Levent Alpöge (Anthropic) and Tristan Buckmaster (NYU) independently produced a resolution of the forced Euler regularity problem using an internal Anthropic model, announced the same day as OpenAI's Navier–Stokes post. Per Buckmaster's statement, the pair had worked on related problems for nearly a year with Claude and Codex (primarily GPT-5.6 Sol), reaching a breakthrough on 2026-08-15; he alleges OpenAI's first prompt on the problem was sent only after information about their work had reached OpenAI, and that OpenAI would not answer whether its model was trained on their Codex drafts. OpenAI acknowledges their priority on forced Euler, says it offered a joint announcement, that no user data was accessed, but cannot rule out that de-identified product-usage data informed model improvements; the two proofs cover different Euler variants (forced vs. unforced). Buckmaster also reports Alpöge was told he could not co-author an OpenAI paper given the OpenAI–Anthropic competitive relationship. The statement's HN thread (2,035 pts) outdrew the announcement itself.
Alpöge and Buckmaster resolve the forced Euler problem with an Anthropic internal model
Levent Alpöge (Anthropic) and Tristan Buckmaster (NYU) independently produced a resolution of the forced Euler regularity problem using an internal Anthropic model, announced the same day as OpenAI's Navier–Stokes post. Per Buckmaster's statement, the pair had worked on related problems for nearly a year with Claude and Codex (primarily GPT-5.6 Sol), reaching a breakthrough on 2026-08-15; he alleges OpenAI's first prompt on the problem was sent only after information about their work had reached OpenAI, and that OpenAI would not answer whether its model was trained on their Codex drafts. OpenAI acknowledges their priority on forced Euler, says it offered a joint announcement, that no user data was accessed, but cannot rule out that de-identified product-usage data informed model improvements; the two proofs cover different Euler variants (forced vs. unforced). Buckmaster also reports Alpöge was told he could not co-author an OpenAI paper given the OpenAI–Anthropic competitive relationship. The statement's HN thread (2,035 pts) outdrew the announcement itself.
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What this means for you
Two readings matter. Technically, a second lab has now driven Millennium-scale mathematics with an internal model, and the collaboration pattern — a year of guided Codex/Claude work preceding the breakthrough — is itself a replicable research workflow. Institutionally, the dispute exposes the questions every agent-platform vendor must eventually answer: whether user sessions can inform competing internal efforts, and how rival-lab contributors are credited. Willison's framing is the sharpest: could your own partial solution, produced in someone's product, help a later model finish it first?
Public artifacts and validated results are different.
The recorded fact is the public work and its artifacts. Author-reported outcomes do not establish independent reproduction. Next checks include usable code, task conditions and third-party validation.
Evidence & related material
Technical details & scores
| Result | resolution of the forced Euler regularity problem; distinct from OpenAI's unforced-Euler and Navier–Stokes results |
|---|---|
| Tooling | a year of work with Claude and Codex (primarily GPT-5.6 Sol), breakthrough 2026-08-15; final resolution with an internal Anthropic model |
| Dispute | Buckmaster alleges OpenAI's first problem prompt came after their work was known to OpenAI; OpenAI declines to say whether the internal model was trained on their Codex drafts, says no user data accessed, cannot rule out de-identified usage data helping model improvement; Alpöge told co-authorship was blocked by the OpenAI–Anthropic competitive relationship |
| Reaction | Buckmaster statement HN thread 2,035 pts / 826 comments (9/8), larger than the announcement thread |