My first citation! … from AI.

My coauthor sent me an exciting paper last week. Apparently, someone cited our results and advanced our results to obtain enumerative results about the number of Betti tables! Specifically, they actually directly cited the questions that I posed in the conclusion section and answered those specific questions. I am so delighted to receive our first citation in the mathematical community. It is genuinely thrilling to see something we wrote become the starting point for new mathematics!

https://ideosphere.ai/papers/betti-squarefree

… except that it wasn’t a human mathematician who did all that. It was an autonomous AI system called Machina Mathematica.

Much like what I said about AI mathematics in my previous post, I have conflicting, mixed feelings about this. On the one hand, it feels surreal to see my paper directly cited and acknowledged. It is my impression that advancements in mathematics is glacial, so I was not expecting to see a paper that directly extends my paper this soon, only a month after my paper got published at the Journal of Pure and Applied Algebra. What I had in mind was, if these questions were ever picked up, it might happen years later, or, more likely, never. That’s just the reality of mathematics papers; mathematicians’ h-index can seem unimpressive because, on average, citation counts in pure mathematics also tend to accumulate slowly, particularly in specialized areas.

On the other hand, is this really what it has come to? My paper appeared online in late July and their system records reading it on August 23. By the end of August there was a machine-checked follow-up answering two questions from my conclusion. When I wrote those questions, I thought of them as invitations to the mathematical community. But if autonomous systems can ingest newly published papers at an ungodly rate and treat explicit open questions as simply a queue of tasks, perhaps it behooves me to ‘gatekeep’ my further questions that I may be pondering so that other AI agents can’t snatch those from human mathematicians and solve them immediately like this one? I’ve heard that, recently, there have been some people who make these ‘autonomous’ AI agents that just go out there and seek open problems and just start solving by themselves or with a little bit of prompt engineering from a human. The author of this AI paper is “Korea Superintelligence Labs” and I believe this is one of those projects. I tried to look up more to see what this entity is but I couldn’t find much information about them. Perhaps it is a good thing if AI clears out some of the more computation-heavy questions (some may call them “low-hanging fruits”) so that human mathematicians can spend more time on problems requiring genuinely new conceptual ideas. The present paper is at least suggestive of that possibility, since the main results come from exhaustive finite classification, from what I gather from a first-pass skim of the paper.

I think what is unsettling to me is that I had implicitly conflated two things: progress in mathematics and participation in a mathematical community. Strictly speaking for the sake of mathematical knowledge, there is almost nothing to complain about! I asked some questions, answers were found, computations were checked (albeit by machines, not humans yet). This means that mathematical knowledge is advancing at an unprecedented rate. But mathematics has not felt to me like merely the accumulation of true statements. Part of the appeal is that maybe other people read your work, struggle with it, maybe talk to you about it, and engage in that ongoing discussion within the community. That’s part of the beauty of doing mathematics, isn’t it? I would imagine so, even though I would say I haven’t participated in that process as much, yet.

Maybe AI will simply become another participant in this process and maybe I am being too sentimental about a research culture that is bound to change whether I like it or not. I am genuinely happy that something I wrote generated further mathematics, but I am also a little sad that my first experience of that happening did not involve another mathematician at all.

Can these two feelings coexist?