Lex Fridman Podcast

#190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries

Jun 13, 2021

Jordan Ellenberg, a mathematician from the University of Wisconsin and author of 'Shape,' explores the fascinating world of geometry and its connection to human experience. He discusses the interplay between creativity and mathematics, emphasizing the beauty of chaos and high-dimensional shapes. Ellenberg shares insights on the relevance of symmetry, the importance of visualization in understanding complex ideas, and the enigma of prime numbers. The conversation touches on artificial intelligence's relationship with mathematics and the philosophical implications of higher dimensions.

02:47:26

Creator website

Episode guests

Jordan Ellenberg

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Episode notes

Intro

2min

The Dance of Genius: Artistry Meets Pragmatism

2min

The Mathematics of Cognition: A Cake Metaphor

3min

The Language of Mathematics and Geometry

17min

Poincaré and the Dimensions of Reality

25min

Exploring Dimensions and Mathematical Perspectives

18min

AI and the Quest for Mathematical Mastery

22min

The Geometry of Understanding

10min

The Enigma of Prime Numbers

13min

10.

Anthropomorphization and Insights in Machine Learning and Human Behavior

2min

11.

Exploring Infinity and Mathematical Thought

12min

12.

Exploring the Simplicity and Complexity of Conway's Game of Life

2min

13.

Exploring Complexity Through Simple Rules in Cellular Automata

4min

14.

Exploring Symmetry in Mathematics and Physics

21min

15.

Embracing the Journey of Math Learning

12min

16.

Exploring the Intersection of Mathematics and the Human Experience

2min

Jordan Ellenberg is a mathematician and author of Shape and How Not to Be Wrong. Please support this podcast by checking out our sponsors:
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EPISODE LINKS:
Jordan’s Website: http://www.jordanellenberg.com
Jordan’s Twitter: https://twitter.com/JSEllenberg

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OUTLINE:
Here’s the timestamps for the episode. On some podcast players you should be able to click the timestamp to jump to that time.
(00:00) – Introduction
(06:44) – Mathematical thinking
(10:21) – Geometry
(14:58) – Symmetry
(25:29) – Math and science in the Soviet Union
(33:09) – Topology
(47:57) – Do we live in many more than 4 dimensions?
(52:28) – How many holes does a straw have
(1:01:53) – 3Blue1Brown
(1:07:40) – Will AI ever win a Fields Medal?
(1:16:05) – Fermat’s last theorem
(1:33:23) – Reality cannot be explained simply
(1:39:08) – Prime numbers
(2:00:37) – John Conway’s Game of Life
(2:12:29) – Group theory
(2:15:45) – Gauge theory
(2:23:47) – Grigori Perelman and the Poincare Conjecture
(2:33:59) – How to learn math
(2:41:08) – Advice for young people
(2:43:13) – Meaning of life

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