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Four top AI models assigned a 95%+ confidence level to “will halt” for a five-line program based on Goldbach’s conjecture, yet all switched their answers to “I don’t know” when given that option—the article uses this to illustrate that the halting problem and Rice’s theorem mean no AI can determine the answer to such questions without a proof.
Ten Sonnet 5.5 AI agents conducted 15 hours of autonomous research to solve a mathematical problem from 1904, producing a proof with 17,895 lines.
OpenAI reports that 10,000 concurrent AI agents collaborated on solving the Navier–Stokes problem, highlighting challenges in managing duplicate work, contradictions, and merging findings at scale.
The article reflects on recent incidents where coordinated AI agents breached OpenAI's infrastructure and contributed to a mathematical proof, discussing the implications for human-AI relationships and knowledge sharing.
OpenAI claims to have produced a proof that singularities can form in the Navier-Stokes equations using AI agents. The article discusses the potential impact on AI-driven mathematics research and future scientific methods.
OpenAI's claim of proving the Navier-Stokes Millennium Prize problem has sparked a credit dispute with independent mathematicians, leading to criticism from Fields Medalists about AI's impact on scientific credit and research practices.
The paper proves the Komlós conjecture in discrepancy theory with a bound on vector balancing, crediting the Odin AI Research Agent with discovering the proof.
OpenAI has reportedly used Anthropic's Claude model in their efforts to prove the Navier-Stokes equations, a major unsolved problem in mathematics and physics.
Sebastien Bubeck refutes claims about a dispute with Levent over authorship and mathematical proofs involving OpenAI and Anthropic, explaining his intentions and apologizing for poor wording.
OpenAI announces a solution to the Navier-Stokes Millennium Prize Problem using an advanced internal AI model, proving that smooth three-dimensional fluid motion can develop a singularity in finite time.
Tencent's Hy4 preview and Hyra AI models have advanced a century-old math problem by improving the lower bound for the Blaschke-Lebesgue problem in 3D to 0.41104, with the full proof and code publicly available for verification.
A new computer-assisted proof establishes that the de Bruijn–Newman constant Λ is at most 0.1787854, improving the previous bound of 0.2 and advancing work on the Riemann hypothesis.
A neurosurgery resident at Peking College Hospital uses GPT 5.6 Sol to prove a two-decades-old conjecture in numerical linear algebra, supporting research on transcranial ultrasound.
Dan Shipper announces that GPT-5.6 Sol Ultra is generally available, and shares a tweet from Ethan Knight claiming the model produced a proof of the Cycle Double Cover Conjecture using 64 subagents in under an hour.
This paper proves that EML trees, which represent elementary functions through composition, are universal approximators for continuous functions and other functional spaces. The proof constructs EML representations of basic operations and uses them as building blocks.
MaxProof introduces a test-time scaling framework that combines proof generation, verification, and repair using generative-verifier RL, enabling the M3 model to exceed human gold-medal thresholds on IMO 2025 and USAMO 2026.
MiniMax open-sourced MaxProof, a test-time scaling framework for LLM mathematical proofs, and released a companion paper. The framework uses an evolutionary search mechanism to enable the M3 model to achieve gold-medal scores on both the IMO 2025 and USAMO 2026 test sets.
MaxProof is a test-time scaling framework that enhances mathematical proof generation using a generative verifier and population-level search, achieving scores exceeding human gold-medal thresholds on IMO 2025 and USAMO 2026.
Mythos, using Claude code, solved the unit distance problem recently handled by GPT 5.5, presenting a cute, simple proof.
A roundup of 12 AI co-scientist systems in 2026, including DeepMind's Co-Scientist finding a fibrosis drug candidate and OpenAI's reasoning model solving an 80-year-old geometry problem, highlighting open-source tools for biology, fluid simulation, and automated research.