schwinger

@thomasfbloom's takes on AI results in combinatorics are always refreshingly balanced and insightful. Being distant from combinatorics myself, I rely on his writing to inform me about what’s going on there. The story I am seeing is remarkable, and in some ways alarming. Amid much noise (as usual), there seem to be several genuinely strong autonomous results, even by the standards of top experts. In my estimation, two results in particular (Unit Distance and Double Cycle) would alone have been enough to earn a tenured professorship, at least before 2026. I know many mathematicians are pointing to the fact that even these impressive AI solutions are short, elementary, almost in the literature already, and concentrated in combinatorics. I am confident that you will soon see impactful examples (autonomously generated Inventiones level papers, by pre-2026 standards) that do not fit any of these characterizations. 2026 is a new world, where it means little how long questions have been open, or who tried and failed to solve them before. It’s undeniable that AI is exposing a striking jaggedness in human understanding of mathematics. That said, I think it’s still the case that the best mathematics being done today is done by humans, with minimal (if any) input from AI. I think this may soon change, but even after that I’m optimistic that humans will be able to add significant value to what AI can do. I think there’s a strong case to be made that we should view AI not as replacing mathematicians, but as empowering them to do their science far better and faster than ever, and that we should support them all the more for it. At the same time, mathematicians need to adapt fast to make this case.