Train Your Math Intuition: Beyond Logic and Proof

Resources

Books

• "Mathematica: A Secret World of Intuition and Curiosity" by David Bessis - This book is the central focus of the episode, exploring how our minds work and make sense of the world through the lens of mathematics, emphasizing intuition over formal logic.
• "Discourse on Method" by René Descartes - Referenced as an example of a historical work where the author claims to have stumbled upon a method that made him smarter, starting from a position of being a "regular person."
• "Thinking, Fast and Slow" by Daniel Kahneman - Mentioned as a canonical example of dual-process thinking (System 1 and System 2), which the guest suggests should be augmented with a "System 3."

Articles & Papers

• "The Discourse on Method" - While not explicitly stated as an article, it's referred to in the context of Descartes' writings about his method.

People Mentioned

• David Bessis (Mathematician and Author) - The guest of the podcast and author of the featured book.
• René Descartes (Philosopher) - Referenced for his writings on method and intuition in "Discourse on Method."
• Alexander Grothendieck (Mathematician) - Cited as an example of a great mathematician who described his journey as not being gifted but doing something special internally.
• Daniel Kahneman (Psychologist) - Known for his work on cognitive biases and decision-making, particularly his dual-process theory.
• Patrick House (Neuroscientist) - Mentioned for his work on consciousness and a story about intuition and processing of information.
• Jean-Pierre Serre (Mathematician) - A highly respected mathematician whose presence at a seminar and subsequent feedback to the guest highlight the nuances of understanding in mathematics.
• Andrew Wiles (Mathematician) - Known for proving Fermat's Last Theorem, his story illustrates the process of intuition, proof, and error correction in mathematics.
• G.H. Hardy (Mathematician) - A prominent formalist mathematician who collaborated with Ramanujan.
• Srinivasa Ramanujan (Mathematician) - A self-taught mathematician from India who produced thousands of theorems, often claiming to receive them in dreams or through divine inspiration.
• Michaël Gromov (Mathematician) - Quoted for his perspective on Ramanujan, suggesting he can be viewed as either a mystical figure or a profoundly human mathematician.
• Vienno (Mathematician) - Taught a course at École Normale Supérieure that used visual aids like dominoes to build intuition for algebraic formulas.

Organizations & Institutions

• Library of Economics and Liberty - The organization that produces EconTalk.
• Shalem College in Jerusalem - Affiliation of host Russ Roberts.
• Hoover Institution at Stanford University - Affiliation of host Russ Roberts.
• Princeton University - Where the guest's friend studied cognitive science.
• Cambridge University - Where G.H. Hardy was a professor.
• École Normale Supérieure - Where the guest took a math course.

Websites & Online Resources

• econtalk.org - The website for the podcast, where listeners can subscribe, comment, and find related information.
• amazon.com - Mentioned for browsing the first pages of books.

Other Resources

• Deep Learning Networks - Used as a metaphor for how the brain operates and learns, particularly in relation to intuition.
• Hindu-Arabic Numerals - Presented as an example of an advanced technology that allows for intuitive understanding of numbers.
• Banana Cake Recipe - Used as an analogy to explain how everyday language and instructions rely on a rich, intuitive understanding of concepts.
• Ball and Bat Problem - A classic cognitive reflection test used by Kahneman to illustrate the difference between intuitive (System 1) and deliberate (System 2) thinking.
• Fermat's Last Theorem - A famous unsolved mathematical problem that Andrew Wiles eventually proved.
• Kaka's Conjecture - Mentioned in the context of Andrew Wiles' proof, suggesting a connection that was part of his intuitive insight.
• Dreams - Discussed as a source of intuition and ideas, particularly in the context of Ramanujan and as a potential training exercise for language and intuition.
• Pointing things in space - An exercise suggested for young children to develop spatial imagination and potentially mathematical ability.