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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

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    Copyright: © Copyright Breaking Math

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    Latest Episodes:
    Why Mathematicians Must Speak Up with Bryna Kra Mar 03, 2026
    Show notes

    In this conversation, Dr. Bryna Kra discusses her journey in mathematics, focusing on her research, dynamical systems, the importance of collaboration, and the role of the American Mathematical Society. She emphasizes the need for better communication within the mathematics community and the challenges it faces, particularly regarding diversity and inclusion. Bryna shares her experiences in mentoring women in mathematics and reflects on her career achievements while looking forward to future contributions in the field.

    Takeaways

    Mathematics is a dynamic field that evolves over time.

    Explaining the applications of mathematical research is essential.

    Collaboration often starts in unexpected places.

    Dynamical systems connect seemingly unrelated mathematical fields.

    The AMS plays a crucial role in supporting mathematicians.

    Communication is key to addressing challenges in the mathematics community.

    Women in mathematics need more support and mentorship.

    Creating pathways for underrepresented groups is vital.

    Asking for help can lead to significant changes in academia.

    Reflecting on one's career can inspire future generations.

    Chapters

    00:00 Introduction to Dynamical Systems

    01:33 The Intersection of Number Theory and Dynamical Systems

    03:23 Communicating Abstract Mathematics

    05:21 The Evolution of Mathematical Fields

    07:09 Quirky Anecdotes in Mathematics

    09:49 Leading the American Mathematical Society

    15:01 Challenges Facing the Mathematics Community

    18:08 Roles in the National Mathematics Community

    21:11 Women in Mathematics and Mentorship

    27:02 Reflections on a Successful Career

    Bryna does not have social media, but you can email us to contact her,

    Follow Noah on Instagram, Twitter, Bluesky

    Follow Breaking Math on Substack, Patreon, Twitter, Instagram, Website, YouTube, TikTok

    Follow Autumn on Twitter, BlueSky, Instagram, Substack

    Become a guest here


    Reaching for the Extreme with Ian Stewart Feb 24, 2026
    Show notes

    In this conversation, Ian Stewart discusses the nature of mathematical inquiry, the motivations behind problem-solving in mathematics, and the importance of storytelling in making math relatable. He explores the relationship between nature and mathematics, emphasizing how patterns in nature inspire mathematical concepts. Stewart also addresses the role of AI in mathematical discovery and the importance of choosing meaningful problems to work on. He concludes by highlighting the vital role of mathematics in society and its significant contributions to the economy.

    Takeaways

    -Mathematics is driven by curiosity and the desire to solve problems

    -Nature serves as a significant source of inspiration for mathematical ideas.

    -Mathematicians often seek deeper understanding beyond just solving problems.

    -AI can be a powerful tool in mathematical discovery, but it raises questions about understanding

    -Choosing problems that interest you is crucial for success in mathematics.

    -Mathematics has a profound impact on various industries and the economy.

    Chapters

    00:00 The Origins of Mathematical Problems

    06:12 Breaking Down Complex Problems

    09:57 The Beauty of Mathematical Proofs

    15:21 The Role of Storytelling in Mathematics

    20:10 Nature as Inspiration for Mathematics

    24:30 The Pursuit of Mathematical Extremes

    27:00 The Complexity of the Four Color Theorem Proof

    28:38 The Impact of Computer-Aided Proofs on Understanding

    31:21 The Quest for Deeper Mathematical Insights

    32:11 AI and the Evolving Boundaries of Mathematics

    34:35 The Dilemma of Solving Without Understanding

    38:49 Guiding the Next Generation of Mathematicians

    You can purchase Ian Stewart’s book here.

    Follow Noah on Instagram, LinkedIn, Twitter, Bluesky

    Follow Breaking Math on Substack, Patreon, Twitter, Instagram, Website, YouTube, TikTok

    Follow Autumn on Twitter, BlueSky, Instagram, Substack

    Become a guest here

    email: breakingmathpodcast@gmail.com


    Rethinking Mathematical Value in the Age of AI with Ravi Vakil Feb 17, 2026
    Show notes

    In this conversation, Ravi Vakil discusses the beauty of mathematics, the impact of AI on the field, and the importance of human interaction in mathematical education. He emphasizes the social nature of mathematics and the potential dangers of AI-generated content flooding the mathematical community. The discussion also touches on the future of education, the role of leadership in mathematics, and the balance between mathematics and other disciplines. Throughout, Vakil encourages aspiring mathematicians to embrace the beauty and interconnectedness of the subject.

