Breaking Math Podcast

This episode explores how AI, specifically OpenAI's recent breakthrough in solving an 80-year-old math conjecture, is transforming the field of mathematics. Featuring insights from Professor Daniel Litt, the discussion covers the implications of AI in mathematical research, the value of human verification, and the future of mathematical practice. Key topics AI solving long-standing mathematical problems The role of human verification in AI-generated proofs Implications of AI breakthroughs in discrete geometry The future of mathematical research with AI Number theory and algebraic constructions in AI discoveries Chapters 00:00 Introduction to the Conjecture and Its Significance 01:15 Understanding the Erdős Problem 04:34 The Role of AI in Solving Mathematical Problems 09:17 The Implications of AI in Mathematics 10:32 AI vs Human Mathematicians: A Comparative Analysis 17:20 Standards for AI-Generated Proofs 21:10 Corporate Interests in Mathematical Research 24:42 The Future of Mathematics and AI 27:50 Final Thoughts on AI and Mathematics 31:37 Revolutionizing Mathematics: AI's Breakthrough in Discrete Geometry 37:37 Exploring the Implications: AI and the Future of Mathematics 38:03 The Role of AI in Mathematics 39:23 Human Value in the Age of AI Follow Daniel Litt on X (https://x.com/maiasz) Website (https://daniellitt.com) Follow Breaking Math on Substack (https://breakingmath.substack.com/) X (https://x.com/breakingmathpod) Instagram (https://www.instagram.com/breakingmathmedia/) Bluesky (https://bsky.app/profile/breakingmath.bsky.social) Website (https://www.breakingmath.io/) YouTube (https://www.youtube.com/@BreakingMathPod) Follow Noah on Instagram (https://www.instagram.com/profnoahgian/) X (https://x.com/ProfNoahGian) Bluesky (https://bsky.app/profile/profnoahgian.bsky.social) Follow Autumn on X (https://x.com/1autumn_leaf) Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social) Instagram (https://www.instagram.com/1autumnleaf/) Substack (https://substack.com/@1autumnleaf) email: breakingmathpodcast@gmail.com

In this episode with award-winning journalist and author Maia Szalavitz challenges the idea that addiction is simply about pleasure or willpower. Instead, she explains addiction as compulsive behavior that continues despite negative consequences — and shows why withdrawal, dependence, and addiction are not the same thing. The conversation explores “wanting” versus “liking,” why dopamine is misunderstood, how social media and AI can exploit reward systems, and why punishment often fails. Ultimately, Szalavitz argues that recovery depends less on tough love and more on connection, purpose, safety, and care. Chapters 00:00 Understanding Addiction: Definitions and Mechanisms 10:43 The Role of Dopamine in Addiction 14:18 Addiction as a Learning Disorder 16:22 Substance vs. Experience: The Nature of Addiction 20:13 Evidence-Based Methods for Overcoming Addiction 25:20 Finding Meaning and Purpose Beyond Addiction 33:30 The Pursuit of Meaningful Experiences 34:15 Understanding Dopamine and Pleasure 39:10 The Complexity of Addiction 43:00 Social Media and Addiction Dynamics 50:42 Generational Perspectives on Technology and Addiction 57:53 Lessons Learned in Addiction Science 01:02:03 Rethinking Addiction: A New Perspective 01:03:54 The Compulsive Nature of Addiction 01:04:14 Understanding Addiction Beyond Pleasure 01:05:27 The Importance of Connection and Compassion Follow Maia Szalavitz on X (https://x.com/maiasz) Follow Breaking Math on Substack (https://breakingmath.substack.com/) X (https://x.com/breakingmathpod) Instagram (https://www.instagram.com/breakingmathmedia/) Bluesky (https://bsky.app/profile/breakingmath.bsky.social) Website (https://www.breakingmath.io/) YouTube (https://www.youtube.com/@BreakingMathPod) Follow Noah on Instagram (https://www.instagram.com/profnoahgian/) X (https://x.com/ProfNoahGian) Bluesky (https://bsky.app/profile/profnoahgian.bsky.social) Follow Autumn on X (https://x.com/1autumn_leaf) Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social) Instagram (https://www.instagram.com/1autumnleaf/) Substack (https://substack.com/@1autumnleaf) email: breakingmathpodcast@gmail.com

