Joel David Hamkins is a mathematician and philosopher specializing in set theory, the foundations of mathematics, and the nature of infinity, and he's the #1 highest-rated user on MathOverflow. He is
Thank you for this. Speaking as a numberphile, I feel like this was the kind of conversation I needed to hear during my first brush with set theory as an undergrad. There was just never enough time in class to have the fun discussions, and back then, we couldn't just look up YouTube videos to do a deep dive. I always ended up feeling like there were things we covered that I was supposed to have learned elsewhere but didn't, and I didn't have a very deep understanding of them. Beyond the calculations and the proofs, it seems very few professors actually took the time to help students conceptualizing what it meant. This is good.
This is awesome Lex. I know it's much less popular to have someone talk at length about something so involved but for the people who watch and are interested in this topic area its a brilliant resource and refreshing to go in depth on a topic, rather than keeping it pop sci.
I was telling my husband how pondering infinity is slowly making me go insane and then this pops up not long after to make it worse 😅 send thoughts and prayers to my husband cause he’s about to be annoyed af for the next few years, as there’s no way I’m shutting up about this
The remark Lex made about professor Hamkins' status as a user of mathoverflow really is no joke: I have lost the count of how many times his answers have been useful for my own curiosity and self-study. The level of detail and clarity is beyond belief, such a gem of a contributor
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See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc.
0:00 - Introduction
2:17 - Infinity & paradoxes
49:27 - Russell's paradox
1:02:35 - Gödel's incompleteness theorems
1:20:06 - Truth vs proof
1:31:30 - The Halting Problem
1:47:23 - Does infinity exist?
2:04:57 - MathOverflow
2:08:49 - The Continuum Hypothesis
2:18:36 - Hardest problems in mathematics
2:28:03 - Mathematical multiverse
2:46:55 - Surreal numbers
2:57:33 - Conway's Game of Life
2:59:49 - Computability theory
3:09:41 - P vs NP
3:12:58 - Greatest mathematicians in history
3:26:43 - Infinite chess
3:45:01 - Most beautiful idea in mathematics
CONTACT LEX:
Feedback - give feedback to Lex: lexfridman.com/survey
AMA - submit questions, videos or call-in: lexfridman.com/ama
Hiring - join our team: lexfridman.com/hiring
Other - other ways to get in touch: lexfridman.com/contact
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Comments (20)
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Thanks for all the likes may your New Year be amazing
Thank you so much for inviting him and for having such an insightful and brilliant conversation
See below for timestamps, transcript, and to give feedback, submit questions, contact Lex, etc.
0:00 - Introduction
2:17 - Infinity & paradoxes
49:27 - Russell's paradox
1:02:35 - Gödel's incompleteness theorems
1:20:06 - Truth vs proof
1:31:30 - The Halting Problem
1:47:23 - Does infinity exist?
2:04:57 - MathOverflow
2:08:49 - The Continuum Hypothesis
2:18:36 - Hardest problems in mathematics
2:28:03 - Mathematical multiverse
2:46:55 - Surreal numbers
2:57:33 - Conway's Game of Life
2:59:49 - Computability theory
3:09:41 - P vs NP
3:12:58 - Greatest mathematicians in history
3:26:43 - Infinite chess
3:45:01 - Most beautiful idea in mathematics
Transcript:
lexfridman.com/joel-david-hamkins-transcript
CONTACT LEX:
Feedback - give feedback to Lex: lexfridman.com/survey
AMA - submit questions, videos or call-in: lexfridman.com/ama
Hiring - join our team: lexfridman.com/hiring
Other - other ways to get in touch: lexfridman.com/contact
EPISODE LINKS:
Joel's X: x.com/JDHamkins
Joel's Website: jdh.hamkins.org/
Joel's Substack: www.infinitelymore.xyz/
Joel's MathOverflow: mathoverflow.net/users/1946/joel