    Takeaways

    • Mathematics is fundamentally about curiosity and connection.
    • The beauty of mathematics can be shared and experienced collectively.
    • AI poses both opportunities and challenges for the field of mathematics.
    • Mathematics thrives on social interaction and collaboration.
    • The influx of AI-generated content may dilute the quality of mathematical research.
    • Education in mathematics requires human interaction and cannot be fully replaced by technology.
    • Leadership in mathematics should focus on long-term investments in education.

    Chapters

    00:00 Introduction and Setting the Stage

    01:11 The Beauty of Mathematics

    03:57 The Intersection of Mathematics and Technology

    05:41 AI's Role in Mathematics

    07:36 Emerging Mathematical Ideas in the Age of AI

    09:12 Community Dynamics in Mathematics

    13:32 Challenges of AI in Academic Publishing

    17:08 The Future of Writing and Learning in Mathematics

    19:42 The Value of Human Interaction in Education

    22:33 The Future of Mathematics and AI

    30:15 Leadership in Mathematics and Education

    35:47 Balancing Mathematics with Liberal Arts

    39:48 Encouragement for Aspiring Mathematicians

    Follow Noah on Instagram, Twitter, Bluesky

    Follow Breaking Math on Substack, Twitter, Instagram, Website, YouTube, TikTok

    Follow Autumn on Twitter, BlueSky, Instagram, Substack

    Become a guest here

    email: breakingmathpodcast@gmail.com


    AI, Pi, Dynamic Pricing, and Math History Lessons Feb 10, 2026
    Show notes

    Summary

    In this episode, Autumn and Noah explore the intersection of AI and mathematics, discussing why AI struggles with math, the differences between calculus and algebra, and the historical contributions of women in mathematics. They delve into the concept of infinity, the significance of pi, and the implications of dynamic pricing in today's economy. The conversation highlights the importance of understanding mathematical tools and the ethical considerations surrounding personalized pricing.

    Takeaways

    AI is not monolithic; it has varying capabilities.

    The difference between calculus and algebra lies in their focus on relationships and change.

    Infinity is a concept that exists in mathematics but not necessarily in the physical world.

    Pi is fundamental in understanding circular motion and symmetry.

    Dynamic pricing is a modern phenomenon influenced by technology and data.

    Choosing the right mathematical tool is crucial for problem-solving.

    Personalized pricing raises ethical questions about fairness and transparency.

    Chapters

    00:00 Introduction and Overview

    00:22 AI and Mathematics: The Dual Nature

    03:25 Understanding Calculus vs. Algebra

    07:40 Historical Perspectives: Women in Mathematics

    13:11 The Concept of Infinity in Mathematics

    16:55 The Origins of Pi

    21:33 Dynamic Pricing and Its Implications

    Follow Noah on Instagram, Twitter, Bluesky

    Follow Breaking Math on Substack, Patreon, Twitter, Instagram, LinkedIn, Website, YouTube, TikTok

    Follow Autumn on Twitter, BlueSky, Instagram, Substack

    Become a guest here

    email: breakingmathpodcast@gmail.com


    A New Chapter of Breaking Math: Get to Know Your Hosts Feb 03, 2026
    Show notes

    In this episode, Autumn and Noah celebrate the ninth anniversary of the Breaking Math podcast, reflecting on its journey and growth. They introduce Noah Giansiracusa as the new co-host and discuss the importance of engaging with the audience, storytelling in math, and the interdisciplinary nature of the topics they plan to cover. The conversation also touches on personal experiences, defining success in podcasting, and the dynamics of co-hosting, all while embracing their nerdy sides and fostering curiosity in their listeners.

