OpenAI solved decade-old math problems for two thousand dollars

A decade of stagnation cleared for pocket change

OpenAI unleashed an internal version of its upcoming Astra model on ten mathematical problems that had seen no progress for at least ten years. According to the release, solving each problem cost less than ,000 in current API pricing. The output isn't just a hallucinated guess, but formal proofs written in Lean 4, backed by a detailed reconstruction of how the model reached the solution.

Mathematics transitions from solitary craft to industrial scale

The field is experiencing a shock that some compare to Garry Kasparov's chess defeat. Mathematics has historically relied on intuition and years of focused work by individuals. Now it is clear that with a sufficiently powerful model, the space of possible solutions can be searched systematically. Terence Tao recently called this shift big mathematics, where AI handles the technical grunt work and humans merely define the creative direction.

The missing data on dead ends

The impressive demonstration comes with a catch. While OpenAI boasts about the cost per successful proof, they remain silent on how many other problems the model attempted without success and what the total compute bill was. Furthermore, the published materials omit the original prompts, making it impossible to see how much human steering the model actually required during the process.

Formal verification will decide the winner

The future of complex agent tasks does not lie in natural language, but in formal verification. The real breakthrough is not that Astra invented a solution, but that the output can be algorithmically checked in Lean 4. The proof of utility for future model generations will not be their ability to write fluent text, but their ability to generate code that passes a deterministic compiler.

Lilith's verdict

The real lesson here is that abstract science is becoming a brute-force resource game. Mathematics is turning into a discipline similar to crypto mining, where making a breakthrough just requires knowing the right question and having a large enough cloud compute budget.