In this episode of Breaking Math, Autumn and Noah speak with Ron Wasserstein, Executive Director of the American Statistical Association, about what statistics means in a world increasingly shaped by AI, misinformation, and fragile public trust. Wasserstein argues that statistics is not merely a “bag of tools,” but a way of thinking: asking where data comes from, what it leaves out, how uncertainty should be communicated, and when numbers are being used to illuminate rather than manipulate. Chapters 00:00 The Golden Age of Statistics 02:36 AI's Impact on Statistics 08:16 Data as Fuel for AI 10:55 Bias in AI and Statistics 14:01 Preparing Future Statisticians 16:58 Bridging the Gap: Academia and Industry 22:58 The Misconception of Statistics 23:08 The Role of Statistics in Public Discourse 26:20 The American Statistical Association's Mission 32:18 Statistics and Politics: A Historical Perspective 36:02 Addressing Misinformation and Misuse of Data 39:51 The Importance of Statistical Literacy 44:01 Misconceptions About Statistics and Expertise 46:57 The Essence of Statistics 47:22 Statistics as a Way of Thinking Follow Ron Wasserstein LinkedIn (https://www.linkedin.com/in/ron-wasserstein/) Follow Breaking Math on Substack (https://breakingmath.substack.com/) Twitter (https://x.com/breakingmathpod) Instagram (https://www.instagram.com/breakingmathmedia/) Bluesky (https://bsky.app/profile/breakingmath.bsky.social) Website (https://www.breakingmath.io/) YouTube (https://www.youtube.com/@BreakingMathPod) Follow Noah on Instagram (https://www.instagram.com/profnoahgian/) Twitter (https://x.com/ProfNoahGian) Bluesky (https://bsky.app/profile/profnoahgian.bsky.social) Follow Autumn on Twitter (https://x.com/1autumn_leaf) Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social) Instagram (https://www.instagram.com/1autumnleaf/) Substack (https://substack.com/@1autumnleaf) email: breakingmathpodcast@gmail.com

What if ransomware did not begin with criminals, but with curiosity? In this episode of Breaking Math, Autumn and Noah talk with Anja Shortland, professor of political economy at King’s College London and author of Dark Screens. This conversation explores how playful hacking evolved into professionalized cybercrime, why ransomware gangs operate like morally questionable internet startups, how cryptocurrency made ransomware scalable, and why hospitals, governments, universities, and critical infrastructure remain especially vulnerable. We also dig into the mathematics behind encryption, asymmetric cryptography, game theory, negotiation, cyber insurance, and the uncomfortable trade-offs between freedom, privacy, and regulation. Chapters 00:00 The origins of ransomware and early hacker culture 02:13 The evolution of ransomware attacks since 2013 03:14 The paradox of cybercriminals as entrepreneurs 06:19 Early hackers: Steve Jobs and Wozniak as pioneers 12:34 The moral and legal landscape of hacking and cybercrime 13:39 The importance of cybersecurity awareness for individuals 15:03 The arms race: attackers vs defenders and the role of math 16:02 The technological innovations behind ransomware 19:21 Asymmetric encryption and cryptocurrency in ransomware 20:53 Bitcoin and the dark web: enabling cybercrime 22:45 The impact of AI on future cyber threats and defenses 34:07 The future of ransomware and cybersecurity challenges Follow Anja Shortland on LinkedIn (https://uk.linkedin.com/in/anja-shortland-53133b231) Book (https://amzn.to/4d6pB4X) Follow Breaking Math on Substack (https://breakingmath.substack.com/) Twitter (https://x.com/breakingmathpod) X (https://www.instagram.com/breakingmathmedia/) Bluesky (https://bsky.app/profile/breakingmath.bsky.social) Website (https://www.breakingmath.io/) Follow Noah on Instagram (https://www.instagram.com/profnoahgian/) Twitter (https://x.com/ProfNoahGian) Bluesky (https://bsky.app/profile/profnoahgian.bsky.social) Follow Autumn on X (https://x.com/1autumn_leaf) Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social) Instagram (https://www.instagram.com/1autumnleaf/) Substack (https://substack.com/@1autumnleaf) email: breakingmathpodcast@gmail.com