    Takeaways

    • Noah is introduced as the new co-host.
    • Engagement with the audience is a priority.
    • Storytelling is crucial in teaching math.
    • Math communication can impact people's understanding of their lives.
    • Success is defined by personal fulfillment, not just metrics.
    • The hosts aim to humanize math and its applications.
    • Embracing nerdiness fosters a relatable and engaging atmosphere.

    Chapters

    01:55 Welcoming Noah as Co-Host

    05:37 Engaging with the Audience

    07:26 Expanding the Narrative and Storytelling

    09:34 The Power Dynamic in Education

    11:18 The Importance of Storytelling in Math

    13:44 Communicating Math Beyond the Classroom

    15:33 Interdisciplinary Approach to Math

    17:40 Future Topics and Directions

    20:37 Personal Insights and Fun Facts

    25:32 Defining Success in the Podcasting World

    30:13 Personal Reflections on Success

    36:19 Embracing Nerdiness and Authenticity

    Follow Noah on Instagram, LinkedIn, Twitter, Bluesky Follow Breaking Math on Substack, Patreon, Twitter, Instagram, LinkedIn, Website, YouTube, TikTok

    Follow Autumn on Twitter, BlueSky, Instagram, LinkedIn, Substack

    Become a guest here

    email: breakingmathpodcast@gmail.com


    The Elements of Power: Supply Chains, Technology, and Energy with Nicolas Niarchos Jan 21, 2026
    Show notes

    In this episode of Breaking Math, Autumn and Nicolas Niarchos critique the "green" narrative of lithium-ion technology. Tracing the industry from its 1991 commercialization to modern geopolitical tensions, the hosts expose the exploitation and environmental degradation inherent in global mining, particularly in the Democratic Republic of the Congo. By challenging the presumed sustainability of electric vehicles, they emphasize the need for supply chain transparency and urge listeners to adopt a more informed, ethically-conscious approach to modern consumption.

    Takeaways

    • What does it really cost to power the future?
    • The bargain as stated is clean energy in one part and at the other end, you have corruption, pollution, and human suffering.
    • The greenest vehicle is not always the electric one; it depends on the entire lifecycle of the product.
    • We need to improve conditions on the ground, not just extract resources.
    • Corruption is unfortunately a fact of life and is very closely related to extraction.

    Chapters

    • 00:00 Introduction and Background
    • 03:24 The Journey to Congo and Corruption
    • 07:13 The Birth of Lithium-Ion Batteries
    • 09:35 The Uneven Global Bargain
    • 12:16 Mining vs. Oil: A Different Kind of Harm
    • 13:56 Onshoring Battery Production: Challenges and Opportunities
    • 17:13 China's Dominance in Battery Manufacturing
    • 18:51 The Race in Battery Technology
    • 21:39 Corruption and Poverty in the Congo
    • 24:31 The Human Cost of Mining
    • 29:12 Health Impacts of Mining
    • 31:52 Colonial Legacy and Modern Mining
    • 34:00 The Future of Battery Technology
    • 39:12 Introduction to Complex Narratives
    • 39:53 The Reality of Resource Extraction
    • 39:59 Embracing Curiosity and Reflection

    Follow Nick on Twitter, and you can get his book here.

    Subscribe to Breaking Math wherever you get your podcasts.

    Follow Breaking Math on Twitter, Instagram, LinkedIn, Website, YouTube, TikTok

    Follow Autumn on Twitter, BlueSky, and Instagram

    Become a guest here

    email: breakingmathpodcast@gmail.com


    The Score: Gamifying the Nature of Metrics with Thi Nguyen Jan 14, 2026
    Show notes

    In this conversation, the discussion with C. Thi Nguyen revolves around the nature of metrics, qualitative knowledge, and the duality of scoring systems, particularly in the context of climbing. The speaker shares personal experiences with climbing as a case study to illustrate how scoring systems can both enhance and detract from the experience. The conversation delves into the beauty of climbing, the subtlety of value in metrics, and the importance of savoring moments in games. It also explores the tension between purpose and game mechanics, the role of enjoyment, and the complexities of scoring systems in both games and life. Ultimately, the conversation highlights the challenges of balancing values in decision-making and the risks associated with the gamification of various aspects of life.

