Terence Tao's mental models

Their wordsUm And yeah, so I believe a lot in serendipity. Um And maybe there's a danger actually that you know, in the mo- modern society, it's not just AI, but we've become really good at optimizing everything.

Their wordsConsequently, excessive optimization for one or two goals may cause the many previously aligned goals of mathematics to diverge from one another;

Their wordsAn excessively AI-polished proof may sand away both the "artificial" friction (typos, awkward phrasing, disorganization) and the "natural" friction, leaving a text that is easy to read and hard to learn from.

Their wordsI think the platform that Lean and other software tools, so GitHub and things like that will allow experimental mathematics to scale up to a much greater degree than we can do now.

Their wordsUm but now it's quite possible at the high school level or or whatever that that you could get involved in math project and actually make a real contribution because of all these AI tools and and and Lean and everything else.

Their wordsso the mathematical community plural is incredibly super intelligent entity that no single human mathematician can come closer to replicating.

Their wordsI'm much more comfortable with the fox paradigm. Yeah. So yeah, I like looking for analogies, narratives. I spend a lot of time… If there's a result, I see it in one field, and I like the result, it's a cool result, but I don't like the proof, it uses types of mathematics that I'm not super familiar with, I often try to re-prove it myself using the tools that I favor.

Their wordsImproper usage of AI offloads thinking, understanding and learning, thus mortgaging future mathematical development.

Their wordsSo, we're now in a situation where suddenly people can generate thousands of theories for a given scientific problem. And now we have to to verify them, evaluate them and this is something which we we have to to change our structures of science to actually sort this out.