christopher Roblesz]

76: Joule Pay for This! (Energy) Jan 15, 2023

Join Sofia Baca and her guests Millicent Oriana from Nerd Forensics and Arianna Lunarosa as they discuss energy.

The sound that you're listening to, the device that you're listening on, and the cells in both the ear you're using to listen and the brain that understands these words have at least one thing in common: they represent the consumption or transference of energy. The same goes for your eyes if you're reading a transcript of this. The waves in the ears are pressure waves, while eyes receive information in the form of radiant energy, but they both are still called "energy". But what is energy? Energy is a scalar quantity measured in dimensions of force times distance, and the role that energy plays depends on the dynamics of the system. So what is the difference between potential and kinetic energy? How can understanding energy simplify problems? And how do we design a roller coaster in frictionless physics land?[Featuring: Sofia Baca; Millicent Oriana, Arianna Lunarosa]

This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. Full text here: https://creativecommons.org/licenses/by-sa/4.0/

75: Existential Physics with Sabine Hossenfelder (Author Interview) Oct 13, 2022

An interview with Dr. Sabine Hossenfelder about her second book Existential Physics. Sabine is host of the famous youtube show Science with Sabine.

74: Lights, Camera, Action! (3D Computer Graphics: Part I) Jun 19, 2022

The world around us is a four-dimensional world; there are three spatial dimensions, and one temporal dimension. Many of these objects emit an almost unfathomable number of photons. As we developed as creatures on this planet, we gathered the ability to sense the world around us; and given the amount of information represented as photons, it is no surprise that we developed an organ for sensing photons. But because of the amount of photons that are involved, and our relatively limited computational resources, it is necessary to develop shortcuts if we want to simulate an environment in silico. So what is raytracing? How is that different from what happens in games? And what does Ptolemy have to do with 3D graphics? All of this and more on this episode of Breaking Math.

73: Materialism: a Material Science Podcast Podcast Episode (Interview with Taylor Sparks) May 28, 2022

Physical objects are everywhere, and they're all made out of molecules, and atoms. However, the arrangement and refinement of these atoms can be the difference between a computer and sand, or between a tree and paper. For a species as reliant on tool use, the ability to conceieve of, design, create, and produce these materials is an ongoing concern. Since we've been around as humans, and even before, we have been material scientists in some regard, searching for new materials to make things out of, including the tools we use to make things. So what is the difference between iron and steel? How do we think up new things to make things out of? And what are time crystals? All of this and more on this episode of Breaking Math.

This episode is released under a Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license. More information here: https://creativecommons.org/licenses/by-nc/4.0/

[Featuring: Sofía Baca, Gabriel Hesch; Taylor Sparks]

72: The Lifestyles of the Mathematical and Famous (an Interview with Author Robert Black) May 15, 2022

Robert Black is an author who has written a six-book series about seven influential mathematicians, their lives, and their work. We interview him and his books, and take a peek into the lives of these influential mathematicians.

Addendum: Hey Breaking Math fans, I just wanted to let y'all know that the second material science podcast is delayed.

[Featuring: Sofía Baca; Robert Black]

71: What's the Matter? An Interview with Chris Cogswell of the Mad Scientist Podcast (Material Science) Apr 12, 2022

Matter is that which takes up space, and has mass. It is what we interact with, and what we are. Imagining a world without matter is to imagine light particles drifting aimlessly in space. Gasses, liquids, solids, and plasmas are all states of matter. Material science studies all of these, and their combinations and intricacies, found in examining foams, gels, meshes, and other materials and metamaterials. Chris Cogswell is a material scientist, and host of The Mad Scientist Podcast, a podcast that takes a critical look at things ranging from technological fads, to pseudoscience, and topics that deserve a critical eye. On the first of a pair of two episodes about material science, we interview Chris about his experience with studying material science, and ask questions about the subject in general.
Links referenced by Chris Cogswell:
- https://www.youtube.com/watch?v=bUvi5eQhPTc is about nanomagnetism and cool demonstration of ferrofluid
- https://www.youtube.com/watch?v=4Dlt63N-Uuk goes over nanomagnetic applications in medicine
- http://yaghi.berkeley.edu/pdfPublications/04MOFs.pdf Great review paper on new class of materials known as MOFs which are going to be very important in coming years
- https://www.youtube.com/watch?v=IkYimZBzguw Crash course engineering on nanomaterials, really good introduction to the field
- https://www.youtube.com/watch?v=t7EYQLOlwDM Oak Ridge national lab paper on using nano materials for carbon dioxide conversion to other carbon molecules
- https://www.youtube.com/watch?v=cxVFopLpIQY Really good paper on carbon capture technology challenges and economics
[Featuring: Sofía Baca, Gabriel Hesch, Meryl Flaherty; Chris Cogswell]
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70.1: Episode 70.1 of Breaking Math Podcast (Self-Reference) Mar 20, 2022

Seldom do we think about self-reference, but it is a huge part of the world we live in. Every time that we say 'myself', for instance, we are engaging in self-reference. Long ago, the Liar Paradox and the Golden Ratio were among the first formal examples of self-reference. Freedom to refer to the self has given us fruitful results in mathematics and technology. Recursion, for example, is used in algorithms such as PageRank, which is one of the primary algorithms in Google's search engine. Elements of self-reference can also be found in foundational shifts in the way we understand mathematics, and has propelled our understanding of mathematics forward. Forming modern set theory was only possible due to a paradox called Russel's paradox, for example. Even humor uses self-reference. Realizing this, can we find harmony in self-reference? Even in a podcast intro, are there elements of self-reference? Nobody knows, but I'd check if I were you. Catch all of this, and more, on this episode of Breaking Math. Episode 70.1: Episode Seventy Point One of Breaking Math Podcast

[Featuring: Sofía Baca, Gabriel Hesch; Millicent Oriana]

70: This Episode Intentionally Left Blank Mar 19, 2022

This episode description intentionally left blank! As in completely on purpose. Fun Fact! The creators of the Breaking Math Podcast, Sofia and Gabriel always thought it was funny that many books that we've read - even going back to our childhood - had a page in it with the sentence printed, "This Page Intentionally Left Blank." Like- okay; what does this 'intentionally left blank page' add to the reading experience? Does anyone know? Oh look here! There is a wikipedia page on it. Huh. Now I know. Now we know. And knowing is half the battle!
Sofia would frequently leave post-it notes on Gabe's laptop saying, "This Post-it note intentionally left blank." Because . . . . why? Sofia would often leave a twitter or facebook post that declared "This post intentionally left blank."
And now - we release an entire podcast episode that is intentionally left blank. Are we trolls? NO! We prefer to think of ourselves as artists in the style of Banksy making a statement!

69: An Interview with Michael Brooks, Author of "The Art of More: How Mathematics Created Civilization" Jan 23, 2022

Michael Brooks is a science writer who specializes in making difficult concepts easier to grasp. In his latest book, Brooks goes through several mathematical concepts and discusses their motivation, history, and discovery. So how do stories make it easier to learn? What are some of the challenges associated with conveying difficult concepts to the general public? And who, historically, has been a mathematician? All of this and more on this episode of Breaking Math. Songs were Breaking Math Intro and Outro by Elliot Smith of Albuquerque. This episode is published under a Creative Commons 4.0 Attribute-ShareAlike-NonCommercial license. For more information, visit CreativeCommons.org [Featuring: Sofía Baca, Gabriel Hesch, Meryl Flaherty; Michael Brooks]

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P12: O My God (Big O Notation) Jan 04, 2022

There are times in mathematics when we are generalizing the behavior of many different, but similar, entities. One such time that this happens is the use cases of Big O notation, which include describing the long-term behavior of functions, and talking about how accurate numerical calculations are. On this problem episode, we are going to discuss Big O notation and how to use it.

