Anthropic claims its AI matched half of OpenAI’s math breakthroughs in 24 hours

OpenAI announced on Saturday that an internal version of its next major AI model, called Astra, has solved or made substantial progress on 10 long-standing open problems in mathematics and theoretical computer science. Within 24 hours, Anthropic researcher Levent Alpöge fired back, claiming he used the publicly available Claude Fable to independently solve five of the same problems.

The exchange marks the latest and perhaps most striking escalation in the rivalry between the two leading AI companies, with advanced mathematical reasoning becoming a new battleground.

Astra's Mathematical Claims

In a blog post titled "Ten advances in mathematics and theoretical computer science," OpenAI said the problems had "seen no progress on the main result for at least a decade." The results span high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, lattice cryptography, and extremal combinatorics.indianexpress+1

Among the claimed achievements, Astra proved that non-sofic groups exist — a question open since 1999 — and solved Alain Connes's rigidity conjecture and Ehrhart's volume conjecture. OpenAI said the proofs were formalized in Lean 4 and that it would publish the model's narration of its reasoning process. The company estimated that reproducing the work would cost roughly $2,000 at GPT-5.6 Sol API rates.openai+3

OpenAI provided no technical details about Astra's architecture or release timeline. Mathematician Terence Tao noted the problems, while hard, were "solvable with known techniques" rather than the deepest unsolved questions in mathematics.instagram

Anthropic's Swift Response

Shortly after the announcement, Alpöge posted on X that Claude Fable had solved five of the same problems in under 24 hours, working autonomously with generic prompts and no internet access. The problems he cited include arithmetic circuit complexity, quantum parallel repetition, and the closest vector problem.moneycontrol+2

Alpöge is no newcomer to AI-assisted mathematics. In July, the former Harvard valedictorian used Claude Fable 5 to disprove the 87-year-old Jacobian conjecture during the World Cup final, a result that has since been independently verified. Anthropic has not published a formal paper verifying the latest claims, and OpenAI has not responded publicly.fortune+2

A New Front in the AI Race

OpenAI acknowledged that AI systems capable of contributing to mathematical research raise unresolved questions about authorship. "Claiming human authorship for a proof generated entirely by an AI system would misrepresent both the system's contribution and human intellectual work," the company wrote. It called on the broader academic community to help develop attribution norms.indianexpress

The back-and-forth suggests that frontier AI models from multiple companies are converging on research-level mathematical capability — and that the next phase of competition may be measured not in chatbot benchmarks but in theorems.