Greatest mathematician of all time | Joel David Hamkins and Lex Fridman

Quick Overview

Joel Hamkins finds ranking mathematicians by greatness incredibly difficult, but if forced to choose, he would select Archimedes for his achievements transcending his early era, while emphasizing that his personal mathematical style prioritizes simple, clear arguments proving surprising results over being the first to discover something complex.

Key Points: Hamkins considers ranking mathematicians difficult, but suggests Archimedes as a candidate because his achievements 'totally transcended the work of the other people in his era.' Hamkins prefers simple, clear, easy-to-understand arguments that prove a surprising result, stating the question of novelty is 'somehow less important to me' than the beauty of the proof. He notes that simultaneous, separate discoveries are common in mathematics because 'certain ideas are in the air and being thought about but not fully articulated.' Hamkins describes his personal process as playful curiosity, involving playing around with ideas, changing little things, and understanding basic cases until a path through to something interesting appears. Hamkins frequently uses thought experiments and anthropomorphization, such as visualizing a set-theoretic model of ZFC as a place to travel to via forcing, to understand mathematical tensions. Contrasting styles, Hamkins notes he could not replicate Andrew Wiles' seven-year solo grind, preferring mathematics as a social activity with nearly one hundred collaborators. Hamkins respects Grigori Perelman's decision to decline prizes, viewing it as a reminder that the greatest minds pursue mathematics for 'the love of it, not for the prizes or the money.'

Context: This is an interview between Lex Fridman and mathematician Joel David Hamkins, focusing on the philosophical aspects of mathematics, including how to define greatness among mathematicians, individual working styles, the nature of mathematical discovery, and recognition within the field. The discussion moves from naming potential candidates like Euler, Gauss, and Newton to Hamkins detailing his preference for elegant proofs and his collaborative approach to research, contrasting it with highly isolated efforts like Andrew Wiles' work on Fermat's Last Theorem.