proof

A guest post on Terence Tao's blog by Kate Stange and Edmund Harriss reflecting on a workshop about rigorous mathematical illustration, arguing that AI has broken the scarcity of deep theorems and that mathematics must value understanding and illustration beyond mere proof-writing.

Mathematicians have proven the long-standing sandwich conjecture in graph theory, showing that large random graphs can be approximated between two simpler graphs, connecting different random processes and advancing the field.

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.