OpenAI announces discoveries in math, CS and physics
Results in harmonic analysis, complexity theory and quantum field theory, released with outside expert groups.
Results in harmonic analysis, complexity theory and quantum field theory, released with outside expert groups.
New results from an internal frontier model, with Lean formalizations of many of the proofs.
Working largely autonomously for 11 days, Claude wrote the first complete computer-checked proof, in Lean.
An unreleased Claude model raised the lower bound on zeta zeros satisfying the Riemann hypothesis from 41.6% to 67.2%.
Results on ten long-standing open problems from an internal version of Astra, each formalized in Lean.
Open Lean 4 proof model, 119B total and 6B active, under Apache 2.0; solves 587 of 672 PutnamBench problems.
An internal general-purpose reasoning model disproved it, and external mathematicians checked the proof.
Open-source code agent for the Lean 4 proof assistant, with 6B active parameters and weights under Apache 2.0.
A Gemini Deep Think agent that generates, verifies and revises solutions to research-level maths problems.
An advanced Gemini Deep Think solved five of six IMO problems in natural language, scoring 35 of 42 points.
A Gemini-powered evolutionary coding agent that discovers and optimizes algorithms for math and computing.
AlphaProof and AlphaGeometry 2 solved four of six IMO 2024 problems, scoring 28 of 42, silver-medal level.
DeepMind's neuro-symbolic system solved 25 of 30 Olympiad geometry problems; code and model open-sourced.
Pairing an LLM with an evaluator, Google DeepMind's FunSearch found new solutions to open math problems.
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