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

Lex Fridman Podcast

Conversations that explore technology, history, philosophy, physics, mathematics, biology, chemistry, engineering, AI, robotics, programming, music, film, art, sports, psychology, neuroscience, geopolitics, business, economics, religion, astronomy, and the human condition with people from all walks of life.

Jordan Ellenberg is a mathematician and author of Shape and How Not to Be Wrong. Please support this podcast by checking out our sponsors:
- Secret Sauce: https://wondery.com/shows/secret-sauce/
- ExpressVPN: https://expressvpn.com/lexpod and use code LexPod to get 3 months free
- Blinkist: https://blinkist.com/lex and use code LEX to get 25% off premium
- Indeed: https://indeed.com/lex to get $75 credit

EPISODE LINKS:
Jordan's Website: http://www.jordanellenberg.com
Jordan's Twitter: https://twitter.com/JSEllenberg

PODCAST INFO:
Podcast website: https://lexfridman.com/podcast
Apple Podcasts: https://apple.co/2lwqZIr
Spotify: https://spoti.fi/2nEwCF8
RSS: https://lexfridman.com/feed/podcast/
YouTube Full Episodes: https://youtube.com/lexfridman
YouTube Clips: https://youtube.com/lexclips

SUPPORT & CONNECT:
- Check out the sponsors above, it's the best way to support this podcast
- Support on Patreon: https://www.patreon.com/lexfridman
- Twitter: https://twitter.com/lexfridman
- Instagram: https://www.instagram.com/lexfridman
- LinkedIn: https://www.linkedin.com/in/lexfridman
- Facebook: https://www.facebook.com/lexfridman
- Medium: https://medium.com/@lexfridman

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

Jordan Ellenberg is a mathematician and author of Shape and How Not to Be Wrong. Please support this podcast by checking out our sponsors: 
– Secret Sauce: <a href="https://wondery.com/shows/secret-sauce/">https://wondery.com/shows/secret-sauce/</a> 
– ExpressVPN: <a href="https://expressvpn.com/lexpod">https://expressvpn.com/lexpod</a> and use code LexPod to get 3 months free 
– Blinkist: <a href="https://blinkist.com/lex">https://blinkist.com/lex</a> and use code LEX to get 25% off premium 
– Indeed: <a href="https://indeed.com/lex">https://indeed.com/lex</a> to get $75 credit
EPISODE LINKS: 
Jordan’s Website: <a href="http://www.jordanellenberg.com">http://www.jordanellenberg.com</a> 
Jordan’s Twitter: <a href="https://twitter.com/JSEllenberg">https://twitter.com/JSEllenberg</a>
PODCAST INFO: 
Podcast website: <a href="https://lexfridman.com/podcast">https://lexfridman.com/podcast</a> 
Apple Podcasts: <a href="https://apple.co/2lwqZIr">https://apple.co/2lwqZIr</a> 
Spotify: <a href="https://open.spotify.com/show/2MAi0BvDc6GTFvKFPXnkCL">https://open.spotify.com/show/2MAi0BvDc6GTFvKFPXnkCL</a> 
RSS: <a href="https://lexfridman.com/feed/podcast/">https://lexfridman.com/feed/podcast/</a> 
YouTube Full Episodes: <a href="https://youtube.com/lexfridman">https://youtube.com/lexfridman</a> 
YouTube Clips: <a href="https://youtube.com/lexclips">https://youtube.com/lexclips</a>
SUPPORT & CONNECT: 
– Check out the sponsors above, it’s the best way to support this podcast 
– Support on Patreon: <a href="https://www.patreon.com/lexfridman">https://www.patreon.com/lexfridman</a> 
– Twitter: <a href="https://twitter.com/lexfridman">https://twitter.com/lexfridman</a> 
– Instagram: <a href="https://www.instagram.com/lexfridman">https://www.instagram.com/lexfridman</a> 
– LinkedIn: <a href="https://www.linkedin.com/in/lexfridman">https://www.linkedin.com/in/lexfridman</a> 
– Facebook: <a href="https://www.facebook.com/lexfridman">https://www.facebook.com/lexfridman</a> 
– Medium: <a href="https://medium.com/@lexfridman">https://medium.com/@lexfridman</a>
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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#190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries

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