Breaking Math Podcast

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
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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

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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

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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)

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This Women in History Mini-Series episode with Dr. Victoria Bateman explores the inspiring story of Mary T. Washington Wylie, 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 Wylie
00:48 Early Life and Challenges
02:58 Breaking Barriers in Accountancy
05:25 Pioneering a Path for Others
07:21 Legacy and Impact

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