What does it actually mean for a number to be “big”? In this episode of Breaking Math, Autumn chats with mathematician Richard Elwes to explore how huge numbers reveal the limits of human intuition, language, and even mathematics itself. The discussion moves from exponential growth in pandemics and finance to numbers larger than the universe itself, emerging in games like chess and abstract possibility spaces. Finally, it reaches one of the most profound ideas in modern mathematics: that there are true statements about numbers that can never be proven. This episode challenges how we think about scale, complexity, and the systems we rely on to make sense of reality. Key Topics Limits of ancient numeral systems like Roman numerals Mathematical logic and the concept of huge numbers Evolution of number notation from Roman to Hindu-Arabic systems The significance of place value in expressing large numbers The Mayan long count and its implications for understanding time scales Chapters 00:00 Introduction and Inspiration for the Book 01:39 Redefining Big Numbers 01:55 Limits of Numerical Systems 05:33 Evolution of Number Sense 10:02 Language and Numerical Understanding 11:53 Cultural Influences on Numerical Systems 14:18 Hacks in Ancient Number Systems 16:55 Archimedes and the Concept of Infinity 22:01 The Importance of Place Value 25:45 Mayan Cosmology and Time Scales 31:55 Exponential Growth and Its Dangers 32:20 Understanding Exponential Growth 36:14 The Dangers of Exponential Growth 37:23 Limits of Exponential Growth in the Physical World 39:42 Exploring Possibility Space 45:38 Goodstein's Theorem and Mathematical Logic Connect with Breaking Math Follow Richard Elwes on X (https://x.com/RichardElwes/ ) Instagram (https://www.instagram.com/richardelwes/) His Book(https://amzn.to/48rk5s9) Follow Breaking Math on Substack (https://breakingmath.substack.com/) Twitter (https://x.com/breakingmathpod) X (https://www.instagram.com/breakingmathmedia/) Bluesky (https://bsky.app/profile/breakingmath.bsky.social) Website (https://www.breakingmath.io/) Follow Autumn on X (https://x.com/1autumn_leaf) Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social) Instagram (https://www.instagram.com/1autumnleaf/) Substack (https://substack.com/@1autumnleaf) email: breakingmathpodcast@gmail.com

In this episode we sit down with Sheamus McGovern, founder of the Open Data Science Conference (ODSC AI), to unpack what AI actually looks like. Sheamus shares what’s really happening behind the scenes of the AI boom and why the biggest shift isn’t job loss, but a complete transformation of skills. From explaining why AI is reshaping—not replacing—jobs, to breaking down the gap between hype and real-world applications, this conversation explores how early algorithmic trading foreshadowed today’s AI revolution, why open-source tools like TensorFlow and PyTorch changed everything, what the “AI Skill Flip” means for your career, and why even data scientists are questioning their future. Along the way, the biggest mistake people make when trying to learn AI, and why the smartest approach isn’t to learn everything—but to start intentionally and build from there. Timestamps 00:00 – The biggest misconception about AI 02:00 – Algorithmic trading and the origins of AI in finance 05:00 – The birth of ODSC AI and the data science movement 09:30 – Breakthrough moments in AI 16:30 – Democratization of AI and open-source tools 19:00 –The AI Skill Flip 24:00 – The truth about AI replacing jobs 27:00 – Real-world AI success stories 32:30 – How to actually start learning AI today Follow Sheamus McGovern on LinkedIn (https://www.linkedin.com/in/sheamus/) ODSC Website (https://odsc.ai/) Follow Breaking Math on Substack (https://breakingmath.substack.com/) Twitter (https://x.com/breakingmathpod) Instagram (https://www.instagram.com/breakingmathmedia/) Bluesky (https://bsky.app/profile/breakingmath.bsky.social) Website (https://www.breakingmath.io/) YouTube (https://www.youtube.com/@BreakingMathPod) Follow Noah on Instagram (https://www.instagram.com/profnoahgian/) Twitter (https://x.com/ProfNoahGian) Bluesky (https://bsky.app/profile/profnoahgian.bsky.social) Follow Autumn on Twitter (https://x.com/1autumn_leaf) Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social) Instagram (https://www.instagram.com/1autumnleaf/) Substack (https://substack.com/@1autumnleaf) email: breakingmathpodcast@gmail.com

