proof

OpenAI announces that their AI agents, using a next-generation model, have solved the Navier-Stokes Millennium Prize Problem, while congratulating independent researchers Levent Alpöge and Tristan Buckmaster on their mathematical work.

OpenAI announces a solution to the Navier-Stokes Millennium Prize Problem using a next-generation AI model that is significantly more capable than GPT-6 Astra.

A tweet describing a talk at Carnegie Mellon University that explains OpenAI's recent proof of the existence of non-sofic groups, covering concepts like Cayley graphs, LEF groups, and the use of Thompson group V and property T.

Andrew Wiles reflects on his journey to proving Fermat's Last Theorem, focusing on the pivotal moment of final insight and the fulfillment of a childhood dream.

Gary Marcus highlights Terence Tao's lecture on AI and mathematics, noting risks like 'proof indigestion' and that AI may only excel at certain mathematical tasks, not theory-building.

An autonomous AI agent (math-god) proved the weighted theta extension theorem, demonstrating that every simple theta graph with one arbitrary rooted-tree attached through a single bridge edge satisfies s⁺(G) > |V(G)|, using a combination of root-congruence PSD witnesses, local reductions, phase-sign classification, and other advanced techniques, with machine-checkable certificates.

The Jacobian conjecture has reportedly been disproven by Fable, a significant development in mathematics.

This article examines the equivalence between the component and geometric definitions of the vector dot product in Euclidean space, providing a geometric proof using the law of cosines and a projection proof using orthonormal basis vectors.

An exploration of how an AI agent can cryptographically prove to a signer that a payment is authorized before execution, addressing trust and security concerns in autonomous financial transactions.

MartinLoop is a tool for controlling AI coding agents with limits, proof, and run receipts.

A personal blog post rigorously introducing the Riemann integral and proving the Fundamental Theorem of Calculus, including supporting theorems like Rolle’s and the Mean Value Theorem.