Cardano founder Charles Hoskinson said on Sept. 9 that artificial intelligence has advanced far beyond his earlier expectations in formal mathematics, describing AI-generated proof work as “pretty remarkable.” In a YouTube broadcast, Hoskinson discussed OpenAI’s claim that an internal system produced a solution to the Navier–Stokes Millennium Prize Problem, one of mathematics’ most famous unsolved challenges.
Hoskinson explained that he originally expected formal mathematical systems to help larger teams of mathematicians collaborate and verify human-written proofs, not for large language models to generate complete proofs themselves. “We never anticipated the extent to which AI would come in,” he said. “The idea of the AI itself would fully write the proof, it was pretty far out. LLMs really surprised us.”
The comments follow OpenAI’s Sept. 8 publication, in which the company said an internal model coordinated roughly 10,000 agents and produced a proposed Navier–Stokes solution after 88 hours. GPT-6 Astra then spent another 17 hours formalizing and checking the argument in Lean. OpenAI released an analytical paper and Lean code, and said it does not plan to seek the associated $1 million prize.
However, the Clay Mathematics Institute still lists the Navier–Stokes problem as “unsolved.” Under its rules, a solution must appear in a qualifying publication, at least two years must pass, and the work must gain general acceptance from the global mathematics community. OpenAI’s announcement therefore does not constitute immediate institutional recognition.
The announcement also drew scrutiny involving New York University mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge, who had been working on a related Euler-equation result. Buckmaster questioned whether private work entered into OpenAI’s Codex system could have contributed. “I do not know whether our data was used,” he said. OpenAI denied accessing their specific work but said it could not completely rule out the possibility that de-identified data helped improve its models.
Hoskinson argued the episode highlights research privacy risks. He warned that scholars using centralized AI services should consider whether prompts, notes and research logs remain confidential, and he used the controversy to promote private AI environments. Hoskinson has a long history in formal mathematics; in 2021, he donated $20 million to Carnegie Mellon University to establish the Hoskinson Center for Formal Mathematics. The discussion also aligns with Cardano’s broader experiments involving AI agents and the privacy-focused Midnight ecosystem.
