Apropos of nothing, I was reminded recently of a fascinating story I heard from Geordie Williamson about AI and go — perhaps this story was the original source. It is a story about how a technology which has the power to greatly increase knowledge can rather create barriers to actually acquiring that knowledge. To give just some excerpts:
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None of these reasons [for cheating] were surprising to us … What personally shocked me, however, was the way our students conceptualised their AI use. In this, Carlo Metta was also a surprisingly predictive case. The original reddit thread discussing his ban featured a comment from a user called “carlo_metta”, which read:
I never let Leela choose move. I just decide myself which one is better, for this reason i think i can find my own style with Leela. Go is an art and Leela help me tyo [sic] express my skill
That account was a burner, quite possibly a troll. However, I couldn’t help but recall the comment when I heard identical arguments coming from our cheating students’ accounts.
I think this story has a number of themes relevant to math, including how AI use by experts can make us worse mathematicians. I think when mathematicians use AI they need to be extremely careful not to fall into the trap of imagining that they (rather than some autonomous agent) are doing mathematics. Amateurs at least don’t have this problem!
I know good mathematicians who have used AI to prove interesting theorems, and they swear that the result started with their own original ideas which were then combined with the insights of AI. And I believe them! But it is very easy to start taking ownership of ideas that are not your own. I think mathematicians need to be very conscious that button pressing has the possibility of warping one’s perception of how much you actually contributed yourself.
For me, I think it helps to have at least one project where you simply do not use AI at all. And for projects that do use AI, make every effort to be honest to yourself about what your contribution is.
In my professional work that has appeared online so far, I have only used AI to “review” one paper after it was written. I have found this very helpful, and I certainly continue to do this. In my experience, AI reviews papers incredibly thoroughly. Ironically, what it seems most likely to miss are arguments that are so poorly written that it’s not even clear exactly what the argument is, but when you actually include some details it has an opportunity to find the hole in the argument.
That said, I definitely do plan to use AI for future research. I have used AI to try to better optimize the choice of the functions \(\psi\) we used in [CDT] (for example, look at Figure A.4.5). I was utterly confused during that paper how to optimize the (very non-linear) holonomy bounds as \(\psi\) ranged over all holomorphic maps \(\varphi: D(0,1) \rightarrow D(0,1-\varepsilon)\). Not only is this a complicated non-linear optimization problem, but there is also the issue of being able to actually compute the answer quickly and rigorously. After using ChatGPT 5.6, I remain utterly confused as to what the optimal choice looks like, but at least it *could* do better, and found a certain Ansatz of functions to try which improved the numerology. The improvements were not quite good enough (yet) to simplify our proof of the irrationality of \(L(2,\chi_{-3})\) in any meaningful way, but they were good enough to prove that the \(\mathbf{Q}(x)\)-vector space generated by functions \(f(x) \in \mathbf{Q}[[x]]\) on \(\mathbf{P}^1 \setminus \{0,1,\infty\}\) which have denominator type \([1,2,\ldots,n]^2\) has dimension at most \(8\) rather than dimension at most \(9\). (We still suspect the actual answer is \(5\).)
My “biggest” (in terms of tokens) use of AI so far is a somewhat quixotic attempt to construct a new finite simple group. Again, more on this later, but as the computation continues, it is my obligation to remain crystal clear about what exactly my contribution is. Note that although the headline goal of this project will certainly end in failure, there is the hope that interesting mathematics will nonetheless come out of this.