This episode is licensed by Sofia Baca under a Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca]

68: LOL!!! SO RANDOM (Random Variables) Dec 23, 2021

The world is often uncertain, but it has only been in the last half millennium that we've found ways to interact mathematically with that concept. From its roots in death statistics, insurance, and gambling to modern Bayesian networks and machine learning, we've seen immense productivity in this field. Every way of looking at probability has something in common: the use of random variables. Random variables let us talk about events with uncertain outcomes in a concrete way. So what are random variables? How are they defined? And how do they interact? All of this, and more, on this episode of Breaking Math.

Interact with the hosts:

@SciPodSofia

@TechPodGabe

Or the guest:

@KampPodMillie

Patreon here: patreon.com/breakingmathpodcast

Featuring music by Elliot Smith. For info about music used in ads, which are inserted dynamically, contact us at breakingmathpodcast@gmail.com

[Featuring: Sofía Baca, Gabriel Hesch; Millicent Oriana]

67: Wrath of Math (Mathematics Used Unwisely) Dec 09, 2021

Mathematics is a subject that has been used for great things over time: it has helped people grow food, design shelter, and in every part of life. It should be, then, no surprise that sometimes mathematics is used for evil; that is to say, there are times where mathematics is used to either implement or justify regressive things like greed, racism, classism, and even genocide. So when has math been used for destructive purposes? What makes us mis-apply mathematics? And why can oversimplification lead to devastation? All of this, and more, on this episode of Breaking Math.
Theme song is Breaking Math Theme by Elliot Smith of Albuquerque.
This episode is distributed under a Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, go to CreativeCommons.org
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P11: Feeling Lucky? (Probability and Intuition) Nov 30, 2021

Join Sofía Baca with her guest Millicent Oriana from the newly launched Nerd Forensics podcast as they discuss some apparent paradoxes in probability and Russian roulette.

Intro is "Breaking Math Theme" by Elliot Smith. Ads feature "Ding Dong" by Simon Panrucker

[Featuring: Sofía Baca; Millicent Oriana]

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This episode is sponsored by

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Support this podcast: https://anchor.fm/breakingmathpodcast/support

66: Hayhoe, Let's Go! (An Interview With Climate Scientist Katharine Hayhoe) Nov 21, 2021

Katharine Hayhoe was the lead author on the 2018 US Climate Assessment report, and has spent her time since then spreading the word about climate change. She was always faced with the difficult task of convincing people who had stakes in things that would be affected by acknowledging the information in her report. In her newest book, “Saving Us: A Climate Scientist’s Case for Hope and Healing in a Divided World”, she discusses the challenges associated with these conversations, at both the micro and macro level. So who is Katherine Heyhoe? How has she learned to get people to acknowledge the reality of climate science? And is she the best, or worst, person to strike up a discussion about how the weather’s been? All of this, and more, on this episode of Breaking Math. Papers Cited: -“99.94 percent of papers agree with the scientific consensus.”

More info: https://journals.sagepub.com/doi/10.1177/0270467617707079

This episode is distributed under a CC BY-NC 4.0 International License. For more information, visit creativecommons.org.

Intro is "Breaking Math Theme" by Elliot Smith. Ads feature "Ding Dong" by Simon Panrucker

[Featuring: Sofía Baca, Gabriel Hesch, Meryl Flaherty; Katherine Heyhoe, Elliot Smith]

P10: Chivalry is Dead (Knights and Knaves #1) Nov 14, 2021

One tells a lie, the other the truth! Have fun with Sofía and Meryl as they investigate knight, knave, and spy problems!

Intro is "Breaking Math Theme" by Elliot Smith. Music in the ads were Plug Me In by Steve Combs and "Ding Dong" by Simon Panrucker. You can access their work at freemusicarchive.org.

[Featuring: Sofia Baca; Meryl Flaherty]

65: An Interview with Author Ian Stewart (Book About Everyday Math) Oct 24, 2021

Welcome to another engaging episode of the Breaking Math Podcast! Today's episode, titled "What is the Use?," features a fascinating conversation with the renowned mathematician and author, Professor Ian Stewart. As Professor Stewart discusses his latest book "What's the Use? How Mathematics Shapes Everyday Life," we dive deep into the real-world applications of mathematics that often go unnoticed in our daily technologies, like smartphones, and their unpredictable implications in various fields.

We'll explore the history of quaternions, invented by William Rowan Hamilton, which now play a critical role in computer graphics, gaming, and particle physics. Professor Stewart will also shed light on the non-commutative nature of quaternions, mirroring the complexities of spatial rotations, and how these mathematical principles find their correspondence in the natural world.

Furthermore, our discussion will encompass the interconnectivity within mathematics, touching upon how algebra, geometry, and trigonometry converge to paint a broader picture of this unified field. We also discuss the intriguing concept of "Fearful Symmetry" and how symmetrical and asymmetrical patterns govern everything from tiger stripes to sand dunes.

With references to his other works, including "Professor Stewart's Cabinet of Mathematical Curiosities" and "The Science of Discworld," Professor Stewart brings an element of surprise and entertainment to the profound impact of mathematics on our understanding of the world.

So stay tuned as we unlock the mysteries and the omnipresent nature of math in this thought-provoking episode with Professor Ian Stewart!

64: What Projection Is This? (Map Projections) Sep 29, 2021

The world is a big place with a lot of wonderful things in it. The world also happens to be spherical, which can make getting to those things a challenge if you don't have many landmarks. This is the case when people are navigating by sea. For this reason, map projections, which take a sphere and attempt to flatten it onto a sheet, were born. So what is a map projection? Why are there so many? And why is Gall-Peters the worst? All of this, and more, on this episode of Breaking Math.

Theme was written by Elliot Smith.

This episode is distributed under a Creative Commons 4.0 Attribution-ShareAlike-NonCommercial International License. For more information, visit CreativeCommons.org.

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RR36: The Most Boring Episode Ever (Rerun: Math Games) Sep 19, 2021

This is a rerun of one of our favorite episodes! We hope that you enjoy it if you haven't listened to it yet. We'll be back next week with new content! Thank you so much for listening to Breaking Math!

Math is a gravely serious topic which has been traditionally been done by stodgy people behind closed doors, and it cannot ever be taken lightly. Those who have fun with mathematics mock science, medicine, and the foundation of engineering. That is why on today's podcast, we're going to have absolutely no fun with mathematics. There will not be a single point at which you consider yourself charmed, there will not be a single thing you will want to tell anyone for the sake of enjoyment, and there will be no tolerance for your specific brand of foolishness, and that means you too, Kevin.

Theme by Elliot Smith.

