Micah Zarin Podcast

What is mathematics, really? | Paolo Aluffi

Paolo Aluffi, author of Algebra: Chapter 0 and professor at Florida State University, sits down to talk about what it actually means to do mathematics, and why most people have never seen the real thing. 00:00 — What does a mathematician actually do? 01:43 — How Algebra: Chapter 0 came to be 03:05 — The three types of students in every math class 07:39 — How Paolo got into mathematics 09:24 — If not math, then music 11:19 — What makes a mathematical structure "natural"? 12:40 — Grothendieck and the bridge between geometry and number theory 16:17 — The rising sea 19:02 — "If mathematics is hard, it's probably wrong" 20:01 — Are we early in the history of mathematics? 20:45 — The four color theorem and mathematical maturity 22:10 — Elliptic curves and the limits of intuition 24:19 — Does the world run on logic? 24:51 — How human intuition solves unsolvable combinatorial problems 29:32 — Is mathematics discovered or invented? 32:50 — Pure math vs applied math — and why Riemann never thought about GPS