    Takeaways

    • Metrics can miss the subtlety of qualitative knowledge.
    • Scoring systems can enhance or detract from experiences.
    • Climbing serves as a unique case study for scoring systems.
    • The beauty of climbing lies in its scoring system.
    • Values can become obscured when metrics are prioritized.
    • Games allow for exploration of different scoring systems.
    • Achievement play focuses on winning, while striving play values the process.
    • External expectations can pressure individuals to conform to metrics.
    • The addictive nature of games can lead to negative experiences.

    Chapters

    • 00:00 The Intricacies of Portability and Judgment
    • 01:12 Introduction and Social Media Presence
    • 03:40 The Value of Climbing and Scoring Systems
    • 07:16 The Impact of Numbers in Climbing
    • 09:42 Savoring the Moment vs. Obsession with Scoring
    • 10:59 Goals vs. Purpose in Games
    • 12:39 Understanding Value Capture
    • 17:53 The Shift in Standards of Success
    • 20:33 The Limitations of Metrics
    • 21:42 Games as a Reflection of Human Desire
    • 24:37 The Purpose Behind Scoring Systems
    • 26:07 The Magic Circle of Games
    • 29:15 Achievement Play vs. Striving Play
    • 34:47 When Games Become Unsafe
    • 38:21 The Pitfalls of Portability in Metrics

    Follow Thi on Twitter, Bluesky, and find his website. You can get his book here.

    Subscribe to Breaking Math wherever you get your podcasts.

    Follow Breaking Math on Twitter, Instagram, LinkedIn, Website, YouTube, TikTok

    Follow Autumn on Twitter, BlueSky, and Instagram

    Become a guest here

    email: breakingmathpodcast@gmail.com


    The Art of Physics: Bridging Science and Creativity with Ronald Gamble Jan 13, 2026
    Show notes

    This conversation explores the fascinating intersection of math, physics, and art, highlighting how these disciplines inform and inspire one another. Dr. Ronald Gamble discusses his journey as a theoretical physicist and artist, emphasizing the importance of recognizing patterns in nature and the role of creativity in scientific discovery. The dialogue delves into various topics, including the significance of symmetry in physics, the visualization of complex concepts like black holes and gravitational waves, and the influence of mathematical principles on artistic expression. Ultimately, the conversation underscores the idea that art and science are deeply interconnected, each enhancing the understanding and appreciation of the other.

    Takeaways

    • Inspiration is pattern recognition.
    • Math serves as a language to describe physics.
    • Art and physics both seek to decode patterns in the universe.
    • Studying nature can enhance understanding of physics concepts.
    • Creativity is essential in theoretical physics.
    • Symmetry plays a crucial role in understanding the universe.
    • Art can influence scientific thought and vice versa.

    Chapters

    • 00:00 The Intersection of Math, Physics, and Art
    • 03:57 Finding Inspiration in Nature
    • 06:16 The Art of Storytelling in Physics
    • 08:31 Patterns in Nature and Art
    • 10:13 The Influence of Physics on Art
    • 12:23 Understanding Symmetry in Physics
    • 16:46 Exploring Black Holes and Particle Physics
    • 21:03 The Role of Tessellations in Physics
    • 25:24 Celebrating Scientific Collaborations
    • 27:24 The Art of Tessellation and Structure
    • 29:06 The Power of Minimalism in Art and Science
    • 31:05 Exploring Black Holes and Gravitational Waves
    • 38:59 The Artistic Journey into Physics Course

    Follow Ron on Twitter, LinkedIn, Instagram, Bluesky, and find his website.

    Subscribe to Breaking Math wherever you get your podcasts.

    Follow Breaking Math on Twitter, Instagram, LinkedIn, Website, YouTube, TikTok

    Follow Autumn on Twitter, BlueSky, and Instagram

    Become a guest here

    email: breakingmathpodcast@gmail.com


    Intelligent Systems: Digital Culture Shock Nov 19, 2025
    Show notes

    In this conversation, Dr. Katharina Reinecke explores the intersection of technology and culture, discussing how cultural assumptions shape the design and functionality of technology. She delves into the implications of self-driving cars, the importance of understanding diverse user experiences, and the challenges posed by a predominantly Western perspective in technology development. The discussion highlights the need for greater cultural sensitivity in technology design and the potential consequences of ignoring these differences.