63: Broken Voting Systems (Voting Systems and Paradoxes) Sep 05, 2021

Voting systems are, in modern times, essential to the way that large-scale decisions are made. The concept of voicing an opinion to be, hopefully, considered fairly is as ancient and well-established as the human concept of society in general. But, as time goes on, the recent massive influx of voting systems in the last 150 years have shown us that there are as many ways to vote as there are flaws in the way that the vote is tallied. So what problems exist with voting? Are there any intrinsic weaknesses in group decision-making systems? And what can we learn by examining these systems? All of this, and more, on this episode of Breaking Math.

Licensed under Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, visit CreativeCommons.org.

62: The Atom Bomb of Information Operations (An Interview with John Fuisz of Veriphix) Aug 22, 2021

Forecasting is a constantly evolving science, and has been applied to complex systems; everything from the weather, to determining what customers might like to buy, and even what governments might rise and fall. John Fuisz is someone who works with this science, and has experience improving the accuracy of forecasting. So how can forecasting be analyzed? What type of events are predictable? And why might Russia think a Missouri senator's race hinges upon North Korea? All of this and more on this episode of Breaking Math.

The theme for this episode was written by Elliot Smith.

[Featuring: Sofía Baca, Gabriel Hesch; John Fuisz]

61: Look at this Graph! (Graph Theory) Apr 25, 2021

In mathematics, nature is a constant driving inspiration; mathematicians are part of nature, so this is natural. A huge part of nature is the idea of things like networks. These are represented by mathematical objects called 'graphs'. Graphs allow us to describe a huge variety of things, such as: the food chain, lineage, plumbing networks, electrical grids, and even friendships. So where did this concept come from? What tools can we use to analyze graphs? And how can you use graph theory to minimize highway tolls? All of this and more on this episode of Breaking Math.

Episode distributed under an Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, visit CreativeCommons.org

[Featuring: Sofía Baca, Meryl Flaherty]

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This episode is sponsored by

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P9: Give or Take (Back-of-the-Envelope Estimates / Fermi Problems) Apr 19, 2021

How many piano tuners are there in New York City? How much cheese is there in Delaware? And how can you find out? All of this and more on this problem-episode of Breaking Math.

This episode distributed under a Creative Commons Attribution-ShareAlike-Noncommercial 4.0 International License. For more information, visit creativecommons.org

Featuring theme song and outro by Elliot Smith of Albuquerque.

[Featuring: Sofía Baca, Meryl Flaherty]

60: HAMILTON! [But Not the Musical] (Quaternions) Apr 03, 2021

i^2 = j^2 = k^2 = ijk = -1. This deceptively simple formula, discovered by Irish mathematician William Rowan Hamilton in 1843, led to a revolution in the way 19th century mathematicians and scientists thought about vectors and rotation. This formula, which extends the complex numbers, allows us to talk about certain three-dimensional problems with more ease. So what are quaternions? Where are they still used? And what is inscribed on Broom Bridge? All of this and more on this episode of Breaking Math.

This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.

The theme for this episode was written by Elliot Smith.

[Featuring: Sofía Baca, Meryl Flaherty]

59: A Good Source of Fibers (Fiber Bundles) Mar 21, 2021

Mathematics is full of all sorts of objects that can be difficult to comprehend. For example, if we take a slip of paper and glue it to itself, we can get a ring. If we turn it a half turn before gluing it to itself, we get what's called a Möbius strip, which has only one side twice the length of the paper. If we glue the edges of the Möbius strip to each other, and make a tube, you'll run into trouble in three dimensions, because the object that this would make is called a Klein flask, and can only exist in four dimensions. So what is a fiber? What can fiber bundles teach us about higher dimensional objects?

All of this, and more, on this episode of Breaking Math.

[Featuring: Sofía Baca, Meryl Flaherty]

58: Bringing Curvy Back (Gaussian Curvature) Mar 03, 2021

In introductory geometry classes, many of the objects dealt with can be considered 'elementary' in nature; things like tetrahedrons, spheres, cylinders, planes, triangles, lines, and other such concepts are common in these classes. However, we often have the need to describe more complex objects. These objects can often be quite organic, or even abstract in shape, and include things like spirals, flowery shapes, and other curved surfaces. These are often described better by differential geometry as opposed to the more elementary classical geometry. One helpful metric in describing these objects is how they are curved around a certain point. So how is curvature defined mathematically? What is the difference between negative and positive curvature? And what can Gauss' Theorema Egregium teach us about eating pizza?

This episode distributed under a Creative Commons Attribution ShareAlike 4.0 International License. For more information, go to creativecommons.org

Visit our sponsor today at Brilliant.org/BreakingMath for 20% off their annual membership! Learn hands-on with Brilliant.

[Featuring: Sofía Baca, Meryl Flaherty]

P8: Tangent Tango (Morikawa's Recently Solved Problem) Feb 25, 2021

Join Sofía and Gabriel as they talk about Morikawa's recently solved problem, first proposed in 1821 and not solved until last year!

Also, if you haven't yet, check out our sponsor The Great Courses at thegreatcoursesplus.com/breakingmath for a free month! Learn basically anything there.

The paper featured in this episode can be found at https://arxiv.org/abs/2008.00922

This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit CreativeCommons.org!

[Featuring: Sofía Baca, Gabriel Hesch]

P7: Root for Squares (Irrationality of the Square Root of Two) Feb 07, 2021

Join Sofía and Gabriel as they discuss an old but great proof of the irrationality of the square root of two.

[Featuring: Sofía Baca, Gabriel Hesch]

Patreon-Become a monthly supporter at patreon.com/breakingmath

Merchandise

Ad contained music track "Buffering" from Quiet Music for Tiny Robots.

Distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit creativecommons.org.

57: You Said How Much?! (Measure Theory) Feb 01, 2021

If you are there, and I am here, we can measure the distance between us. If we are standing in a room, we can calculate the area of where we're standing; and, if we want, the volume. These are all examples of measures; which, essentially, tell us how much 'stuff' we have. So what is a measure? How are distance, area, and volume related? And how big is the Sierpinski triangle? All of this and more on this episode of Breaking Math.

Ways to support the show:

Patreon-Become a monthly supporter at patreon.com/breakingmath

The theme for this episode was written by Elliot Smith.

Episode used in the ad was Buffering by Quiet Music for Tiny Robots.

[Featuring: Sofía Baca; Meryl Flaherty]

P6: How Many Angles in a Circle? (Curvature; Euclidean Geometry) Jan 28, 2021

Sofía and Gabriel discuss the question of "how many angles are there in a circle", and visit theorems from Euclid, as well as differential calculus.

This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.

Ways to support the show:

Patreon-Become a monthly supporter at patreon.com/breakingmath

The theme for this episode was written by Elliot Smith.

Music in the ad was Tiny Robot Armies by Quiet Music for Tiny Robots.

[Featuring: Sofía Baca, Gabriel Hesch]

56: More Sheep than You Can Count (Transfinite Cardinal Numbers) Jan 24, 2021

Look at all you phonies out there.

You poseurs.

All of you sheep. Counting 'til infinity. Counting sheep.

*pff*

What if I told you there were more there? Like, ... more than you can count?

But what would a sheeple like you know about more than infinity that you can count?

heh. *pff*

So, like, what does it mean to count til infinity? What does it mean to count more? And, like, where do dimensions fall in all of this?

