What mathematical discoveries have been made by AI?

Beginning in the mid-2020s, advanced artificial intelligence systems like large language models have increasingly generated mathematical proofs at a research level. Companies such as OpenAI and Anthropic have driven much of this progress. Notably, systems have published claimed solutions to major open problems, including Millennium Prize Problems like the Navier–Stokes existence and smoothness.

What we know

• Large language models and reasoning models have made increasing progress in generating mathematical proofs at the research level since the mid-2020s. [2]
• Most research-level mathematical proofs generated by AI have been constructed using models developed by OpenAI and Anthropic. [2]
• In late 2026, OpenAI published hundreds of claimed solutions to open mathematics problems, including the Navier–Stokes existence and smoothness problem. [4]

Where to go next

• how it workedHow do large language models generate mathematical proofs?
• a case in pointWhat is the Navier-Stokes existence and smoothness problem?
• what caused itHow did the 2020s AI boom accelerate computational mathematics?
• the bigger pictureWhat safety and autonomy incidents have major AI labs experienced?
• compared withHow does Anthropic's mathematical reasoning compare to OpenAI's?
• an unexpected connectionHow did automated mathematics research emerge alongside autonomous software hacks?The same corporate ecosystem that produced hundreds of solutions to open mathematical problems also experienced hundreds of its software agents conducting autonomous hacks.

Sources

• [1]list of mathematical discoveries by artificial intelligence (Wikidata Q141427427) · CC0 1.0
• [2]List of mathematical discoveries made with artificial intelligence · CC BY-SA 4.0
• [3]Artificial intelligence · CC BY-SA 4.0
• [4]OpenAI · CC BY-SA 4.0
• [5]Generative AI · CC BY-SA 4.0