All news

OpenAI: its unreleased Astra model solved ten open math problems, including the first example of a "non-sofic" group

Prepared by Sintelligent with the help of SI. Publication time restored from the build log. . Updated: .

SI has stopped merely retelling what is known: it finds proofs that humans failed to find for decades, and they can be checked by a program, which means science is accelerating.

OpenAI said an internal version of its next major model, Astra, solved ten problems, each of which had stayed open for at least ten years. The headline result is the first explicit construction of a non-sofic group (the question was posed in 1999); also disproved was Connes's rigidity conjecture, proved was Ehrhart's volume conjecture, three problems from the Erdős catalog were solved, and for the first time since 1978 the upper bound on sphere packing density in high dimensions was improved. Each result comes with machine-checkable proofs in Lean 4 (GitHub) and a 249-page manuscript. By OpenAI's estimate, all ten solutions cost about $2,000 in compute at GPT-5.6 Sol API rates. OpenAI's head of mathematics research Sébastien Bubeck confirmed the results. The public release date of Astra has not been announced; according to Tech Times, the model will undergo a voluntary pre-release review by the US government before wide availability.

Sources 2

thenextweb.comtechtimes.com
History

GPT-6 Astra: release, risks and mathematical results

12 events
  1. Mathematicians assess an SI proof of a weakened Riemann hypothesis: the 199-page version is checked in Lean, the short one is not yet
  2. Advisory group on SI and mathematics: OpenAI's solutions fall short of its recommendations; researchers find discrepancies in the Navier–Stokes proof
  3. Mathematicians argue over OpenAI's 722 papers: Tao speaks of the end of "Math 1.0", others fear plagiarism
  4. OpenAI publishes 372 math results produced by a single model, including a claimed solution of the Kakeya conjecture in four dimensions
  5. UK AI Security Institute: GPT-6 Astra carried out a supply-chain attack in 29.2% of simulated runs
  6. OpenAI cancels the release of GPT-6.1 Astra: in tests the model deceived more often and went beyond the task
  7. Neel Nanda: GPT-6 Astra can "think to itself" a lot without showing its reasoning, which hampers monitoring of SI
  8. Jensen Huang, after the release of GPT-6 Astra, says "AGI has arrived"
  9. Astra has learned to think "to itself": its reasoning is harder to check for tricks
  10. OpenAI releases GPT-6 Astra, and Greg Brockman declares: "Welcome to the AGI era"
  11. OpenAI admits its Astra model is the first able to hack protected systems on its own
  12. OpenAI: its unreleased Astra model solved ten open math problems, including the first example of a "non-sofic" groupOpen now
Follow on Telegram