open-problem

Possible solutions to some millennium prize problems have been proposed, as indicated in a tweet linking to further discussion.

An Anthropic researcher reported that Claude helped solve a Hadamard matrix of order 668, a long-standing open problem in combinatorics, potentially marking an AI-assisted breakthrough in the Hadamard conjecture.

Levent Alpöge has apparently used Claude to construct a 668x668 Hadamard matrix via an obfuscated shell script, potentially resolving the smallest open Hadamard case and all 12 unresolved orders below 2000, pending verification.

David Turturean solved a 40-year-old open problem in p-adic Galois theory using voice input, in collaboration with problem proposer David Roe, under EpochAI Research's FrontierMath initiative.

A tweet reports that an AI (likely GPT-5.6 Pro) disproved the Dinitz-Garg-Goemans conjecture, a long-standing open problem in graph theory, using simple prompts like 'do a breakthrough'.

Researchers used AI, specifically ChatGPT 5.5 Pro, to solve the 35-year-old Signed BAR Conjecture in queuing theory, proving uniqueness of stationary distributions for reflected diffusions. The result advances understanding of equilibrium in stochastic networks and demonstrates AI's role in mathematical discovery.

The article describes the author's journey building a word game that requires pure deduction without guessing, and how information theory helped overcome the challenge of generating solvable puzzles.

The article critiques current neural network theory for lacking a governing equation, arguing that AGI remains an extrapolation rather than a well-posed scientific object until learning, inference, and convergence are unified mathematically.

Kyle Kabasares claims to have used OpenAI's ChatGPT-5.5 Pro to generate a candidate counterexample to an open problem from Don Knuth's The Art of Computer Programming, and requests verification.

Sequoia Capital highlights the gap between current AI models that train once and human continuous learning, and points to EngramLab's work on AI that never stops learning with memory inside the model.

Over the weekend, Mythos was tested on the Erdos unit distance problem (Problem #90) and successfully solved it.

Sam Altman announces that a general-purpose AI model has solved a major open problem in mathematics, calling it a big milestone and expressing mixed feelings about AI's expanding capabilities.

OpenAI's general-purpose reasoning model autonomously solved the planar unit distance problem, a famous open problem in mathematics posed by Paul Erdős in 1946, marking the first time AI has independently solved a prominent open problem in a field of mathematics.

An OpenAI model has autonomously solved the planar unit distance problem, a famous open mathematics question from 1946, disproving an 80-year-old assumption and achieving a first for AI.