In this episode, mathematician and award-winning magician Matt Baker explores the fascinating intersection of mathematics and magic, revealing how mathematical principles, intuition, and storytelling create unforgettable illusions. From a mind-reading trick based on the classic concept of “casting out nines” to his groundbreaking research on the Riemann–Roch theorem for graphs, Baker demonstrates how creativity and pattern recognition drive both mathematical discovery and magical performance. Chapters 00:00 The Interplay of Math and Magic 04:58 Aesthetic Connections in Math and Magic 08:57 Balancing Family, Math, and Magic 12:34 The Impact of Magic on Mathematical Thinking 16:32 The Art of Clarity in Communication 16:44 A Live Magic Demonstration 25:14 Intuition and Pattern Recognition in Math 30:03 The Riemann-Roch Theorem for Graphs 41:42 The Role of AI in Mathematics and Magic 50:21 The Art of Communicating Mathematics 50:47 The Magic of Math and Performance Follow Matt Baker on Facebook (https://www.facebook.com/mbakermath) Academic (https://sites.google.com/view/mattbakermath/home/) Magic (http://mattbakermagic.com/) Follow Breaking Math on Substack (https://breakingmath.substack.com/) Twitter (https://x.com/breakingmathpod) Instagram (https://www.instagram.com/breakingmathmedia/) Bluesky (https://bsky.app/profile/breakingmath.bsky.social) Website (https://www.breakingmath.io/) YouTube (https://www.youtube.com/@BreakingMathPod) Follow Noah on Instagram (https://www.instagram.com/profnoahgian/) Twitter (https://x.com/ProfNoahGian) Bluesky (https://bsky.app/profile/profnoahgian.bsky.social) Follow Autumn on Twitter (https://x.com/1autumn_leaf) Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social) Instagram (https://www.instagram.com/1autumnleaf/) Substack (https://substack.com/@1autumnleaf) email: breakingmathpodcast@gmail.com

In this episode, Thomas Plümper and Eric Neumayer explore the hidden challenges in modern science, from outright fraud to the subtler practice of “tweaking” data that distorts results. They examine why the self-correcting nature of science often falls short, how incentives and academic pressure drive misconduct, and the double-edged role of AI in both enabling and detecting fraud. The conversation also tackles debates around p-values and statistical reasoning, shares cautionary case studies, and proposes solutions like greater data transparency and stronger verification standards. Chapters 00:00 Introduction to Fraud in Research 06:21 The Nature of Fraud Detection 08:56 Incentives and Motivations for Fraud 10:43 Self-Correction in Science 12:13 Understanding Statistical Significance 13:04 The Role of Replication in Research 14:32 Bayesian vs Frequentist Approaches 23:09 Understanding Bayesian Statistics and Its Implications 26:24 The Humility of Empirical Science 27:16 Concrete Examples of Scientific Fraud 32:52 Proposed Solutions to Scientific Fraud 34:50 The Reality of Scientific Fraud and Human Nature Guest Links You can purchase their book here (https://amzn.to/3Ole3lY) Follow Eric Neumayer on LinkedIn - (https://linkedin.com/in/ericneumayer) Follow Breaking Math on Substack (https://breakingmath.substack.com/) Twitter (https://x.com/breakingmathpod) Instagram (https://www.instagram.com/breakingmathmedia/) Bluesky (https://bsky.app/profile/breakingmath.bsky.social) Website (https://www.breakingmath.io/) YouTube (https://www.youtube.com/@BreakingMathPod) Follow Noah on Instagram (https://www.instagram.com/profnoahgian/) Twitter (https://x.com/ProfNoahGian) Bluesky (https://bsky.app/profile/profnoahgian.bsky.social) Follow Autumn on Twitter (https://x.com/1autumn_leaf) Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social) Instagram (https://www.instagram.com/1autumnleaf/) Substack (https://substack.com/@1autumnleaf) email: breakingmathpodcast@gmail.com

