Dylan
283 posts



First, Happy New Year everyone! It's been a wild ride. I can't wait for 2026, LFG! I love you all! ❤️ Second, here's my conversation with Joel David Hamkins (@JDHamkins), mathematician and philosopher specializing in set theory, the foundations of mathematics, and the nature of infinity. We talk about paradoxes that challenged some of the greatest mathematicians of the 20th century, Gödel Incompleteness theorems, the mathematical multiverse, the nature of truth, computation, and much more. By the way, Joel is the #1 highest-rated user on MathOverflow, and writes a great blog called "Infinitely More". It's here on X in full and is up everywhere else (see comment). Timestamps: 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