Ways to support the show:

Patreon-Become a monthly supporter at patreon.com/breakingmath

(Correction: at 12:00, the paradox is actually due to Galileo Galilei)

Distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit CreativeCommons.org

Music used in the The Great Courses ad was Portal by Evan Shaeffer

[Featuring: Sofía Baca, Gabriel Hesch]

55: Order in the Court (Transfinite Ordinal Numbers) Jan 14, 2021

As a child, did you ever have a conversation that went as follows:

"When I grow up, I want to have a million cats"

"Well I'm gonna have a billion billion cats"

"Oh yeah? I'm gonna have infinity cats"

"Then I'm gonna have infinity plus one cats"

"That's nothing. I'm gonna have infinity infinity cats"

"I'm gonna have infinity infinity infinity infinity *gasp* infinity so many infinities that there are infinity infinities plus one cats"

What if I told you that you were dabbling in the transfinite ordinal numbers? So what are ordinal numbers? What does "transfinite" mean? And what does it mean to have a number one larger than another infinite number?

[Featuring: Sofía Baca; Diane Baca]

Ways to support the show:

Patreon

Become a monthly supporter at patreon.com/breakingmath

This episode is released under a Creative Commons attribution sharealike 4.0 international license. For more information, go to CreativeCommoms.org

This episode features the song "Buffering" by "Quiet Music for Tiny Robots"

54: Oodles (Large Numbers) Dec 21, 2020

There are a lot of things in the universe, but no matter how you break them down, you will still have far fewer particles than even some of the smaller of what we're calling the 'very large numbers'. Many people have a fascination with these numbers, and perhaps it is because their sheer scale can boggle the mind. So what numbers can be called 'large'? When are they useful? And what is the Ackermann function? All of this and more on this episode of Breaking Math

[Featuring: Sofía Baca; Diane Baca]

Ways to support the show:

Patreon

Become a monthly supporter at patreon.com/breakingmath

Merchandise

Purchase a Math Poster on Tensor Calculus at our facebook store at facebook.com/breakingmathpodcast

53: Big Brain Time (An Interview with Peter Zeidman from the UCL Institute of Neurology) Dec 11, 2020

Neuroscience is a topic that, in many ways, is in its infancy. The tools that are being used in this field are constantly being honed and reevaluated as our understanding of the brain and mind increase. And it's no surprise: the brain is responsible for the way we interact with the world, and the idea that ideas hone one another is not new to anyone who possesses a mind. But how can the tools that we use to study the brain and the mind be linked? How do the mind and the brain encode one another? And what does Bayes have to do with this? All of this and more on this episode of Breaking Math.

[Featuring: Sofía Baca, Gabriel Hesch; Peter Zeidman]

Patreon

Become a monthly supporter at patreon.com/breakingmath

This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.

52: Round (Circles and Spheres) Dec 05, 2020

Spheres and circles are simple objects. They are objects that are uniformly curved throughout in some way or another. They can also be defined as objects which have a boundary that is uniformly distant from some point, using some definition of distance. Circles and spheres were integral to the study of mathematics at least from the days of Euclid, being the objects generated by tracing the ends of idealized compasses. However, these objects have many wonderful and often surprising mathematical properties. To this point, a circle's circumference divided by its diameter is the mathematical constant pi, which has been a topic of fascination for mathematicians for as long as circles have been considered.

[Featuring Sofía Baca; Meryl Flaherty]

Patreon

Become a monthly supporter at patreon.com/breakingmath

P5: All Your Base Are Belong to Us (Fractional Base Proof) Nov 26, 2020

Join Sofia and Gabriel on this problem episode where we explore "base 3-to-2" — a base system we explored on the last podcast — and how it relates to "base 3/2" from last episode.

[Featuring: Sofía Baca; Gabriel Hesch]

51: Episode "-2,0,1" (Bases; Exotic Bases) Nov 15, 2020

A numerical base is a system of representing numbers using a sequence of symbols. However, like any mathematical concept, it can be extended and re-imagined in many different forms. A term used occasionally in mathematics is the term 'exotic', which just means 'different than usual in an odd or quirky way'. In this episode we are covering exotic bases. We will start with something very familiar (viz., decimal points) as a continuation of our previous episode, and then progress to the more odd, such as non-integer and complex bases. So how can the base systems we covered last time be extended to represent fractional numbers? How can fractional numbers be used as a base for integers? And what is pi plus e times i in base i + 1?

This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca; Merryl Flaherty]

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50: Episode "101" (Bases) Aug 31, 2020

Numbering was originally done with tally marks: the number of tally marks indicated the number of items being counted, and they were grouped together by fives. A little later, people wrote numbers down by chunking the number in a similar way into larger numbers: there were symbols for ten, ten times that, and so forth, for example, in ancient Egypt; and we are all familiar with the Is, Vs, Xs, Ls, Cs, and Ds, at least, of Roman numerals. However, over time, several peoples, including the Inuit, Indians, Sumerians, and Mayans, had figured out how to chunk numbers indefinitely, and make numbers to count seemingly uncountable quantities using the mind, and write them down in a few easily mastered motions. These are known as place-value systems, and the study of bases has its root in them: talking about bases helps us talk about what is happening when we use these magical symbols.

49: Thinking Machines II (Techniques in Artificial Intelligence) May 26, 2020

Machines have been used to simplify labor since time immemorial, and simplify thought in the last few hundred years. We are at a point now where we have the electronic computer to aid us in our endeavor, which allows us to build hypothetical thinking machines by simply writing their blueprints — namely, the code that represents their function — in a general way that can be easily reproduced by others. This has given rise to an astonishing array of techniques used to process data, and in recent years, much focus has been given to methods that are used to answer questions where the question or answer is not always black and white. So what is machine learning? What problems can it be used to solve? And what strategies are used in developing novel approaches to machine learning problems? This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org. For more Breaking Math info, visit BreakingMathPodcast.app [Featuring: Sofía Baca, Gabriel Hesch] References: https://spectrum.ieee.org/tag/history+of+natural+language+processing
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48: Thinking Machines (Philosophical Basis of Artificial Intelligence) May 18, 2020

Machines, during the lifetime of anyone who is listening to this, have advanced and revolutionized the way that we live our lives. Many listening to this, for example, have lived through the rise of smart phones, 3d printing, massive advancements in lithium ion batteries, the Internet, robotics, and some have even lived through the introduction of cable TV, color television, and computers as an appliance. All advances in machinery, however, since the beginning of time have one thing in common: they make what we want to do easier. One of the great tragedies of being imperfect entities, however, is that we make mistakes. Sometimes those mistakes can lead to war, famine, blood feuds, miscalculation, the punishment of the innocent, and other terrible things. It has, thus, been the goal of many, for a very long time, to come up with a system for not making these mistakes in the first place: a thinking machine, which would help eliminate bias in situations. Such a fantastic machine is looking like it's becoming closer and closer to reality, especially with the advancements in artificial intelligence. But what are the origins of this fantasy? What attempts have people made over time to encapsulate reason? And what is ultimately possible with the automated manipulation of meaning? All of this and more on this episode of Breaking Math. Episode 48: Thinking Machines References: * https://publicdomainreview.org/essay/let-us-calculate-leibniz-llull-and-the-computational-imagination * https://spectrum.ieee.org/tag/history+of+natural+language+processing https://en.wikipedia.org/wiki/Characteristica_universalis https://ourworldindata.org/coronavirus-source-data This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org. [Featuring: Sofía Baca, Gabriel Hesch]

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P4: Go with the Flow (Conceptual Calculus: Related Rates of Change) Mar 10, 2020

Join Gabriel and Sofía as they delve into some introductory calculus concepts.

