Jasmine OttoMar 4
Martin Escardo

A lot of what Bill Thurston says here resonates with my personal experience:

https://arxiv.org/abs/math/9404236

I don't understand his mathematical work, and, if he were alive, he probably wouldn't understand mine.

But this is precisely the kind of things he discusses! Among many other interesting things.

I am sure his experience will resonate with yours too!

On proof and progress in mathematics

In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms of progress in mathematics that are not captured by formal proofs of theorems, especially in his own work in the theory of foliations and geometrization of 3-manifolds and dynamical systems.

arXiv.org
Sep 19, 2025 at 5:52pmWeb
Show threadScott HottonSep 20, 2025

@MartinEscardo Here is video of Thurston from 2008 on "What is the future for 3-dimensional geometry and topology?". He gave the talk not long after Perelman was awarded the Field's medal. At 3:45 minutes into the video he brings up some of the points from his paper "On proof and progress in mathematics". He thought there was a simpler proof of his Geometrization conjecture. He was concerned that if people gave up working on it then the knowledge that had built up in people's minds over the years would be forgotten and it would take a much longer time to discover that simpler proof.

https://www.bing.com/videos/riverview/relatedvideo?&q=Thurston+What+is+the+future+for+3-dimensional+geometry+and+topology

Thurston What is the future for 3-dimensional geometry and topology - Search Videos