This Women in History Mini-Series episode with Dr. Victoria Bateman explores the inspiring story of Mary T. Washington Wiley, the first African-American woman CPA, her challenges, achievements, and legacy in breaking racial and gender barriers in the early 20th century. Mathematics is supposed to be objective—but access to it has never been equal. Chapters 00:00 Introduction to Mary T. Washington Wiley 00:48 Early Life and Challenges 02:58 Breaking Barriers in Accountancy 05:25 Pioneering a Path for Others 07:21 Legacy and Impact Follow Breaking Math on Substack (https://breakingmath.substack.com/) Twitter (https://x.com/breakingmathpod) Instagram (https://www.instagram.com/breakingmathmedia/) Bluesky (https://bsky.app/profile/breakingmath.bsky.social) Website (https://www.breakingmath.io/) YouTube (https://www.youtube.com/@BreakingMathPod) Follow Victoria on Website (http://www.vnbateman.com/) Instagram (https://www.instagram.com/women.wealth.power/) Twitter (https://x.com/vnbateman) Bluesky (https://bsky.app/profile/vnbateman.bsky.social) Follow Autumn on Twitter (https://x.com/1autumn_leaf) Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social) Instagram (https://www.instagram.com/1autumnleaf/) Substack (https://substack.com/@1autumnleaf) TikTok (https://www.tiktok.com/@1autumn_leaf_)

In this episode of Breaking Math, we sit down with Dr. Hortensia Soto, former president of the Mathematical Association of America, to explore the role of mathematics in a world shaped by AI, education, and access. We discuss how debates in math are often really about opportunity and inclusion, how educators can navigate the rapid pace of AI, and why communication and human connection matter more than ever. The conversation also highlights the importance of financial literacy, embodied learning, and collaboration, reframing mathematics not as a set of answers, but as a way of thinking grounded in curiosity, effort, and relationships. Chapters 00:00 Introduction to Hortensia Soto and the Math Community 02:48 The Role of AI in Mathematics 05:17 Access to Mathematics and Its Political Nature 07:34 The Importance of Financial Literacy in Math Education 10:19 Communication Skills for Mathematicians 13:06 The Culture of the Mathematical Association of America 15:29 Reflections on Leadership in the Math Community 25:01 Innovative Approaches to Mathematics Education 25:50 Recognizing Math Identity in Students 27:02 Nurturing Student Potential 35:31 The Role of AI in Learning 38:26 The Human Element in Mathematics 39:51 Mathematics Beyond Symbols and Procedures Follow Hortensia Soto on LinkedIn (https://www.linkedin.com/in/hortensia-soto-41230188/) Follow Breaking Math on Substack (https://breakingmath.substack.com/) Twitter (https://x.com/breakingmathpod) Instagram (https://www.instagram.com/breakingmathmedia/) Bluesky (https://bsky.app/profile/breakingmath.bsky.social) Website (https://www.breakingmath.io/) YouTube (https://www.youtube.com/@BreakingMathPod) Follow Noah on Instagram (https://www.instagram.com/profnoahgian/) Twitter (https://x.com/ProfNoahGian) Bluesky (https://bsky.app/profile/profnoahgian.bsky.social) Follow Autumn on Twitter (https://x.com/1autumn_leaf) Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social) Instagram (https://www.instagram.com/1autumnleaf/) email: breakingmathpodcast@gmail.com

