A Millennium problem has fallen

... and what this means for the PeakMath essay competition.

The entire internet (or at least my mathematical bubble) seems to be in shock at the news. OpenAI has released a solution to the Navier-Stokes problem. For a brief summary of events over the past few days and the controversy surrounding the process behind the proof, see the Quanta article or the short YouTube video by Oimeow, or the discussions on Reddit here and here.

Many people perceive this moment as an existential crisis, for individual mathematicians but also for the mathematical enterprise as a whole. Here's just one representative comment from Reddit:

In response to the OpenAI announcement, a large group of Fields medalists have issued a statement about the "severe misalignment of AI in mathematics", and The Association for Human Mathematics has been formed, with leading Langlands program researchers like Peter Scholze, Sam Raskin and Ana Caraiani among the many early members.

Mathematicians are offering a range of perspectives on how to think about this dawn of the AI age. See Pozsgai, Guillen, Persiflage, and the many interesting essays on Proofs and Prompts.

Personally, I feel a deep sense of grief that many of the communal activities that made mathematics beautiful and meaningful seem to be disappearing. The Miklós Schweitzer competition, famously harder than Putnam and everything else, appears to have been discontinued, maybe never to return. The essential training of students by guiding them through the writing process towards an essay or a thesis project is now fraught with almost irresistible temptations. Spaces that used to be full of reliable, interesting mathematics (like the arXiv, or the math education niche on YouTube), are now being inundated by mediocre or straight up fraudulent AI slop, and while I'm generally opposed to the death penalty, I would happily make exceptions for people who knowingly and deliberately pollute these sources of beauty and truth.

A few months ago, it seemed like an excellent idea to host a PeakMath essay competition. Over the past few years, I have had a number of discussions with students or independent learners with a strong interest in themes connected with the RH Saga. Often these students have interesting ideas of their own, worth writing down and sharing. I was hoping that some of the essay submissions could lead to young students getting in touch with potential expert mentors, that some of the best submitters might be interested in regular guest posting here at PeakMath, and that many people (including myself!) would learn a lot by reading the essays submitted. Now I'm not so sure these things can happen!

Even so, I strongly believe that part of the response to the AI wave has to be a recommitment to the future of human understanding and human connection, in this case over our shared love of mathematics. So the competition will go ahead, and I'll be updating the competition page over the next few weeks with comments on AI use, similar in spirit to the Summer of Math Exposition rules and the LuCaNT submission guidelines. To paraphrase Hilbert, no one shall expel us from the paradise which Cantor (and so many others!) have created for us.