OpenAI's Next Model Solves 10 Open Math Problems for $2,000 in Tokens

2. OpenAI's Next Model Solves 10 Open Math Problems for $2,000 in Tokens

On August 3, 2026, OpenAI posted that an internal version of its next major model produced 10 new results on long-standing open problems in mathematics and theoretical computer science. The compute bill: roughly $2,000 at GPT-5.6 Sol API rates. The results span sphere packing, coding theory, group theory, quantum complexity, lattice cryptography, and extremal combinatorics. Among the specific advances: establishing the existence of non-sofic groups and exponential improvements to bounds on high-dimensional sphere packing. OpenAI is releasing the manuscripts, formal Lean certificates, and reasoning walkthroughs for public examination.

The $2,000 figure is the sharpest competitive signal here. Google DeepMind's AlphaProof and AlphaGeometry have pursued formal math reasoning as a flagship capability, but neither has published a cost-per-discovery benchmark this concrete. If OpenAI's next model can close open problems in lattice cryptography and quantum complexity at that price point, the competitive frame shifts from "which model scores highest on benchmarks" to "which model can replace a postdoctoral researcher for a semester." That reframes the pricing conversation for every research institution, national lab, and defense contractor currently evaluating frontier model contracts.

The Lean certificate release matters as much as the results themselves. Formal verification lets the mathematics community check claims without trusting OpenAI's word, which lowers the adoption barrier for institutions that cannot afford reputational risk on unverified AI output. Watch whether Google DeepMind or Anthropic responds with a comparable cost-anchored disclosure, and whether any of the 10 results hold up to peer scrutiny. If they do, the argument that frontier AI accelerates foundational science stops being theoretical.

Source: OpenAI on X