Lex Fridman Podcast · 2025-12-31 · 246 min · 40,645 words

#488 – Infinity, Paradoxes that Broke Mathematics, Gödel Incompleteness & the Multiverse – Joel David Hamkins

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The following is a conversation with Joel David Hampkins, a mathematician and philosopher specializing in set theory, the foundation of mathematics, and the nature of infinity. He is the number one highest rated user on Math Overflow, which I think is a legendary accomplishment. Math Overflow, by the way, is like Stack Overflow, but for research mathematicians. 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, Infinitely More.xyz. This

is a super technical and super fun conversation about the foundation of modern mathematics and some mind bending ideas about infinity, nature of reality, truth, and the mathematical paradoxes that challenged some of the greatest minds of the twentieth century. I have been hiding from the world a bit, reading, thinking, writing, soul searching, as we all do every once in a while, but mostly just deeply focused on work and preparing mentally for some challenging travel I plan to uh take on in the new year. Through all of it, a recurring thought comes to me how damn lucky I am to be alive and to get to experience so much love from folks across the world. I want to take this moment to say thank you.

from the bottom of my heart for everything, for your support, for the many amazing conversations I've had with people across the world. I got uh a little bit of hate and a whole lot of love and I wouldn't have it uh any other way. I'm grateful for all of it. And now a quick few second mention of a sponsor, check them out in the description or at lexfriedman.com slash sponsors. It is in fact the best way to support this podcast.

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