An internal OpenAI reasoning model disproved a conjecture in discrete geometry that had been open since 1946. It found a polynomial improvement to the best known lower bound for the planar unit distance problem — n^(1+δ) with δ = 0.014 — by importing tools from algebraic number theory that no human mathematician had previously applied to this problem. The proof was verified and endorsed by several leading mathematicians, including Fields Medalist Tim Gowers.
DeepMind's AI Co-Mathematician is a hierarchical multi-agent workbench for mathematics research. Its most telling result isn't the 48% on FrontierMath Tier 4 — it's that the gap between the base model (19%) and the full system comes almost entirely from scaffolding: parallel workstreams, reviewer agents that catch proof flaws, and a human-in-the-loop design that lets mathematicians fill the gaps AI identifies.
Sander Dieleman's post on flow maps frames diffusion model distillation as learning to compute the integral of the velocity field directly, rather than stepping along tangent directions. The reformulation unifies 20+ recent papers under three consistency constraints and explains why single-step sampling is achievable without sacrificing bijectivity.
