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Recent results in mathematics, newest first, a few lines each with a link. Some are easy to state and good for a classroom. Last checked: 4 November 2026.

When What changed More
July 2025 AI at the Mathematical Olympiad. AI systems reach gold-medal level at the IMO, solving five of six problems with written proofs; a year earlier one had reached silver with proofs checked in the Lean proof assistant. Where logic goes
February 2025 The Kakeya conjecture in three dimensions is proved by Hong Wang and Joshua Zahl: a set in which a needle can point in every direction must still be "fully three-dimensional". Where analysis goes
November 2024 The moving sofa problem: Jineon Baek posts a proof that Gerver's 1992 sofa is the largest that turns a right-angled corner in a hallway (claimed; experts are checking it). Where geometry goes
October 2024 A new largest known prime, \(2^{136279841} - 1\), with 41,024,320 digits, found by Luke Durant using cloud GPUs. Where number theory goes
July 2024 The fifth Busy Beaver number, BB(5) = 47,176,870, is settled by an online collaboration, with a computer-checked proof in Coq. Where logic goes
May 2024 The geometric Langlands conjecture is proved by Gaitsgory, Raskin and seven others, in about 800 pages. Where algebra goes
March 2023 The "hat": Smith, Myers, Kaplan and Goodman-Strauss find a single tile that covers the plane only in patterns that never repeat (an "einstein"), then the "spectre", which needs no mirror images. Geometry topic
March 2023 Ramsey numbers: Campos, Griffiths, Morris and Sahasrabudhe give the first exponential improvement in 80 years on the upper bound for diagonal Ramsey numbers. Ramsey theory

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