OpenAI’s New Matrix Multiplication Bound: ω ≤ 2.25

One result family in OpenAI’s October 2026 mathematics release concerns the exponent ω of matrix multiplication.

#matrixmultiplication #complexitytheory #algorithms #lean

Why 0.878 Is Max-Cut’s Approximation Wall

Max-Cut asks for a split of a graph’s vertices that sends as many edges as possible across the divide.

#maxcut #approximationalgorithms #complexitytheory #uniquenessgames

OpenAI’s Unique Games Claim Is Not P vs NP

A manuscript in OpenAI’s October 2026 mathematics release tackles Unique Games, a conjecture open for more than two decades.

#uniquegames #complexitytheory #nphard #lean

Two new quantum algorithms achieve tight query complexity bounds for ground-state preparation: one with optimal expected-case complexity O(α/γ∆ + α/∆·log(1/ε)) and another with optimal worst-case bounds. Matching lower bounds prove optimality.

#QuantumAlgorithms #ComplexityTheory #Research

New formulation of the multiplicative adversary method yields the strongest quantum query lower bounds yet, enabling first time-space tradeoffs for general quantum algorithms and proving list-decoding theorems extending classical results.

#QuantumAlgorithms #ComplexityTheory #Research

Proves explicit finite-n bounds on sets of square quadratic systems with no vs. exactly one solution, establishing fundamental limits relevant to post-quantum cryptographic hardness assumptions.

#PostQuantumCryptography #ComplexityTheory #Research