x.com/polynoamial/status/2083467194663571701
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An internal version of Astra, @OpenAI's next major model family, solved 10 major open problems in mathematics, quantum complexity, and theoretical computer science.
OpenAI’s own release does not say Astra fully solved 10 open problems. It describes the work as "ten advances" and says several items are new bounds or hardness results rather than complete solutions to the broader problems.
Full reasoning
OpenAI’s official announcement is titled “Ten advances in mathematics and theoretical computer science”, not “ten solved open problems.” In the body of the post, OpenAI says: “We provide new results for the following problems.”
That distinction matters, because several of the ten items are explicitly described by OpenAI as partial advances rather than full solutions to the broader named problem areas:
- Sphere packing: OpenAI says this result gives “new upper bounds” and its Lean repo describes it as “Improved asymptotic upper bounds on sphere-packing density”.
- Binary and spherical codes: OpenAI describes “Exponentially improved bounds” / “Exponentially stronger upper bounds”.
- Arithmetic circuit complexity: OpenAI describes “New lower bounds”.
- Closest vector problem: OpenAI describes “Polynomial-factor hardness of approximation”.
Some entries do resolve conjectures or open questions (for example, non-sofic groups, Connes’s rigidity conjecture, Ramsey numbers, and the extremal graph conjectures). But the blanket statement that Astra “solved 10 major open problems” overstates what OpenAI itself claims for the full set.
So the misleading part is not that Astra produced important research results; it is the stronger claim that all ten were complete “solves.” OpenAI’s own materials describe the package more carefully as a set of advances and new results, several of which are substantial progress rather than total resolution of the broader problem area.
2 sources
- Ten advances in mathematics and theoretical computer science | OpenAI
The page title is “Ten advances in mathematics and theoretical computer science.” It says, “We provide new results for the following problems,” then lists items including “New upper bounds on sphere-packing density,” “Exponentially improved bounds,” “New lower bounds,” and “Polynomial-factor hardness of approximation.”
- openai/ten-proofs | GitHub
The README describes several results as partial advances rather than complete solves: “Improved asymptotic upper bounds on sphere-packing density,” “Exponentially stronger upper bounds,” “New lower bounds for computing the permanent,” and “Polynomial-factor hardness of approximation for the closest vector problem.”