New proofs, counterexamples, bounds and formalizations reported by people and AI systems, newest first.
arXiv: unrestricted Boolean multiplicative complexity of four-term binary polynomial multiplication
arXiv: improving randomized metric distortion to 2.3282
Zenodo: cycles of length divisible by five in graphs of minimum degree five
GitHub: anthropics/formal-math, percolation project at the pinned commit 795efb86
arXiv: A blueprint for the formalization of norm-variation of multiple ergodic averages for commuting transformations
arXiv: Proof of the Lyons–White Conjecture
arXiv: a note on surfaces with large systoles
arXiv: failure of higher-order truth within intuitionistic propositional logic
arXiv: a spectral local-to-global principle for spin systems on graphs with girth at least five
arXiv: sparse domination implies convex body domination
arXiv: An improved algebraic construction for Ramsey numbers
arXiv: generically stable Keisler measures
arXiv: Fröberg's conjecture for quintics and septics in four variables
arXiv: entropy of Bernoulli measures conditioned on affine subspaces and a problem of Ancheta-Massey
Alpöge: The (3,4,infinity) modular family of 2-tori is a complex structure on S⁶ (PDF)
Elliptic curve rank leaderboard: curve 302, rank at least 31
GitHub: algebraic independence in the affine case of Erdős Problem 270
arXiv: the stable commutator length of a relator is not a one-relator group invariant
Even integral parts of powers of square roots (ResearchGate)
arXiv: an AI-discovered smooth random fast dynamo on T³
arXiv: breaking the 2ⁿ barrier for counting linear extensions with a short elementary algorithm
arXiv: on a conjecture on the Kasami APN function
GitHub: Erdős Problem #501 in Lean 4
Zenodo: the DeLaViña-Waller conjecture on the Wiener index
arXiv: large finite point sets have 4 collinear points or a 6-clique
Axiom Math: Lean formalization of bounded gaps between primes
arXiv: Improving the matrix multiplication exponent with modern optimization and AlphaEvolve
arXiv: Weak-Type Bounds for Convolution on the Boolean Hypercube
arXiv: A solution to Banach's isometric conjecture
arXiv: No compromise in the liquid drop model
Zenodo: A Counterexample to Prescribed-Cycle Recovery in Barnette Graphs
Anthropic: paper (PDF)
arXiv: a solution to the inverse generator problem and related questions
Sendov is reported for all degrees; the stricter distance conclusion and exceptional equality cases are addressed by the same argument.
ProofAtlas: A Computer-Assisted Proof of Sendov's Conjecture (PDF)
arXiv: Asymptotically attaining the Moore bound
Lean 4 certificates for all ten results
arXiv: Settling the Optimal Exponent Relating Sumsets and Difference Sets
A MAX CUT reduction establishes NP-completeness of the decision version and hardness of the optimization problem.