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For quite a few years of my adult life, I was in a situationship with pure mathematics. Specifically, a small lonely subfield of functional analysis. In his book on the subject, John Conway quipped that functional analysis, itself a somewhat modest corner of real analysis, is so vast that two researchers both working in it might not understand each other’s work. From my tiny specialized subfield, math looked very, very large and whatever progress I might make looked very, very inconsequential.
The situationship ended, and my ascendant career as a data-themed, quantitative substacker eventually began. However, I never lost at least high-level interest in mathematical progress and now it turns out that 2026 is mathematics’ annus mirabilis.
If you haven’t been following this, it started in May with OpenAI disproving the unit distance conjecture, which had been open since 1946. Wow! Then in July an Anthropic researcher disproved the Jacobian conjecture, open since 1939, by way of Twitter.
https://x.com/__alpoge__/status/2079028340955197566?s=20
The professional mathematics community was under siege. The tech bro barbarians were at the gates!
The barbarians broke through the gates on September 8th when OpenAI published a long, recondite paper claiming to resolve one of the Clay Institute’s stated Millennium problems, the Navier-Stokes global regularity problem. These problems are the crown jewels of cutting edge mathematical research, though just this morning I saw a preprint claiming the formalization of this result might be sketchy. This was so shocking that some people (completely implausibly in my view) believed OpenAI had looked at the user chats from mathematicians working on the Navier-Stokes problem in coming up with their solution.
And I’d say the city was sacked in October, two days ago as of my writing this, when OpenAI published a github repository, laconically entitled “math”, with almost 800 novel mathematical results, a titanic corpus sprawled over almost