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

Lex Fridman Podcast

Lex Fridman

Technology, Society & Culture, Philosophy, Science

4.7 • 13.6K Ratings

🗓️ 13 June 2021

⏱️ 167 minutes

🔗️ Recording | iTunes | RSS

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Summary

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

Transcript

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0:00.0	The following is a conversation with Jordan Ellberg, a mathematician at University of Wisconsin,
0:05.4	and an author who masterfully reveals the beauty and power of mathematics in his 2014 book,
0:12.2	How Not to Be Wrong in His New Book, just released recently called Shape.
0:17.5	The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else.
0:23.3	Quick mention of our sponsors.
0:25.3	Secret sauce, ExpressVPN, Blinkist, and Indeed.
0:29.8	Check them out in the description to support this podcast.
0:33.1	As a side note, let me say that geometry is what made me fall in love with mathematics
0:37.3	when I was young.
0:38.5	It first showed me that something definitive could be stated about this world through intuitive
0:44.0	visual proofs.
0:45.4	Somehow, that convinced me that math is not just abstract numbers, devoid of life, but
0:50.7	a part of life, part of this world, part of our search for meaning.
0:55.7	As usual, I'll do a few minutes of ads now.
0:57.7	I try to make these interesting, but I give you time stamps, so if you skip, please tell
1:01.5	check out the sponsors by clicking the links in the description.
1:04.7	It's the best way to support this podcast.
1:06.6	I don't do ads in the middle.
1:08.0	I think, for me at least, they get in the way of the conversation.
1:12.4	Unfortunately, to be able to be very selective with the sponsors we take on, so hopefully,
1:16.7	if you buy their stuff, you'll find value in it just as I have.
1:20.7	This show is sponsored by Wandery's series called Secret Sauce.
	...

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