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

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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

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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

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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

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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

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