[Featuring: Sofía Baca, Gabriel Hesch]

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47: Blast to the Past (Retrocausality) Feb 29, 2020

Time is something that everyone has an idea of, but is hard to describe. Roughly, the arrow of time is the same as the arrow of causality. However, what happens when that is not the case? It is so often the case in our experience that this possibility brings not only scientific and mathematic, but ontological difficulties. So what is retrocausality? What are closed timelike curves? And how does this all relate to entanglement?

This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca, Gabriel Hesch]

P3: Radiativeforcenado (Radiative Forcing) Feb 03, 2020

Learn more about radiative forcing, the environment, and how global temperature changes with atmospheric absorption with this Problem Episode about you walking your (perhaps fictional?) dog around a park. This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca, Gabriel Hesch]

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46: Earth Irradiated (the Greenhouse Effect) Jan 20, 2020

Since time immemorial, blacksmiths have known that the hotter metal gets, the more it glows: it starts out red, then gets yellower, and then eventually white. In 1900, Max Planck discovered the relationship between an ideal object's radiation of light and its temperature. A hundred and twenty years later, we're using the consequences of this discovery for many things, including (indirectly) LED TVs, but perhaps one of the most dangerously neglected (or at least ignored) applications of this theory is in climate science. So what is the greenhouse effect? How does blackbody radiation help us design factories? And what are the problems with this model?

This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca, Gabriel Hesch]

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45: Climate Denialism and Cranky Uncles (Interview with John Cook of Skeptical Science) Dec 10, 2019

Climate change is an issue that has become frighteningly more relevant in recent years, and because of special interests, the field has become muddied with climate change deniers who use dishonest tactics to try to get their message across. The website SkepticalScience.com is one line of defense against these messengers, and it was created and maintained by a research assistant professor at the Center for Climate Change Communication at George Mason University, and both authored and co-authored two books about climate science with an emphasis on climate change. He also lead-authored a 2013 award-winning paper on the scientific consensus on climate change, and in 2015, he developed an open online course on climate change denial with the Global Change Institute at the University of Queensland. This person is John Cook.

This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca, Gabriel Hesch; John Cook]

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44: Vestigial Math (Math That Is Not Used like It Used to Be) Nov 03, 2019

Mathematics, like any intellectual pursuit, is a constantly-evolving field; and, like any evolving field, there are both new beginnings and sudden unexpected twists, and things take on both new forms and new responsibilities. Today on the show, we're going to cover a few mathematical topics whose nature has changed over the centuries. So what does it mean for math to be extinct? How does this happen? And will it continue forever?

This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca, Gabriel Hesch]

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P2: Walk the Dog (Calculus: Chain Rule) Oct 30, 2019

Learn more about calculus, derivatives, and the chain rule with this Problem Episode about you walking your (perhaps fictional?) dog around a park.

This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca, Gabriel Hesch]

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43: Interview II with Author Ben Orlin (Change is the Only Constant: the Wisdom of Calculus in a Madcap World) Oct 23, 2019

Ben Orlin has been a guest on the show before. He got famous with a blog called 'Math With Bad Drawings", which is what it says on the tin: he teaches mathematics using his humble drawing skills. His last book was a smorgasbord of different mathematical topics, but he recently came out with a new book 'Change is the Only Constant: the Wisdom of Calculus in a Madcap World', which focuses more on calculus itself.

This episode is distributed under a CC BY-SA license. For more info, visit creativecommons.org

P1: Peano Addition Sep 29, 2019

On this problem episode, join Sofía and guest Diane Baca to learn about what an early attempt to formalize the natural numbers has to say about whether or not m+n equals n+m.
This episode is distributed under a CC BY-SA 4.0 license (https://creativecommons.org/licenses/by-sa/4.0/)
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42: Maybe? (Probability and Statistics) Aug 15, 2019

Statistics is a field that is considered boring by a lot of people, including a huge amount of mathematicians. This may be because the history of statistics starts in a sort of humdrum way: collecting information on the population for use by the state. However, it has blossomed into a beautiful field with its fundamental roots in measure theory, and with some very interesting properties. So what is statistics? What is Bayes' theorem? And what are the differences between the frequentist and Bayesian approaches to a problem?

Distributed under a Creative Commons Attribution-ShareAlike 4.0 International License (creativecommons.org)

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41: Reality Is More Than Complex (Group Theory and Physics) Jul 29, 2019

Children who are being taught mathematics often balk at the idea of negative numbers, thinking them to be fictional entities, and often only learn later that they are useful for expressing opposite extremes of things, such as considering a debt an amount of money with a negative sum. Similarly, students of mathematics often are puzzled by the idea of complex numbers, saying that it makes no sense to be able to take the square root of something negative, and only realizing later that these can have the meaning of two-dimensional direction and magnitude, or that they are essential to our modern understanding of electrical engineering. Our discussion today will be much more abstract than that. Much like in our discussion in episode five, "Language of the Universe", we will be discussing how math and physics draw inspiration from one another; we're going to talk about what different fields (such as the real, complex, and quaternion fields) seem to predict about our universe. So how are real numbers related to classical mechanics? What does this mean complex numbers and quaternions are related to? And what possible physicses exist?

Update: Dr. Alex Alaniz and the Breaking Math Podcast have teamed up to create a new youtube show called the "Turing Rabbit Holes Podcast." We discuss science, math, and society with spectacular visuals. Available at youtube.com/TuringRabbitHolesPodcast and on all other podcast platforms.

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License is Creative Commons Attribution-ShareAlike 4.0 (See https://creativecommons.org/licenses/by-sa/4.0/)

39: Syntax Matters: Syntax... Matters? (Formal Grammar) May 29, 2019

We communicate every day through languages; not only human languages, but other things that could be classified as languages such as internet protocols, or even the structure of business transactions. The structure of words or sentences, or their metaphorical equivalents, in that language is known as their syntax. There is a way to describe certain syntaxes mathematically through what are known as formal grammars. So how is a grammar defined mathematically? What model of language is often used in math? And what are the fundamental limits of grammar?

38: The Great Stratagem Heist (Game Theory: Iterated Elimination of Dominated Strategies) Apr 23, 2019

Game theory is all about decision-making and how it is impacted by choice of strategy, and a strategy is a decision that is influenced not only by the choice of the decision-maker, but one or more similar decision makers. This episode will give an idea of the type of problem-solving that is used in game theory. So what is strict dominance? How can it help us solve some games? And why are The Obnoxious Seven wanted by the police?

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37: The One Where They Parody Saw [audio fixed again] (Game Theory) Feb 25, 2019

Hello listeners. You don't know me, but I know you. I want to play a game. In your ears are two earbuds. Connected to the earbuds are a podcast playing an episode about game theory. Hosting that podcast are two knuckleheads. And you're locked into this episode. The key is at the end of the episode. What is game theory? Why did we parody the Saw franchise? And what twisted lessons will you learn?

-See our New Youtube Show "Turing Rabbit Holes Podcast" at youtube.com/TuringRabbitHolesPodcast. Also available on all podcast players.

