Joel David Hamkins on Infinity, Gödel's Theorems and Set Theory | Philosophical Trials #1

Joel David Hamkins is an American Mathematician who is currently Professor of Logic at the University of Oxford. He is well known for his important contributions in the fields of Mathematical Logic, Set Theory and Philosophy of Mathematics. Moreover, he is very popular in the mathematical community for being the highest rated user on MathOverflow. Outline of the conversation: 00:00 Podcast Introduction 00:50 MathOverflow and books in progress 04:08 Mathphobia 05:58 What is mathematics and what sets it apart? 08:06 Is mathematics invented or discovered (more at 54:28) 09:24 How is it the case that Mathematics can be applied so successfully to the physical world? 12:37 Infinity in Mathematics 16:58 Cantor's Theorem: the real numbers cannot be enumerated 24:22 Russell's Paradox and the Cumulative Hierarchy of Sets 29:20 Hilbert's Program and Godel's Results 35:05 The First Incompleteness Theorem, formal and informal proofs and the connection between mathematical truths and mathematical proofs 40:50 Computer Assisted Proofs and mathematical insight 44:11 Do automated proofs kill the artistic side of Mathematics? 48:50 Infinite Time Turing Machines can settle Goldbach's Conjecture or the Riemann Hypothesis 54:28 Nonstandard models of arithmetic: different conceptions of the natural numbers 1:00:02 The Continuum Hypothesis and related undecidable questions, the Set-Theoretic Multiverse and the quest for new axioms 1:10:31 Minds and computers: Sir Roger Penrose's argument concerning consciousness Enjoy! Apple Podcasts: https://podcasts.apple.com/gb/podcast/philosophical-trials/id1513707135 Spotify: https://open.spotify.com/show/3Sz88leU8tmeKe3MAZ9i10 Google Podcasts: https://podcasts.google.com/?q=philosophical%20trials Instagram: https://www.instagram.com/tedynenu/