Tim Gowers and Norman Wildberger Playing With Robots
He's very polite: because some of these responses he got from ChatGPT are hilarious. The main observation seems to be that AIs don't do well with maths because of the way most published mathematical literature is written, as students know only too well, is missing most of the dynamical elements in the proof process and is presented entirely in terms of truth-functional statements. Imre Lakatos described the process at length in his book Proofs and Refutations . During the development of the subject now called Additive combinatorics certain definitions such sumset were made, and because these somewhat arbitrary definitions turned out to be fruitful in some way, they became widely used and thereby imposed a certain structure on the development of the field. But those definitions were not a priori necessary, yet they now have a central rôle in the subject as it was developed. So, having thus defined the field, the process of proving theorems becomes heavily constrained by thes...