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    Mathematics

    Breaking Math Podcast

    Breaking Math is a deep-dive science, technology, engineering, AI, and mathematics podcast that explores the world through the lens of logic, patterns, and critical thinking. Hosted by Autumn Phaneuf, an expert in industrial engineering, operations research, and applied mathematics, and Noah Giansiracusa, a mathematician and leading voice in algorithmic literacy and technology ethics, the show is dedicated to uncovering the mathematical structures behind science, technology, and the systems shaping our future.

    What began as a conversation about math as a pure and elegant discipline has evolved into a platform for bold, interdisciplinary dialogue. Each episode of Breaking Math takes listeners on an intellectual journey—into the strange beauty of chaos theory, the ethical dilemmas of AI and algorithms, the hidden math of biology and evolution, or the physics governing black holes and the cosmos. Along the way, Autumn and Noah speak with working scientists, researchers, and thinkers across fields: computer scientists, physicists, chemists, engineers, economists, philosophers, and more.

    But this isn’t just a podcast about equations. It’s a show about how mathematics shapes the way we think, decide, build, and understand the world. Breaking Math pushes back against the idea that STEM belongs behind a paywall or an academic podium. It’s for the curious, the critical, and the creative—for anyone who believes that ideas should be rigorous, accessible, and infused with wonder.

    If you’ve ever wondered:

    • What’s the math behind machine learning and modern algorithms?
    • How do we quantify uncertainty in climate and economic models?
    • Can intelligence or consciousness be meaningfully described in AI?
    • Why does beauty matter in an equation?

    You’re in the right place.

    At its heart, Breaking Math is about building bridges—between disciplines, between experts and the public, and between abstract mathematics and the messy, magnificent reality we live in. With humor, clarity, and deep respect for complexity, Autumn and Noah invite you to rethink what math can be—and how it can help us shape a better future.

    Listen wherever you get your podcasts.

    Website: https://breakingmath.io

    Linktree: https://linktr.ee/breakingmathmedia

    Email: breakingmathpodcast@gmail.com

    Advertise

    Copyright: © Copyright Breaking Math

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    Latest Episodes:
    Bayes' Theorem Explains It All: An Interview with Tom Chivers May 07, 2024
    Show notes

    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.

    Subscribe to Breaking Math wherever you get your podcasts.

    Become a patron of Breaking Math for as little as a buck a month

    Follow Breaking Math on Twitter, Instagram, LinkedIn, Website

    Follow Autumn on Twitter and Instagram

    Folllow Gabe on Twitter.

    email: breakingmathpodcast@gmail.com

    Interview with Steve Nadis, Co-author of 'Gravity of Math' Apr 30, 2024
    Show notes

    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

    Subscribe to Breaking Math wherever you get your podcasts.

    Become a patron of Breaking Math for as little as a buck a month

    Follow Breaking Math on Twitter, Instagram, LinkedIn, Website

    Follow Autumn on Twitter and Instagram

    Folllow Gabe on Twitter.

    email: breakingmathpodcast@gmail.com

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

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

    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: Follow us on X: @BreakingMathPod

    Follow us on Instagram: @Breaking Math Media

    Email us: BreakingMathPodacst@gmail.com

    Brain Organelles, AI, and Other Scary Science - An Interview with GT (Part 2) Apr 04, 2024
    Show notes

    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.30% Off ZenCastr Discount

    Use My Special Link to save e 30% Off Your First Month of Any ZenCastr Paid Plan

    LEAN Theorem Provers used to model Physics and Chemistry Mar 16, 2024
    Show notes

    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.

    Help Support The Podcast by clicking on the links below:

    • Try out ZenCastr w/ 30% DiscountUse my special link to save 30% off your first month of any Zencastr paid plan
    • Patreon
    • YouTube
    • Breaking Math WebsiteEmail us for copies of the transcript!
    Brain Organelles, AI, and the Other Scary Science - An Interview with GT (Part 1) Mar 05, 2024
    Show notes

    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

    1. 00:00 Introduction: Brain Organoids and Robots
    2. 00:39 Brain Organoids and Development
    3. 01:21 Ethical Implications of Brain Organoids
    4. 03:14 Summary and Introduction to Guest
    5. 03:41 Sentience and Consciousness in Brain Organoids
    6. 04:10 Neuron Count and Pain Receptors in Brain Organoids
    7. 05:00 Unanswered Questions and Discomfort
    8. 05:25 Psychological Discomfort in Brain Organoids
    9. 06:21 Early Videos and Brain Organoid Learning
    10. 07:20 Efficiency of Human Neural Networks
    11. 08:12 Sleep in Brain Organoids
    12. 09:13 Delta Brainwaves and Brain Organoids
    13. 10:11 Creating Brain Organoids with Specific Components
    14. 11:10 Genetic Memories in Brain Organoids
    15. 12:07 Efficiency and Learning in Human Brains
    16. 13:00 Sequential Memory and Chimpanzees
    17. 14:18 Different Thinking Skill Sets and Collaboration
    18. 16:13 ADHD and Hyperfocusing
    19. 18:01 Ethical Considerations in Brain Research
    20. 19:23 Understanding Genetic Mutations
    21. 20:51 Brain Organoids in Rat Bodies
    22. 22:14 Dendrite Growth in Brain Organoids
    23. 23:11 Duration of Dendrite Growth
    24. 24:26 Genetic Memory Transfer in Brain Organoids
    25. 25:19 Social Media Presence of Brain Organoid Companies
    26. 26:15 Brain Organoids Controlling Robot Spiders
    27. 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)

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

    Help Support The Podcast by clicking on the links below:

    • Start YOUR podcast on ZenCastr! Use my special link ZenCastr Discount to save 30% off your first month of any Zencastr paid plan
    • Visit our Patreon

    Summary:

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

    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.

    Help Support The Podcast by clicking on the links below:

    • Try out ZenCastr: Use my special link ZenCastr Discount to save 30% off your first month of any Zencastr paid plan
    • Patreon Link: All content is available commercial free on patreon
    • YouTube Channel: Enjoy this content? subscribe to our YouTube Channel
    OpenAi SORA, Physics-Informed ML, and a.i. Fraud- Oh My! Feb 20, 2024
    Show notes

    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

    Help Support The Podcast by clicking on the links below:

    • Start YOUR podcast on ZenCastr! Use my special link ZenCastr Discount to save 30% off your first month of any Zencastr paid plan
    • Visit our Patreon

    Contact us at breakingmathpodcast@gmail.com

    Summary

    #OpenAiSora #

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

    Help Support The Podcast by clicking on the links below:

    • Try out ZenCastr w/ 30% Discount Use my special link to save 30% off your first month of any Zencastr paid plan
    • Patreon
    • YouTube

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

    Follow us on X (Twitter)

    Follow us on Social Media Pages (Linktree)

    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

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