OpenAI's Astra solves 10 previously unsolved math problems

OpenAI's new Astra model has solved 10 previously unsolved mathematical problems, according to a company blog post.

The problems span six areas of mathematics, including high-dimensional geometry and lattice-based cryptography. The most notable result is the first explicit construction of a non-sofic group, a mathematical object whose existence researchers have debated since 1999.

All 10 proofs were formally verified using the Lean 4 theorem prover. OpenAI has also published a 249-page manuscript and machine-readable certificates on GitHub, allowing researchers to independently verify every step of the proofs.

According to OpenAI's estimates, finding all 10 solutions cost roughly $2,000 at API pricing. Mathematician Thomas Bloom described the results as "big news" and said they go beyond previous achievements by AI systems in mathematics. He also noted that the models still build on human mathematical knowledge and are not about to replace researchers.

Astra has not yet made a serious attempt at the Millennium Prize Problems, some of the most famous unsolved questions in mathematics. OpenAI plans to continue experimenting with the model and says it will publish more detailed technical documentation soon.The results follow another recent mathematical achievement from OpenAI, when one of its AI systems autonomously disproved a conjecture posed by Paul Erdős in 1946.