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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.
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.
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.