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36: The Most Boring Episode Ever. (Math Games) Nov 23, 2018

Math is a gravely serious topic which has been traditionally been done by stodgy people behind closed doors, and it cannot ever be taken lightly. Those who have fun with mathematics mock science, medicine, and the foundation of engineering. That is why on today's podcast, we're going to have absolutely no fun with mathematics. There will not be a single point at which you consider yourself charmed, there will not be a single thing you will want to tell anyone for the sake of enjoyment, and there will be no tolerance for your specific brand of foolishness, and that means you too, Kevin.

35: Please Be Discrete (Discrete Math) Nov 05, 2018

Centuries ago, there began something of a curiosity between mathematicians that didn't really amount to much but some interesting thoughts and cool mathematical theorems. This form of math had to do with strictly integer quantities; theorems about whole numbers. Things started to change in the 19th century with some breakthroughs in decrypting intelligence through examining the frequency of letters. In the fervor that followed to increase the security of existing avenues of communication, and to speed up the newfound media of telegraphy, came a field of mathematics called discrete math. It is now an essential part of our world today, with technologies such as online banking being essentially impossible without it. So what have we learned from discrete math? What are some essential methods used within it? And how is it applied today?

34: An Interview with Mathbot.com's JW Weatherman Oct 20, 2018

In this episode, we interview JW Weatherman of mathbot.com, and ask him about his product, why he made it, and what he plans on doing with it.
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33: Interview with Math with Bad Drawings (Ben Orlin) Oct 03, 2018

An interview with Ben Orlin, author of the book 'Math with Bad Drawings,' as well as the blog of the same name. The blog can be found at www.mathwithbaddrawings.com.

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32X: Black Hole Heist (Comedy Sketch) Sep 23, 2018

The hosts of Breaking Math had too much time on their hands.

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32: Gaze into the Abyss (Part Three; Black Holes) Sep 23, 2018

A lot of the information in this episode of Breaking Math depends on episodes 30 and 31 entitled "The Abyss" and "Into the Abyss" respectively. If you have not listened to those episodes, then we'd highly recommend going back and listening to those. We're choosing to present this information this way because otherwise we'd waste most of your time re-explaining concepts we've already covered.

Black holes are so bizarre when we measured against the yardstick of the mundanity of our day to day lives that they inspire fear, awe, and controversy. In this last episode of the Abyss series, we will look at some more cutting-edge problems and paradoxes surrounding black holes. So how are black holes and entanglement related? What is the holographic principle? And what is the future of black holes?

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31: Into the Abyss (Part Two; Black Holes) Aug 23, 2018

Black holes are objects that seem exotic to us because they have properties that boggle our comparatively mild-mannered minds. These are objects that light cannot escape from, yet glow with the energy they have captured until they evaporate out all of their mass. They thus have temperature, but Einstein's general theory of relativity predicts a paradoxically smooth form. And perhaps most mind-boggling of all, it seems at first glance that they have the ability to erase information. So what is black hole thermodynamics? How does it interact with the fabric of space? And what are virtual particles?

30: The Abyss (Part One; Black Holes) Aug 02, 2018

The idea of something that is inescapable, at first glance, seems to violate our sense of freedom. This sense of freedom, for many, seems so intrinsic to our way of seeing the universe that it seems as though such an idea would only beget horror in the human mind. And black holes, being objects from which not even light can escape, for many do beget that same existential horror. But these objects are not exotic: they form regularly in our universe, and their role in the intricate web of existence that is our universe is as valid as the laws that result in our own humanity. So what are black holes? How can they have information? And how does this relate to the edge of the universe?

29: War Jul 14, 2018

In the United States, the fourth of July is celebrated as a national holiday, where the focus of that holiday is the war that had the end effect of ending England’s colonial influence over the American colonies. To that end, we are here to talk about war, and how it has been influenced by mathematics and mathematicians. The brutality of war and the ingenuity of war seem to stand at stark odds to one another, as one begets temporary chaos and the other represents lasting accomplishment in the sciences. Leonardo da Vinci, one of the greatest western minds, thought war was an illness, but worked on war machines. Feynman and Von Neumann held similar views, as have many over time; part of being human is being intrigued and disgusted by war, which is something we have to be aware of as a species. So what is warfare? What have we learned from refining its practice? And why do we find it necessary?

28: Bell's Infamous Theorem (Bell's Theorem) Jun 19, 2018

The history of physics as a natural science is filled with examples of when an experiment will demonstrate something or another, but what is often forgotten is the fact that the experiment had to be thought up in the first place by someone who was aware of more than one plausible value for a property of the universe, and realized that there was a way to word a question in such a way that the universe could understand. Such a property was debated during the quantum revolution, and involved Einstein, Polodsky, Rosen, and Schrödinger. The question was 'do particles which are entangled "know" the state of one another from far away, or do they have a sort of "DNA" which infuses them with their properties?' The question was thought for a while to be purely philosophical one until John Stewart Bell found the right way to word a question, and proved it in a laboratory of thought. It was demonstrated to be valid in a laboratory of the universe. So how do particles speak to each other from far away? What do we mean when we say we observe something? And how is a pair of gloves like and unlike a pair of walkie talkies?

27: Peer Pressure (Cellular Automata) May 14, 2018

The fabric of the natural world is an issue of no small contention: philosophers and truth-seekers universally debate about and study the nature of reality, and exist as long as there are observers in that reality. One topic that has grown from a curiosity to a branch of mathematics within the last century is the topic of cellular automata. Cellular automata are named as such for the simple reason that they involve discrete cells (which hold a (usually finite and countable) range of values) and the cells, over some field we designate as "time", propagate to simple automatic rules. So what can cellular automata do? What have we learned from them? And how could they be involved in the future of the way we view the world?

26: Infinity Shades of Grey (Paradox) Apr 26, 2018

A paradox is characterized either by a logical problem that does not have a single dominant expert solution, or by a set of logical steps that seem to lead somehow from sanity to insanity. This happens when a problem is either ill-defined, or challenges the status quo. The thing that all paradoxes, however, have in common is that they increase our understanding of the phenomena which bore them. So what are some examples of paradox? How does one go about resolving it? And what have we learned from paradox?

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25: Pandemic Panic (Epidemiology) Apr 13, 2018

The spectre of disease causes untold mayhem, anguish, and desolation. The extent to which this spectre has yielded its power, however, has been massively curtailed in the past century. To understand how this has been accomplished, we must understand the science and mathematics of epidemiology. Epidemiology is the field of study related to how disease unfolds in a population. So how has epidemiology improved our lives? What have we learned from it? And what can we do to learn more from it?

24: Language and Entropy (Information Theory in Language) Mar 07, 2018

Information theory was founded in 1948 by Claude Shannon, and is a way of both qualitatively and quantitatively describing the limits and processes involved in communication. Roughly speaking, when two entities communicate, they have a message, a medium, confusion, encoding, and decoding; and when two entities communicate, they transfer information between them. The amount of information that is possible to be transmitted can be increased or decreased by manipulating any of the aforementioned variables. One of the practical, and original, applications of information theory is to models of language. So what is entropy? How can we say language has it? And what structures within language with respect to information theory reveal deep insights about the nature of language itself?

