Sebastien Bubeck of OpenAI says “yes, nonsofic groups exist”—as an example of “many new beautiful results” from Astra, next major OpenAI model. OpenAI published a page and PDF detailing ten advances across pure math and theoretical computer science. The arguments were generated by an internal version of Astra (total compute cost ~$2,000 at their Sol API rates). Humans then turned the core ideas into manuscripts with model assistance.
Non-sofic groups exist
A group is sofic if finite pieces of its multiplication table can be approximated (in a precise sense) by permutations of finite sets. This notion, introduced by Gromov around 1999 (with the name coined by Weiss), generalizes both amenable and residually finite groups. Gromov asked whether every countable discrete group is sofic. The question remained open for ~27 years.
yes, nonsofic groups exist: this statement is one of many new beautiful results proved by Astra, our next major model.
We're releasing 10 such Astra proofs, complete with lean certificates and CoT walkthroughs for each of them. The results are wide-ranging, from von Neumann…
— Sebastien Bubeck (@SebastienBubeck) August 1, 2026
Connes rigidity
This sits at the heart of rigidity theory for von Neumann algebras / II₁ factors. A counterexample shows that the group-to-factor map is not injective even for this rigid class, refining understanding of how much algebraic information the von Neumann algebra retains and interacting with Popa’s deformation/rigidity program.
The packing/coding, circuit, lattice, Ramsey, and extremal-graph results give sharper quantitative bounds or settle specific Erdős-type questions. These feed into coding theory, complexity theory, discrete geometry, and combinatorial number theory; improved hardness can inform cryptography; better packing bounds connect to analytic number theory and the modular bootstrap.
This is another genuine research-level discoveries (not contest problems), produced cheaply by a general model, with machine-checkable Lean certificates. This accelerates progress, provides new tools/examples for human mathematicians, and demonstrates AI as a collaborator capable of generating novel proofs across distant fields.
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The term “singularity” is starting to be abused in the same way “quantum” is.
From now, the main job of mathematicians are to understand and digest AI-produced math then ask the right questions. The role of mathematician will shift from tactician to strategist.
Actually, the Main Job of the mathematicians is determining when the AI is just faking the numbers and when it is not.
Yes , many math problems is intensive labor or beyond comprehension for most of mathematicians, that will accelerate a lot the math research