OpenAI claims it has used an internal version of its Astra model to solve ten long-standing mathematical problems, spending less than $2,000 per problem on token costs. The company has released formal proofs and a paper describing the work, a move that has rippled through the mathematics community.
The announcement comes just days after Anthropic revealed it had discovered cryptographic weaknesses using its Claude model with Mythos Preview. Anthropic spent $100,000 on tokens for that research. Its prompts included "again we are not looking for low hanging fruit, we want proper research to find genuinly hard findings."
The Ten Problems
OpenAI set "an internal version of Astra, our next major model" on ten mathematical problems that, according to the company, "have seen no progress on the main result for at least a decade." The model reportedly solved all ten, with each solution costing less than $2,000 at GPT-5.6 Sol token prices.
That figure stands in stark contrast to Anthropic's $100,000 spend. The difference in cost is striking, though the two efforts tackled very different kinds of work.
The company has not said how many problems it spent $2,000 on without reaching a solution. That gap in reporting leaves an open question about the true success rate behind the headline numbers.
What OpenAI Released
The openai/ten-proofs repository on GitHub contains Lean 4 formalizations of the results. Lean 4 is a proof assistant used to verify mathematical arguments mechanically. A paper describing the solutions is also available.
OpenAI additionally released an LLM-generated PDF in which the model "reconstructs how the proof came together" based on unpublished reasoning traces. That document offers a rare look at how the model approached the problems.
The transparency is decent, but not complete. The prompts used to direct the model are not shown. As Simon Willison, the blogger and software developer behind the link post, put it: "That's a decent level of transparency, but I want to see the prompts they used!"
A Deep Blue Moment
Many mathematicians online are experiencing what the article describes as a collective burst of "Deep Blue." That reference points to the IBM chess computer that beat Garry Kasparov in 1997, a moment that symbolized machines surpassing human experts in a once-sacred domain.
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The reaction suggests a similar shock now spreading through mathematics. If an AI can crack problems that resisted human effort for a decade, at a cost of under $2,000 each, the field's assumptions about who does the work may be shifting.
Terence Tao's Vision
Terence Tao, one of the most respected mathematicians alive, is neither dismissive of AI nor fearful of it. In June, he published an article in IEEE Spectrum describing what he calls "big mathematics."
Tao sees AI as a catalyst for a fundamental shift in the discipline. He envisions large-scale, decentralized collaborations between humans and machines. Complex mathematical tasks, in his view, can be diced and sliced, with humans claiming the creative parts and AI handling the technical grunt work.
That vision now looks less like speculation and more like a roadmap. OpenAI's ten proofs, whatever their ultimate significance, fit squarely within the pattern Tao described.
The Cost Question
The economics of AI-assisted research are changing fast. Anthropic spent $100,000 on its cryptographic work. OpenAI claims to have spent less than $2,000 per problem on its ten mathematical solutions. That is a total of under $20,000 for the entire set.
Willison's post, published on 1st August 2026, frames the news as a link post aggregating other sources. He notes that sponsors can support his work for $10 a month, which gets a curated email digest of the month's most important LLM developments.
The contrast between the two companies' approaches is instructive. Anthropic paid more and showed its prompts. OpenAI paid less and hid them. Both are pushing the boundaries of what AI can do in research settings, but the transparency gap remains a sticking point for observers like Willison.
For mathematicians, the message is clear: the machines are coming for the hard problems, and they are doing it cheaply. Whether that is a threat or an opportunity may depend on how the field adapts to the new reality.