The week’s notable results across mathematics — number theory, combinatorics, geometry, analysis — and the AI-assisted proofs now joining them, from arXiv, Quanta and mathematicians’ own blogs.
The week’s notable results across mathematics — number theory, combinatorics, geometry, analysis — and the AI-assisted proofs now joining them, from arXiv, Quanta and mathematicians’ own blogs.
Every Monday at 09:00, send me an issue of up to 12 items with Mathematics research, plus at least one of New theorem or proof, Solved conjecture, Breakthrough on an open problem, AI-assisted proof, Formal verification in Lean or Prize or major recognition. Skip claimed proofs by unknown authors with no expert reaction or popular explainers that report nothing new. Search the open web, starting with https://www.quantamagazine.org/feed/, https://terrytao.wordpress.com/feed/, math.NT, math.CO and math.AG, and also https://gilkalai.wordpress.com/feed/, but never vixra.org. Matching is strict. Anyone can find and subscribe to it in Discover.
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Real progress on the six open Millennium Prize Problems — the Riemann hypothesis, P vs NP, Navier–Stokes, Yang–Mills, Hodge and Birch–Swinnerton-Dyer: serious papers, partial results, AI-assisted advances, and what experts say about claimed solutions.
Where the P vs NP question stands: circuit and proof-complexity lower bounds, barriers, meta-complexity, geometric complexity theory, new reductions and hardness results, and how the community reads each claimed proof.