OpenAI Reveals Astra After Solving 10 Longstanding Math Problems

OpenAI has revealed Astra, an upcoming frontier model designed to succeed the GPT-5.6 series. An internal version reportedly generated new results for ten longstanding problems in mathematics and theoretical computer science.

OpenAI selected problems that had seen little or no progress on their central results for at least ten years. The company has now released supporting materials so outside researchers can examine the model’s work.

Astra produced the results at a relatively low cost

OpenAI says Astra did not require unusually large amounts of computing power to produce the discoveries.

The combined token usage for all ten solutions would have cost approximately $2,000 at GPT-5.6 Sol API prices. After identifying the solutions, Astra also helped transform the mathematical arguments into research manuscripts.

The reported costs suggest that advanced mathematical research may not always require massive inference budgets. However, independent researchers still need to verify the results and assess their significance.

OpenAI used Lean to verify Astra’s proofs

Astra formalized every mathematical argument using Lean, a programming language and theorem prover designed for checking formal proofs.

The resulting proof certificates allow computers to verify each logical step. This process reduces reliance on human review alone and can help researchers identify hidden gaps or incorrect assumptions.

OpenAI is publishing the research manuscripts, Lean proofs, and model-generated explanations for independent examination. Mathematicians can therefore review both the written arguments and their machine-checkable versions.

Researchers will now review Astra’s work

OpenAI is asking the mathematics community to examine the proofs independently and determine the importance of each result.

Researchers will need to confirm that the formal proofs match the intended mathematical claims. They will also assess whether Astra introduced genuinely useful techniques that could lead to further discoveries.

The results could provide an early indication of how frontier AI models may support advanced mathematical research. Their wider importance will depend on independent verification and the usefulness of the methods behind them.

In other OpenAI news, the company recently dropped GPT-5.6 API prices and released new voice transcription models.