OpenAI’s Astra AI Just Cracked 10 Unsolved Math Problems for $2,000

The tech giant unleashed a 249-page paper alongside a public repository containing machine-verifiable proofs generated by their internal research model, Astra. Instead of guessing the next word like a glorified autocomplete, the system spent compute time analyzing complex open questions and formulating fully verified logic trees in the Lean theorem prover.

Among its triumphs, the system constructed the first explicit example of a non-sophic group in abstract algebra, a structural entity mathematicians have questioned for ages without ever actually seeing one in the wild. It also outright disproved Connes' rigidity conjecture in functional analysis, dismantling decades of theoretical assumptions with cold, calculated machine precision.

The AI didn't stop at pure algebra; it also proved the quantum parallel repetition theorem for general two-player games and solved Ehrhart's volume conjecture in high-dimensional geometry. Furthermore, it achieved the first improvement to the general upper bound for sphere packing density since 1978, breaking a 46-year standstill with a handful of algorithmic runs.

Unlike standard conversational bots, Astra acts as an autonomous mathematician, inventing core proof ideas, writing formal code, and letting the Lean compiler guarantee zero hallucination errors. The mathematical community is now left staring at thousands of lines of machine code that solve problems older than most software engineers.

Human mathematicians face an uncomfortable future where centuries of prestige are replaced by server compute time, proving that even the most abstract human intellectual triumphs can be automated for the price of a modest cloud subscription.

Source: OpenAI