This Women in History Mini-Series episode with Dr. Victoria Bateman explores the groundbreaking contributions of Florence Nightingale, highlighting her use of data and statistics to revolutionize healthcare and public health during the 19th century. Discover how her innovative use of data visualization and her perseverance against gender biases transformed modern nursing and public health policy. Chapters 00:00 Introduction to Florence Nightingale's Legacy 02:21 The Crimean War and Nightingale's Impact 05:18 Data Collection and Analysis in Healthcare 07:18 Overcoming Gender Bias in Medicine 09:23 Innovations in Data Visualization 11:59 Nightingale's Lasting Influence and Conclusion Follow Breaking Math on Substack (https://breakingmath.substack.com/) Twitter (https://x.com/breakingmathpod) Instagram (https://www.instagram.com/breakingmathmedia/) Bluesky (https://bsky.app/profile/breakingmath.bsky.social) Website (https://www.breakingmath.io/) YouTube (https://www.youtube.com/@BreakingMathPod) Follow Victoria on Website (http://www.vnbateman.com/) Instagram (https://www.instagram.com/women.wealth.power/) Twitter (https://x.com/vnbateman) Bluesky (https://bsky.app/profile/vnbateman.bsky.social) Follow Autumn on Twitter (https://x.com/1autumn_leaf) Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social) Instagram (https://www.instagram.com/1autumnleaf/) Substack (https://substack.com/@1autumnleaf) TikTok (https://www.tiktok.com/@1autumn_leaf_)

Mathematics quietly shapes some of the most important decisions in public life, from redistricting and congressional apportionment to federal research funding and AI policy. In this episode, Autumn and Noah speak with Dr. Karen Saxe, Director of Government Relations at the American Mathematical Society, about how mathematical ideas influence representation, fairness, education, and the future of research. From gerrymandering and geometric compactness to life inside the U.S. Senate and the growing policy debates around AI, Karen reveals how deeply math is woven into the systems that govern everyday life. Chapters 00:00 Introduction to the Conversation 01:15 The Hot Tea in DC 01:24 Gerrymandering and Mathematics 03:42 Understanding Gerrymandering and Redistricting 08:07 The Role of Mathematicians in Politics 12:19 Experiences in the Senate with Al Franken 19:32 Government Relations and the Role of Mathematics 23:01 The Impact of AI on Mathematics and Policy 28:41 Community Readiness for AI Transformations 29:22 Diversity in Education and Its Challenges 29:40 Bridging Mathematics and Politics 29:58 Career Pathways: Academia to Policy Follow Karen Saxe on LinkedIn (https://www.linkedin.com/in/karen-saxe-5015038a/) Website (https://www.ams.org/government) Follow Breaking Math on Substack (https://breakingmath.substack.com/) Twitter (https://x.com/breakingmathpod) Instagram (https://www.instagram.com/breakingmathmedia/) Bluesky (https://bsky.app/profile/breakingmath.bsky.social) Website (https://www.breakingmath.io/) YouTube (https://www.youtube.com/@BreakingMathPod) Follow Noah on Instagram (https://www.instagram.com/profnoahgian/) Twitter (https://x.com/ProfNoahGian) Bluesky (https://bsky.app/profile/profnoahgian.bsky.social) Follow Autumn on Twitter (https://x.com/1autumn_leaf) Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social) Instagram (https://www.instagram.com/1autumnleaf/) Substack (https://substack.com/@1autumnleaf) email: breakingmathpodcast@gmail.com

This Women in History Mini-Series episode with Dr. Victoria Bateman explores the groundbreaking work of Anna Schwartz, a pioneering economist who transformed macroeconomics through data-driven research. Discover how her meticulous analysis of monetary history shaped economic policy and the legacy she left for future generations. Chapters 00:00 Introduction to Anna Schwartz and Her Impact 01:45 The Historical Context of Economic Data 04:10 Challenges Faced by Women in Economics 06:03 A Monetary History of the United States 09:04 The Methodology of Anna Schwartz 11:46 Legacy and Personal Insights on Anna Schwartz Follow Breaking Math on Substack (https://breakingmath.substack.com/) Twitter (https://x.com/breakingmathpod) Instagram (https://www.instagram.com/breakingmathmedia/) Bluesky (https://bsky.app/profile/breakingmath.bsky.social) Website (https://www.breakingmath.io/) YouTube (https://www.youtube.com/@BreakingMathPod) Follow Victoria on Website (http://www.vnbateman.com/) Instagram (https://www.instagram.com/women.wealth.power/) Twitter (https://x.com/vnbateman) Bluesky (https://bsky.app/profile/vnbateman.bsky.social) Follow Autumn on Twitter (https://x.com/1autumn_leaf) Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social) Instagram (https://www.instagram.com/1autumnleaf/) Substack (https://substack.com/@1autumnleaf) TikTok (https://www.tiktok.com/@1autumn_leaf_)

