x.com/polynoamial/status/2083467194663571701
1 correction found
solved 10 major open problems in mathematics, quantum complexity, and theoretical computer science.
OpenAI’s own announcement does not say Astra solved ten open problems outright. It says the model produced ten results on long-open problems, and several listed items are partial advances like improved bounds or new lower bounds rather than complete problem solutions.
Full reasoning
OpenAI’s August 1, 2026 post is titled "Ten advances in mathematics and theoretical computer science," not ten solved open problems. In the body, OpenAI says: "Today, we are sharing a selection of ten results to problems that have been open" and "We provide new results for the following problems."
That distinction matters, because several entries in OpenAI’s own list are explicitly phrased as partial advances rather than full resolutions of the broad named problem area:
- "High-dimensional sphere packing" — described as "New upper bounds on sphere-packing density".
- "Binary and spherical codes" — described as "Exponentially improved bounds".
- "Arithmetic circuit complexity" — described as "New lower bounds".
The accompanying paper makes the same point in its abstract, presenting "a collection of results" and then listing items such as improved bounds and lower bounds alongside some fully resolving results. So the post’s wording overstates what OpenAI actually claimed: the publication reports ten advances/results on open problems, not ten outright solved open problems.
2 sources
- Ten advances in mathematics and theoretical computer science | OpenAI
The page says, "Today, we are sharing a selection of ten results to problems that have been open" and "We provide new results for the following problems," then lists items including "New upper bounds on sphere-packing density," "Exponentially improved bounds," and "New lower bounds".
- Ten Advances in Mathematics and Theoretical Computer Science
The paper abstract says, "We present a collection of results obtained by an internal OpenAI model," and includes entries such as improved sphere-packing bounds, improved code bounds, and new lower bounds for arithmetic circuit complexity.