OpenAI's unreleased Astra model just solved ten maths problems nobody had cracked in decades

Mathematicians have spent decades stuck on some of these problems. OpenAI says an unreleased model cracked ten of them in a matter of days, for about the price of a decent dinner.

On 1 August, OpenAI revealed that an internal build of its next major model, known as Astra, had produced solutions to ten open problems spanning eight fields, including high dimensional geometry, group theory, coding theory and lattice cryptography. One of them, the first explicit construction of a non-sofic group, had been open since 1999.

The compute cost to find all ten sat at roughly two thousand dollars, which is a strange number to sit next to "solved a maths problem open since before Google existed."

What sets this apart from the usual AI benchmark headline is verification. Rather than simply asserting the results, OpenAI published machine checkable Lean proof files on GitHub alongside a 249 page manuscript, so any mathematician can independently confirm the work rather than take the company's word for it. That distinction matters enormously in a field that has grown rightly sceptical of AI generated maths claims that fall apart under scrutiny.

Fields Medallist Timothy Gowers, among the most respected working mathematicians alive, responded positively while noting the wider mathematical community is still digesting exactly what the proofs mean and how far the technique generalises.

It is worth being honest about what this is and is not. Astra has not been released publicly, and this was an internal capability demonstration rather than a shipped product. But if the results hold up under continued scrutiny, it points to AI moving from assisting mathematicians with routine work towards genuinely original contributions in areas humans have been stuck on for a long time.

Whether that is thrilling or unsettling probably depends on how attached you are to humans being the only ones capable of a genuine mathematical breakthrough. Either way, the proofs are public, so anyone with the Lean expertise to check them is welcome to try and find the catch.