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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 also the author of several books, including Proof and the Art of Mathematics and Lectures on the Philosophy of Mathematics. And he has a great blog called Infinitely More.
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Transcript:
https://lexfridman.com/joel-david-hamkins-transcript
CONTACT LEX:
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EPISODE LINKS:
Joel’s X: https://x.com/JDHamkins
Joel’s Website: https://jdh.hamkins.org
Joel’s Substack: https://www.infinitelymore.xyz
Joel’s MathOverflow: https://mathoverflow.net/users/1946/joel-david-hamkins
Joel’s Papers: https://jdh.hamkins.org/publications
Joel’s Books:
Lectures on the Philosophy of Mathematics: https://amzn.to/3MThaAt
Proof and the Art of Mathematics: https://amzn.to/3YACc9A
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OUTLINE:
(00:00) – Introduction
(01:58) – Sponsors, Comments, and Reflections
(15:40) – Infinity & paradoxes
(1:02:50) – Russell’s paradox
(1:15:57) – Gödel’s incompleteness theorems
(1:33:28) – Truth vs proof
(1:44:52) – The Halting Problem
(2:00:45) – Does infinity exist?
(2:18:19) – MathOverflow
(2:22:12) – The Continuum Hypothesis
(2:31:58) – Hardest problems in mathematics
(2:41:25) – Mathematical multiverse
(3:00:18) – Surreal numbers
(3:10:55) – Conway’s Game of Life
(3:13:11) – Computability theory
(3:23:04) – P vs NP
(3:26:21) – Greatest mathematicians in history
(3:40:05) – Infinite chess
(3:58:24) – Most beautiful idea in mathematics
Are you looking for investment opportunities in 2026? So are we and we covered three stocks we love going into the year.Travis Hoium, Lou Whiteman, and Rachel Warren discuss:
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This summer, the island of Puerto Rico was under the thrall of Bad Bunny. His 31-concert residency at a stadium in San Juan was a homecoming for the global superstar.
It's also a homecoming for many thousands of people who left home – but are flocking back for the shows.
NPR’s Adrian Florido reports on how the concerts resonated with Puerto Ricans on and off the island.
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Email us at considerthis@npr.org.
This episode was produced by Kathryn Fink, Elena Burnett, Liz Baker and Marc Rivers. It was edited by Patrick Jarenwattananon and Gigi Douban. Our executive producer is Sami Yenigun.
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Plus: In markets, some of the biggest winners in 2025 included Western Digital and Micron Technology. And some of the losers included Strategy and Gartner. Julie Chang hosts.
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By Safia Elhillo
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As we look back at our international reporters' most memorable stories of the last year, we revisit a story about families from Ireland learning their full history. There, the Catholic Church once ran homes for unwed mothers. Until recently the church dominated life in Ireland and pregnancy outside marriage was considered shameful. Behind one of these homes a ghastly discovery has recently been made. It was a secret most people in the town knew about, but no one took any action until recently. And through reporting the story, our correspondent learned of a personal connection to this history.
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As government continues to engage in reckless actions from inflation to starting wars, people develop shorter time horizons, creating social vacuums. Increased gambling and other irresponsible behaviors then fill the void.
Original article: https://mises.org/mises-wire/kalshi-culture-how-gambling-speculation-and-degeneracy-went-mainstream