    Takeaways

    • Technology is not culturally neutral; it reflects the values of its creators.
    • Self-driving cars are based on American commuting assumptions.
    • Cultural differences significantly impact user experience and technology design.
    • Efficiency in technology can undermine social interactions and relationships.
    • WEIRD populations dominate technology research, leading to biased outcomes.
    • Universal design principles often fail when applied globally.
    • Stack Exchange exemplifies individualistic design, contrasting with collectivist values.
    • AI systems must be designed with cultural sensitivity to avoid reinforcing biases.

    Chapters

    • 00:00 Understanding Digital Culture Shock
    • 03:53 The Challenges of Autonomous Vehicles
    • 06:21 Cultural Assumptions in Technology
    • 08:37 The Impact of AI and Data Bias
    • 10:32 Efficiency vs. Social Interaction in Design
    • 12:14 The Concept of 'Weird' Populations
    • 14:24 Cultural Values in Digital Platforms
    • 21:53 The Simplicity of Design and Its Cultural Impact
    • 22:51 Efficiency vs. Community: The Stack Exchange Debate
    • 25:41 Adapting Global Platforms to Local Norms
    • 31:52 The Implications of AI and Digital Infrastructure
    • 34:34 Recognizing Cultural Bias in Technology Design
    • 37:42 Technology as Culture

    Follow Katharina on Twitter, LinkedIn, Bluesky, and find her new book here.

    You can find Lab in the Wild on Twitter and Bluesky

    Subscribe to Breaking Math wherever you get your podcasts.

    Follow Breaking Math on Twitter, Instagram, LinkedIn, Website, YouTube, TikTok

    Follow Autumn on Twitter, BlueSky, and Instagram

    Become a guest here

    email: breakingmathpodcast@gmail.com


    Who is Francis Crick? Nov 11, 2025
    Show notes

    This conversation delves into the life and legacy of Francis Crick, co-discoverer of the DNA structure. Dr. Matthew Cobb, the guest, explores Crick's multifaceted personality, his poetic inspirations, collaborative nature, and his later pursuits in consciousness. The discussion also touches on the controversies surrounding his work, particularly regarding the contributions of Rosalind Franklin, and reflects on Crick's complex character, blending modern scientific thought with outdated socio-political ideas.

    Takeaways

    • Crick's story is often simplified to his DNA discovery.
    • He had a deep appreciation for poetry and its connection to science.
    • Collaboration was a key aspect of Crick's success.
    • His early life was marked by average academic performance.
    • Crick's transition to biology was driven by a desire to understand life.
    • The discovery of DNA was a complex, collaborative effort.
    • Controversies exist regarding the ethics of scientific discovery.
    • Crick's later work focused on the nature of consciousness.
    • He had a unique blend of intuition and logical thinking.
    • Crick's outdated socio-political views contrast with his scientific modernity.

    Chapters

    • 00:00 The Legacy of Francis Crick
    • 01:13 Introduction to Matthew Cobb and His Book
    • 03:43 The Influence of Francis Crick
    • 06:19 Crick's Unique Approach to Science
    • 07:19 Crick's Early Life and Self-Perception
    • 10:04 The Impact of Naval Service on Crick
    • 12:34 Crick's Transition to Biology
    • 15:06 The Role of Schrodinger's Work
    • 17:26 The Dynamic Between Watson and Crick
    • 20:13 The Discovery of the Double Helix
    • 23:02 The Controversy of Rosalind Franklin's Contribution
    • 28:23 The Diplomatic Row and Pauling's Mistake
    • 29:38 The Discovery of DNA's Structure
    • 34:31 Crick and Brenner's Collaboration
    • 38:41 Crick's Exploration of Consciousness
    • 43:03 Crick's Complex Legacy

    Follow Matthew on Twitter, and find his new book here.

    Subscribe to Breaking Math wherever you get your podcasts.

    Follow Breaking Math on Twitter, Instagram, LinkedIn, Website, YouTube, TikTok

    Follow Autumn on Twitter, BlueSky, and Instagram

    Become a guest here

    email: breakingmathpodcast@gmail.com


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