OpenAI has unveiled its next-generation Astra model, which has achieved breakthroughs on 10 major unsolved problems in mathematics and theoretical computer science that researchers have struggled with for decades. The company compiled the AI-generated proofs into a 249-page research paper, demonstrating that artificial intelligence is beginning to participate in core scientific discovery, not just process existing knowledge.

What Are the 10 Mathematical Breakthroughs Astra Achieved?

The problems Astra solved span multiple advanced fields and represent some of the most stubborn challenges in modern mathematics. All of these problems have remained open for at least 10 years with no meaningful progress on their core conclusions, and most have research histories stretching back decades.

• Sphere Packing: Astra provided a new upper bound for sphere packing density, marking the first improvement to the general sphere packing exponent since 1978, a gap of 48 years.
• Binary and Spherical Codes: The model achieved exponential improvements on the maximum size of binary codes under given minimum distance constraints, with similar results for high-dimensional spherical codes.
• Group Theory: Astra constructed an explicit non-sofic group, disproving a long-standing conjecture that all countable groups are sofic groups, a core open problem since around 2000.
• Connes Rigidity Conjecture: The model disproved a conjecture suggesting certain groups are uniquely determined by their von Neumann algebras, proving different groups can correspond to the same algebra.
• Arithmetic Circuit Complexity: New lower bounds were established for calculating the permanent using arithmetic circuits and formulas.
• Quantum Complexity: Astra proved an exponential parallel repetition theorem for general two-player quantum games, expanding fundamental principles of classical complexity theory.
• Lattice Theory and Cryptography: The closest vector problem was proved to have polynomial approximation hardness, with implications for post-quantum cryptography security.
• Geometry and Volume: Astra determined the maximum volume a convex body with exactly one lattice point at its center can reach in any dimension.
• Ramsey Theory: A super-exponential lower bound was given for the multicolor triangle Ramsey number, solving one of mathematician Paul Erdős's numbered problems.
• Extremal Graph Theory: Results were obtained on the compactness and degeneracy conjectures in extremal graph theory, solving two more of Erdős's problems.

How Much Computing Power Did This Take?

The computational cost of finding these solutions was surprisingly modest by modern AI standards. Calculated at OpenAI's API pricing rates, the total token cost for Astra to discover all 10 solutions was approximately 2,000 US dollars, or about 13,500 Chinese yuan. This relatively low cost suggests that the breakthrough wasn't simply a matter of throwing massive computing resources at the problem, but rather the model's reasoning capability and problem-solving approach.

Why Is Sam Altman Showing This to Policymakers?

Before OpenAI publicly announced these results, CEO Sam Altman previewed Astra to key US policymakers in Washington, DC, including White House officials, cabinet members, and members of Congress. This strategic briefing suggests that OpenAI views these mathematical breakthroughs as significant enough to warrant direct engagement with government leadership, possibly to shape policy discussions around AI development and safety.

The timing and audience for this preview indicate that OpenAI is positioning Astra as evidence of AI's capacity to contribute meaningfully to fundamental science. This matters for policy discussions around AI regulation, compute allocation, and the strategic importance of advanced AI systems to national competitiveness.

How Does OpenAI Handle Authorship and Responsibility for AI-Generated Proofs?

OpenAI has taken a transparent stance on the role of AI versus human researchers in these discoveries. The company stated that while the mathematical arguments were generated entirely by the AI system, OpenAI participated in compiling the paper and verifying the proofs using Lean, a formal proof verification system. OpenAI takes responsibility for the correctness of the results, even though the AI generated the core arguments.

This approach reflects OpenAI's view that crediting AI-generated work to human authors would distort both the contribution of the AI system and the nature of original human work. The company released not only the 249-page proof paper but also a separate 62-page document explaining the problem-solving ideas behind each solution, allowing the mathematical community to understand the reasoning process.

What Does This Mean for the Future of AI in Scientific Research?

These breakthroughs demonstrate that Astra can do more than process and summarize existing knowledge. The model is beginning to participate in the core activities of scientific research: exploring solutions to open problems, generating novel mathematical arguments, and contributing to formal verification of proofs. This represents a meaningful shift in what AI systems can accomplish in academic and research contexts.

However, OpenAI acknowledges that these results still require further testing and evaluation by the mathematical community. The company is inviting mathematicians to scrutinize the proofs, place them in the context of existing research, and build new work on top of them. Whether Astra can consistently extend this capability across different scientific fields remains an open question that will be tested before the model's official release.

This announcement also builds on OpenAI's earlier work in AI-assisted mathematics. In May 2026, the company disclosed a counterexample to the Erdős distinct distances conjecture discovered by an unreleased model during evaluation, which has already prompted follow-up studies in mathematics and theoretical computer science.