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23: Don't Touch My Circles! (Geometry) Jan 15, 2018

In the study of mathematics, there are many abstractions that we deal with. For example, we deal with the notion of a real number with infinitesimal granularity and infinite range, even though we have no evidence for this existing in nature besides the generally noted demi-rules 'smaller things keep getting discovered' and 'larger things keep getting discovered'. In a similar fashion, we define things like circles, squares, lines, planes, and so on. Many of the concepts that were just mentioned have to do with geometry; and perhaps it is because our brains developed to deal with geometric information, or perhaps it is because geometry is the language of nature, but there's no doubt denying that geometry is one of the original forms of mathematics. So what defines geometry? Can we make progress indefinitely with it? And where is the line between geometry and analysis?

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22: Incomplet (Gödel, Escher, Bach: an Eternal Golden Braid: Chapter IV Discussion) Dec 23, 2017

Gödel, Escher, Bach is a book about everything from formal logic to the intricacies underlying the mechanisms of reasoning. For that reason, we've decided to make a tribute episode; specifically, about episode IV. There is a Sanskrit word "maya" which describes the difference between a symbol and that which it symbolizes. This episode is going to be all about the math of maya. So what is a string? How are formal systems useful? And why do we study them with such vigor?

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21: Einstein's Biggest Idea (General Relativity) Dec 04, 2017

Some see the world of thought divided into two types of ideas: evolutionary and revolutionary ideas. However, the truth can be more nuanced than that; evolutionary ideas can spur revolutions, and revolutionary ideas may be necessary to create incremental advancements. General relativity is an idea that was evolutionary mathematically, revolutionary physically, and necessary for our modern understanding of the cosmos. Devised in its full form first by Einstein, and later proven correct by experiment, general relativity gives us a framework for understanding not only the relationship between mass and energy and space and time, but topology and destiny. So why is relativity such an important concept? How do special and general relativity differ? And what is meant by the equation G=8πT?

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20: Rational (Ratios) Nov 18, 2017

From MC²’s statement of mass energy equivalence and Newton’s theory of gravitation to the sex ratio of bees and the golden ratio, our world is characterized by the ratios which can be found within it. In nature as well as in mathematics, there are some quantities which equal one another: every action has its equal and opposite reaction, buoyancy is characterized by the displaced water being equal to the weight of that which has displaced it, and so on. These are characterized by a qualitative difference in what is on each side of the equality operator; that is to say: the action is equal but opposite, and the weight of water is being measured versus the weight of the buoyant object. However, there are some formulas in which the equality between two quantities is related by a constant. This is the essence of the ratio. So what can be measured with ratios? Why is this topic of importance in science? And what can we learn from the mathematics of ratios?

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19: Tune of the Hickory Stick (Beginning to Intermediate Math Education) Nov 07, 2017

The art of mathematics has proven, over the millennia, to be a practical as well as beautiful pursuit. This has required us to use results from math in our daily lives, and there's one thing that has always been true of humanity: we like to do things as easily as possible. Therefore, some very peculiar and interesting mental connections have been developed for the proliferation of this sort of paramathematical skill. What we're talking about when we say "mental connections" is the cerebral process of doing arithmetic and algebra. So who invented arithmetic? How are algebra and arithmetic related? And how have they changed over the years?

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18: Frequency (Fourier and Related Analyses) Oct 11, 2017

Duration and proximity are, as demonstrated by Fourier and later Einstein and Heisenberg, very closely related properties. These properties are related by a fundamental concept: frequency. A high frequency describes something which changes many times in a short amount of space or time, and a lower frequency describes something which changes few times in the same time. It is even true that, in a sense, you can ‘rotate’ space into time. So what have we learned from frequencies? How have they been studied? And how do they relate to the rest of mathematics?

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17: Navier Stoked (Vector Calculus and Navier-Stokes Equations) Oct 05, 2017

From our first breath of the day to brushing our teeth to washing our faces to our first sip of coffee, and even in the waters of the rivers we have built cities upon since antiquity, we find ourselves surrounded by fluids. Fluids, in this context, mean anything that can take the shape of its container. Physically, that means anything that has molecules that can move past one another, but mathematics has, as always, a slightly different view. This view is seen by some as more nuanced, others as more statistical, but by all as a challenge. This definition cannot fit into an introduction, and I’ll be picking away at it for the remainder of this episode. So what is a fluid? What can we learn from it? And how could learning from it be worth a million dollars?
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BFNB2: Thought for Food (Discussion about Learning) Sep 19, 2017

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BFNB1: Food for Thought (Discussion about Learning) Sep 16, 2017

This is the first group podcast for the podcasting network ___forNon___ (pronounced "Blank for Non-Blank"), a podcasting network which strives to present expert-level subject matter to non-experts in a way which is simultaneously engaging, interesting, and simple. The episode today delves into the problem of learning. We hope you enjoy this episode.
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Minisode 0.6: Four Problems Aug 18, 2017

Jonathan and Gabriel discuss four challenging problems.
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15: Consciousness Jul 30, 2017

What does it mean to be a good person? What does it mean to make a mistake? These are questions which we are not going to attempt to answer, but they are essential to the topic of study of today’s episode: consciousness. Conscious is the nebulous thing that lends a certain air of importance to experience, but as we’ve seen from 500 centuries of fascination with this topic, it is difficult to describe in languages which we’re used to. But with the advent of neuroscience and psychology, we seem to be closer than ever to revealing aspects of consciousness that we’ve never beheld. So what does it mean to feel? What are qualia? And how do we know that we ourselves are conscious?

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Minisode 0.5: ___forNon___ Jul 20, 2017

Jonathan and Gabriel discuss ___forNon___ (blank for non-blank); a podcasting collective they've recently joined. Check out more at blankfornonblank.com.
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14: Artificial Thought (Neural Networks) Jul 11, 2017

Go to www.brilliant.org/breakingmathpodcast to learn neural networks, everyday physics, computer science fundamentals, the joy of problem solving, and many related topics in science, technology, engineering, and math.

Mathematics takes inspiration from all forms with which life interacts. Perhaps that is why, recently, mathematics has taken inspiration from that which itself perceives the world around it; the brain itself. What we’re talking about are neural networks. Neural networks have their origins around the time of automated computing, and with advances in hardware, have advanced in turn. So what is a neuron? How do multitudes of them contribute to structured thought? And what is in their future?

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13: Math and Prison Riots (Interview with Frank Salas) Jun 27, 2017

Frank Salas is an statistical exception, but far from an irreplicable result. Busted on the streets of Albuquerque for selling crack cocaine at 17, an age where many of us are busy honing the skills that we've chosen to master, and promply incarcerated in one of the myriad concrete boxes that comprise the United States penal system. There, he struggled, as most would in his position, to better himself spiritually or ethically, once even participating in a prison riot. After two stints in solitary confinement, he did the unthinkable: he imagined a better world for himself. One where it was not all him versus the world. With newfound vigor, he discovered what was there all along: a passion for mathematics and the sciences. After nine years of hard time he graduated to a halfway house. From there, we attended classes at community college, honing his skills using his second lease on life. That took him on a trajectory which developed into him working on a PhD in electrical engineering from the University of Michegan. We're talking, of course, about Frank Salas; a man who is living proof that condition and destiny are not forced to correlate, and who uses this proof as inspiration for many in the halway house that he once roamed. So who is he? What is his mission? And who is part of that mission? And what does this have to do with Maxwell's equations of electromagnetism?

