Lex Fridman Podcast

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

Jun 13, 2021

02:47:26

Creator website

Highlights

AI Chapters

Episode notes

Gregori Perlman's Punk-Res Conjecture

03:31

Is There a Random Process Within the Nature of Reality?

02:07

Poincare's Theory of Chaos

03:04

Introduction

6min

If the Brain Is a Cake, It Is.

2min

Is Language Attachable?

3min

How Did You Fall in Love With Geometry?

4min

What Is Symmetry?

4min

What Kind of Symmetries Are Enough to Solve the MNIST Dataset?

3min

The Transition Time Question

3min

Is There a Cold War in the United States?

2min

The Challenge of Mathematics and Science in the Soviet Union

6min

10.

Poincare's Theory of Chaos

3min

11.

Pongkarei Conjecture

4min

12.

The Shape of the Universe

3min

13.

Do You Live on a Mobius Strip?

2min

14.

You See Something's Doing a Lot of Work

2min

15.

The Universe Is Many More Dimensions Than We Perceive as Human Beings?

2min

16.

How to Intuitively Mess With the Other Dimensions in a Three-Dimensional World

2min

17.

How Many Holes Does a Straw Have?

2min

18.

Is There a Hole in a Straw?

3min

19.

What's the One Color for the Straw?

2min

20.

The Inflow on the Top of the Pants Equals the Outflow on the Bottom of the Pants

2min

21.

The Flowering of Math YouTube

4min

22.

Is There a Value in Visualizing Mathematics?

2min

23.

Is There a Fields Matter?

2min

24.

The Conway Knot, a Book Review

3min

25.

Is There a Simple Answer?

2min

26.

Why Is the Andrew Wiles Proof of the Pharmacellis Theorem So Beautiful?

2min

27.

The Last Theorem by Andrew Wells

2min

28.

Do You Know How to Solve the Fairmont Problem?

2min

29.

Complication Is a Big Thing in Number Theory

2min

30.

Is There Interesting Insights From Angela Wiles's Proof?

5min

31.

Two to the Power of a Large and Two to a Negative Power

2min

32.

Is There a Goal in Mathematica?

2min

33.

How Can I Change the Distance Function?

2min

34.

Is There Some Deeper Truth in It?

2min

35.

I Love Poems, but a Poetic Is Not an Explanation

4min

36.

The Beauty of Binding Gaps

2min

37.

Is There a Difference Between Primes and Atoms?

2min

38.

Is There a Category of Fake Primes?

3min

39.

Is There an Infinite Number of Primes?

4min

40.

Is There a Random Process Within the Nature of Reality?

2min

41.

Machine Learning

2min

42.

Intuitionism, Ultra Finitism

2min

43.

The Difference in Ultra Finitism

4min

44.

The Idea of Cellular Automata in Computer Science

3min

45.

John Conway - I Feel Like You Have a Unique Personality

4min

46.

Golly on IOS - The Game of Life

2min

47.

A Darwinian Approach to Complexity

2min

48.

Can You Predict the Middle Column?

2min

49.

What Is Group Theory?

3min

50.

What Are the Symmetries of the Real World?

2min

51.

Is There a Simple Explanation of Gauge Symmetries?

2min

52.

Monoculture Is Bad, Right?

2min

53.

Is There a Difference Between Prose and Poetry?

2min

54.

Gregori Perlman's Punk-Res Conjecture

4min

55.

Do You Think Peter Scholze Turned Down the Field's Metal?

2min

56.

Why He Turned Down the Nobel Prize?

4min

57.

How Do You Learn Math?

4min

58.

Learning Math Is Hard, I Hate Exercise

2min

59.

What Advice Would You Give to Young People Today?

2min

60.

The Meaning of Life

3min

61.

How Not to Be Wrong

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