The cost of producing results on ten long-running math problems just dropped to $2.000, according to OpenAI, which states that Astra's model created mechanically testable evidence for questions that had resisted human progress for decades.
OpenAI published the paper on August 1 (PDF) and used it to give its next major model family a name: Astra.
The results cover group theory, high-dimensional geometry, coding theory, quantum complexity, lattice cryptography, and extreme combinatorics. It is a 249-page collection and, alongside it, a mechanically verifiable certificate for each individual result.
The problems were not textbook exercises. Each one had been open for at least ten years, most of them much longer:
- – A construct that establishes the existence of non-sophisticated groups, a question that has preoccupied group theorists for years.
- – A refutation of the Connes rigidity conjecture, a long-standing problem in the theory of von Neumann algebras.
- – An improvement in the general upper limit of the packing density of spheres in high dimensions, a limit that had been in place since 1978.
- – Three problems come from the list of open questions left behind by Paul Erdos.
The announcement comes later. from another result in May, when OpenAI used a similar reasoning model to produce an original mathematical proof that disproves a famous unsolved conjecture in geometry, first posed by Paul Erdos in 1946.
Although the press releases will range from very select to rare, I said I'd pass...because sometimes the editors hide.