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12: Math Factory (Algorithms) Jun 13, 2017

In a universe where everything is representable by information, what does it mean to interact with that world? When you follow a series of steps to accomplish a goal, what you're doing is taking part in a mathematical tradition as old as math itself: algorithms. From time immemorial, we've accelerated the growth of this means of transformation, and whether we're modeling neurons, recognizing faces, designing trusses on a bridge, or coloring a map, we're involving ourselves heavily in a fantastic world, where everything is connected to everything else through a massive network of mathematical factories. So does it mean to do something? What does it mean for something to end? And what is time relative to these questions?
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11: A Culture of Hacking (Hacker Culture) May 31, 2017

The culture of mathematics is a strange topic. It is almost as important to the history of mathematics as the theorems that have come from it, yet it is rarely commented upon, and it is almost never taught in schools. One form of mathematical inquiry that has cropped up in the last two centuries has been the algorithm. While not exclusive to this time period, it has achieved a renaissance, and with the algorithm has come what has come to be known as "hacker culture". From Lord Byron to Richard Stallman, from scratches on paper to masses of wire, hacker culture has influenced the way in which we interact with conveniences that algorithms have endowed upon our society. So what are these advances? How have they been affected by the culture which birthed them? And what can we learn from this fragile yet pervasive relationship?
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10: Cryptomath (Cryptography) May 16, 2017

Language and communication is a huge part of what it means to be a person, and a large part of this importance is the ability to direct the flow of that information; this is a practice known as cryptography. There are as many ways to encrypt data as there are ways to use them, ranging from cryptoquips solvable by children in an afternoon to four kilobit RSA taking eons of time. So why are there so many forms of encryption? What can they be used for? And what are the differences in their methodology, if not philosophy?
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9: Humanity 2.0 (Transhumanism) May 02, 2017

Humanity, since its inception, has been nebulously defined. Every technological advancement has changed what it means to be a person, and every person has changed what it means to advance. In this same vein, there is a concept called “transhumanism”, which refers to what it will mean to be a person. This can range from everything from genetic engineering, to artificial intelligence, to technology which is beyond our current physical understanding. So what does it mean to be a person? And is transhumanism compatible with our natural understanding, if it exists, of being?

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Minisode 0.4: Comin' Up Next May 01, 2017

Jonathan and Gabriel talk about the next four episodes coming down the pike, including Humanity 2.0, which debuts Tuesday, April 2nd 2017.
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Minisode 0.3: Lights, Camera, Action! Apr 20, 2017

Jonathan and Gabriel discuss their recent news debut! You can find what they're talking about at news.unm.edu
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8: Evolution and Engineering (Genetic Algorithms) Apr 18, 2017

Computation is a nascent science, and as such, looks towards the other sciences for inspiration. Whether it be physics, as in simulated annealing, or, as now is popular, biology, as in neural networks, computer science has shown repeatedly that it can learn great things from other sciences. Genetic algorithms are one such method that is inspired, of course, by biological evolution. So what are genetic algorithms used for? What have they taught us about the natural process of evolution? And how can we use them to improve our world?

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Minisode 0.2: What's Up, Bangalore? Apr 10, 2017

Jonathan and Gabriel discuss everything Bangalore, evolutionary algorithmic, and more!
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7: QED? Prove it. (Proofs) Apr 04, 2017

Proofs are sometimes seen as an exercise in tedium, other times as a pure form of beauty, and often as both. But from time immemorial, people have been using mathematics to demonstrate new theorems, and advance the state of the art of mathematics. However, it is only relatively recently, within the last 3,000 years, that the art of mathematical proof has been considered essential to the study of mathematics. Mathematicians constantly fight over what constitutes a proof, and even what makes a proof valid, partially because proof requires delicate insight. So what is the art of mathematical proof? How has it changed? And who can do it?

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Minisode 0.1: Hypercubes and Other Stranger Things Apr 01, 2017

We are proud to announce that we have recorded our very first minisode! In addition, we are introducing a new blog which can be found at www.breakingmathpodcast.com/blog.html
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6: Word (Linguistics) Mar 21, 2017

Mathematics has a lot in common with language. Both have been used since the dawn of time to shape and define our world, both have sets of rules which one must master before bending, both are natural consequences of the way humans are raised, and both are as omnipresent as they are seemingly intangible. Language has thrived for almost, or as long as humans have possessed the ability to use it. But what can we say that language is? Is it a living breathing organism, a set of rigid ideals, somewhere in between, or something else altogether?

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5: Language of the Universe (Relationship Between Physics and Math) Mar 07, 2017

1948. A flash, followed by an explosion. Made possible by months of mathematical computation, the splitting of the atom was hailed as a triumph of both science and mathematics. Mathematics is seen by many as a way of quantifying experiments. But is that always the case? There are cases where it seems as though mathematics itself has made predictions about the universe and vice versa. So how are these predictions made? And what can we learn about both physics and math by examining the way in which these topics intermingle?

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4: Digital Evolution (Digital Computing) Feb 21, 2017

We live in an era of unprecedented change, and the tip of the spear of this era of change is currently the digital revolution. In fact, in the last decade we’ve gone from an analog to a digitally dominated society, and the amount of information has recently been increasing exponentially. Or at least it seems like it’s recent; in fact, however, the digital revolution has been going on for hundreds of centuries. From numerals inscribed in“We live in an era of unprecedented change, and the tip of the spear of this era of change is currently the digital revolution. In fact, in the last decade we’ve gone from an analog to a digitally dominated society, and the amount of information has recently been increasing exponentially. Or at least it seems like it’s recent; in fact, however, the digital revolution has been going on for hundreds of centuries. From numerals inscribed in bone to signals zipping by at almost the speed of light, our endeavors as humans, and some argue, our existence in the universe, is ruled by the concept of digital information. So how did we discover digital information? And what has it been used for?

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3: TMI (Information Theory) Feb 07, 2017

“ABABABABABABABAB”. How much information was that? You may say “sixteen letters worth”, but is that the true answer? You could describe what you just read as “AB 8 times”, and save a bunch of characters, and yet have the same information. But what is information in the context of mathematics? The answer is nothing short of miraculous; information theory has applications in telephony, human language, and even physics. So what is information theory, and what can we learn from it?
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2: Wreaking Chaos (Chaos Theory) Feb 07, 2017

The void has always intrigued mankind; the concept of no concept defies the laws of human reasoning to such a degree that we have no choice but to pursue it. But ancient Assyrian, Norse, Judeo-Christian creation stories, and even our own scientific inquiries have one thing in common: creation from “nothingness”. But is it really nothingness? The ancients used the term “chaos”, and, although to some “chaos” has become synonymous with “bedlam” or “randomness”, it has much more to do with the timeless myths of creation of form from the formless. So how does chaos take form? And is there meaning to be found in the apparent arbitrariness of chaos, or is it a void that defines what we think it means to be?

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1: Forbidden Formulas (Elitism in Math) Feb 07, 2017

From Pythagoras to Einstein, from the banks of the Nile to the streamlined curves of the Large Hadron Collider, math has shown itself again and again to be fundamental to the way that humans interact with the world. Then why is math such a pain for so many people? Our answer is simple: math is, and always has been, in one way or another, guarded as an elite skill. We visit the worlds that were shaped by math, the secrets people died for, the false gods created through this noble science, and the gradual chipping away of this knowledge by a people who have always yearned for this magical skill. So what is it? And how can we make it better?

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