OpenAI Solved 10 Math Mysteries. The Price Per Proof? Two Thousand Dollars

A goldmine in tokens

On August 1, 2026, OpenAI announced a major milestone in automated reasoning. Their internal model, described as the upcoming Astra, solved ten mathematical and cryptographic problems where human research had stalled for over a decade. The team published complete formal proofs in the Lean 4 language in a GitHub repository. But the most intriguing metric is the cost of discovery: OpenAI claims they spent less than $2,000 worth of compute on each successful solution.

What marketing isn't saying aloud

The $2,000 figure sounds mesmerizingly cheap for a decade-old problem. However, OpenAI's report elegantly glosses over how many other problems the model hallucinated or failed on without yielding any result. The published amount represents successful hits converted to the API prices of the GPT-5.6 Sol model at the time, not the research department's total budget for the project. Furthermore, the supplementary PDF where the model "reconstructs" its thought process was generated ex post from the original hidden reasoning logs.

The limits of a formalized world

The model's ability to spit out a valid Lean 4 certificate is a massive step for rigorous mathematics. But does this mean AI can solve anything? No. Mathematics and cryptography provide deterministic rules of the game where a solution is either demonstrably right or demonstrably wrong. In applied real-world problems lacking a clear objective function, the model has nothing to lean on. Astra excels here because it can endlessly validate its intermediate steps against a mathematical simulator.

Eyes on scientific adoption

If a machine can verifiably push the boundaries of a field for a fraction of an academic's salary, it will change grant policies. The proof won't be more OpenAI press releases, but whether universities and research centers begin routinely redirecting budgets from human post-doc positions into massive API budgets for o-series and Astra models.

Lilith's verdict

Two thousand dollars for a math breakthrough looks amazing until you realize that outside a safe simulator, the model burns money without a compass.