Explaining Huge Numbers with Richard Elwes

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 ( ) Instagram ( ) His Book( ) Follow Breaking Math on Substack ( ) Twitter ( ) X ( ) Bluesky ( ) Website ( ) Follow Autumn on X ( ) Bluesky ( ) Instagram ( ) Substack ( ) email: breakingmathpodcast@gmail.com

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Explaining Huge Numbers with Richard Elwes is an episode from Breaking Math Podcast by Autumn Phaneuf & Noah Giansiracusa.

This episode is 56:37 long.

This episode was published on Apr 28, 2026.

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