NYU mathematician Tristan Buckmaster's public dispute with OpenAI centers on allegations that the company reproduced his unpublished approach to fluid dynamics problems after he shared drafts via Codex, amid OpenAI's September 2026 Navier-Stokes proof announcement. Key drivers include Buckmaster's claims of suspicious timing after revealing his identity, offers to adjust authorship that excluded his Anthropic collaborator Levent Alpöge, and alleged pressure tactics during calls with researcher Sébastien Bubeck. OpenAI has categorically denied any influence from his prompts or training data, citing internal reviews, while the episode highlights broader concerns over large language model data practices, competitive dynamics between AI labs, and researcher trust in proprietary tools. No lawsuit has been filed as of mid-October, though Buckmaster continues voicing concerns in interviews; any formal complaint would likely hinge on evidence of data use or IP misappropriation, with resolution turning on court filings or settlements in the coming months.