I was interviewed by Theodor Nenu as the first installment of his Philosophical Trials interview series with philosophers, mathematicians and physicists.
Theodor provided the following 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