In this episode, Lauren Williams, professor of mathematics at Harvard University and a 2025 MacArthur Fellow, speaks about the surprising and often messy reality of mathematical research. The conversation begins with a turbulent moment in academia, when federal grants supporting her work were suddenly canceled—only months before she received the MacArthur “Genius Grant,” an unexpected recognition that allowed her to continue her research. Williams explains her work in algebraic combinatorics, illustrating how abstract mathematics can connect to real-world systems. The discussion also explores the human side of discovery, from collaborations that span continents to the strange coincidence of research papers and babies arriving the same week. Finally, the episode dives into one of the most intriguing experiments in modern mathematics: the First Proof project, which tests whether artificial intelligence can produce genuine mathematical proofs, revealing both the promise and the current limitations of AI-generated reasoning. Chapters 01:27 Winning the MacArthur Genius Grant 01:43 Becoming a Woman in Mathematics at Harvard 04:25 Research Applications 10:04 The Human Side of Research 12:20 The First Proof Project 18:29 Advice for Young Mathematicians 22:51 The Intersection of Mathematics and AI Follow Lauren Williams on Instagram (https://www.instagram.com/laurenkwilliams42/ ) Website (https://people.math.harvard.edu/~williams/) Follow Breaking Math on Substack (https://breakingmath.substack.com/) Twitter (https://x.com/breakingmathpod) Instagram (https://www.instagram.com/breakingmathmedia/) Bluesky (https://bsky.app/profile/breakingmath.bsky.social) Website (https://www.breakingmath.io/) YouTube (https://www.youtube.com/@BreakingMathPod) Follow Noah on Instagram (https://www.instagram.com/profnoahgian/) Twitter (https://x.com/ProfNoahGian) Bluesky (https://bsky.app/profile/profnoahgian.bsky.social) Follow Autumn on Twitter (https://x.com/1autumn_leaf) Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social) Instagram (https://www.instagram.com/1autumnleaf/) email: breakingmathpodcast@gmail.com

This Women in History Mini-Series with Dr. Victoria Bateman explores the life and contributions of Priscilla Wakefield, a revolutionary figure in financial literacy and women's empowerment during the Industrial Revolution. Wakefield's work in establishing savings banks and community insurance schemes for women highlights her belief in the practical application of mathematics for everyday life. The discussion also addresses the challenges women faced in finance during her time and her lasting impact on feminist economics. Takeaways Chapters 00:00 Introduction to Priscilla Wakefield 01:19 Priscilla Wakefield: A Revolutionary Mathematician 04:28 The Financial Landscape of Georgian Britain 06:34 Groundbreaking Contributions to Banking and Finance 07:41 Fun Facts and Legacy of Priscilla Wakefield Follow Breaking Math on Substack (https://breakingmath.substack.com/) Twitter (https://x.com/breakingmathpod) Instagram (https://www.instagram.com/breakingmathmedia/) Bluesky (https://bsky.app/profile/breakingmath.bsky.social) Website (https://www.breakingmath.io/) YouTube (https://www.youtube.com/@BreakingMathPod) Follow Victoria on Website (http://www.vnbateman.com/) Instagram (https://www.instagram.com/women.wealth.power/) Twitter (https://x.com/vnbateman) Bluesky (https://bsky.app/profile/vnbateman.bsky.social) Follow Autumn on Twitter (https://x.com/1autumn_leaf) Bluesky (https://bsky.app/profile/1autumnleaf.bsky.social) Instagram (https://www.instagram.com/1autumnleaf/) Substack (https://substack.com/@1autumnleaf)

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

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

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 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

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. i was a pioneering woman in calculus. 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 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

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 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