OpenAI just put an internal version of its next major model, Astra, to work on ten mathematical problems that had seen no progress on the main result for at least a decade. It solved them, and according to Simon Willison, the company claims it spent less than $2,000 in GPT-5.6 Sol token prices on each one. Willison reports the results landed on 1st August 2026, alongside a public repository, a paper, and Lean 4 formalizations that let anyone verify the proofs.
This matters because it moves the goalposts on what AI can do in original research. Solving a genuinely hard, open math problem is a different animal from acing a benchmark. These weren’t warm-up exercises. They were problems the field had been stuck on for ten years or more.
What OpenAI actually shipped
The openai/ten-proofs repository includes Lean 4 formalizations, which means the proofs are machine-checkable rather than just plausible-looking prose. That’s the part that should reassure skeptics. On top of the formal work, OpenAI released:
- A paper describing the solutions to all ten problems.
- An LLM-generated PDF where the model reconstructs how each proof came together, based on its own unpublished reasoning traces.
- Public code you can inspect and check yourself.
Willison calls this “a decent level of transparency,” and he’s right. But he also flags the gap that keeps this from being fully open: the prompts. We don’t know exactly how OpenAI steered the model. We also don’t know how many problems it burned $2,000 on and failed to crack. The $2,000-per-solution figure only counts the wins.
The context you need
This follows a similar flex from a rival just days earlier. According to Willison, Anthropic used Claude with its Mythos Preview to discover cryptographic weaknesses, spending $100,000 on tokens and explicitly instructing the model with prompts like “we are not looking for low hanging fruit, we want proper research to find genuinely hard findings.” Two labs, two demonstrations, one message: frontier models are now being aimed at real research, not just chat.
The status quo before this was AI as an assistant. It drafted, summarized, and autocompleted. What OpenAI and Anthropic are now showing is AI producing findings that human experts couldn’t reach on their own for years.
The human reaction
Mathematicians are not taking it quietly. Willison points to a “collective burst of Deep Blue” energy online, a reference to the 1997 moment when a machine beat the world chess champion and people wondered what was left for humans. Mathematician Kirwin Hampshire published an essay titled “The Dark Night of Mathematics,” describing “a profound spiritual crisis” brought on by earlier, less significant results.
Not everyone sees doom. Terence Tao, one of the most respected mathematicians alive, framed a different path in IEEE Spectrum in June. He calls it “big mathematics”: large-scale, decentralized collaborations between humans and machines, where hard problems get diced and sliced. Humans claim the creative parts. AI does the technical grunt work. Tao is neither dismissive nor fearful. He sees a catalyst for how the discipline works, not a replacement for the people in it.
Why practitioners should care
What stands out here is the price. Less than $2,000 per solved problem puts serious research capability within reach of anyone, not just labs with nine-figure budgets. If that holds up outside cherry-picked demos, expect a wave of teams pointing these models at their own hard, unsolved problems in cryptography, optimization, and formal verification.
A few things worth watching:
- Whether independent mathematicians confirm the Lean proofs hold.
- Whether OpenAI releases the prompts, which would let others reproduce the method.
- The failure rate. The cost of the misses is the number that tells us how reliable this really is.
The honest read is that this is a real milestone with an asterisk. The proofs are verifiable. The transparency is partial. The full story lives in the prompts and the failures OpenAI hasn’t shared yet. For the deeper breakdown, including the links to the repository and papers, check the original write-up at Simon Willison’s blog.