By Audrey Im, J.D. Class of 2029
On September 8, 2026, OpenAI claimed a solution to the Navier-Stokes existence and smoothness problem, one of seven Millennium Prize Problems widely regarded as among the most consequential open questions in mathematics, each of which carries a $1 million prize. The frontier lab leveraged roughly 10,000 parallel agents of an internal model “significantly more capable than GPT‑6 Astra” to produce the proof that the Navier-Stokes equations, under a smooth external force, can develop a singularity in finite time, a “blowup” counterexample so to speak.
OpenAI’s announcement quickly became embroiled in much controversy over its potential appropriation of the NYU mathematics professor Tristan Buckmaster’s and Anthropic staff member Levent Alpöge’s work on the closely related forced Euler questions. On September 7, 2026, Buckmaster and Alpöge announced their blowup result on the forced Euler equations (a frictionless case of Navier-Stokes and a widely recognized milestone toward the full solution), employing both Anthropic’s models and OpenAI’s Codex. Hours before OpenAI’s September 8th announcement, Buckmaster raised concerns that his unpublished work may have influenced OpenAI’s internal model, thereby shaping the prompts that influenced the agents in OpenAI’s own solution.
Though OpenAI denies these claims, such claims are indeed plausible, especially given the mounting prevalence of AI in various research domains during the pre-publication phase. While AI proves to be an academic boon, propelling revolutionary advancements from protein structure prediction with Google Deepmind’s AlphaFold to global weather forecasting enhancements with GraphCast, researchers’ growing reliance on AI tools funnels a vast corpus of nonpublic intellectual work into AI platforms, entangling research endeavours with issues of confidentiality, data retention, and training processes. Additionally, copyright concerns also may exist as frontier labs grapple with the risks of infringing academic output in internal R&D contexts. Unfortunately, current laws afford the academic community few concrete solutions to questions of either platform liability or intellectual property.
On Researcher Confidentiality and Legal Recourse
AI’s relative nascence breeds uncertainty around platform accountability and confidentiality as researchers entrust more of their work into these commercial models, raising the question of whether an AI company owes any fiduciary duty (such as a duty of loyalty that emerges from an undertaking to act on the researcher’s behalf) to the researcher upon receipt of unpublished work through its platform. An organic solution is to first review the platform’s terms of service, confidentiality representations, or privacy policies. Alternatively, if the researcher’s work derives economic value from its secrecy and reasonable measures are taken by the researcher to protect such findings, trade secret law may prove useful in recovering damages.
However, the aforementioned protections are not wholly comprehensive. Typically, the terms of service are drafted by the platform itself and may not afford a scholar sufficient recourse, perhaps even permitting retention of user inputs for internal use. Similarly, a company’s privacy policies may not constitute contractual obligations, with some courts equating them as mere “notices.” Nevertheless, the absence of such contractual obligations does not necessarily preclude regulatory liability, since misleading privacy representations may amount to deceptive practices enforceable by the FTC. In addition, if the submission of research to a lab’s AI model is interpreted as a forfeiture of secrecy, then trade secret law may not apply.
The Shortfalls of Current Copyright Law
Presently, copyright law protects “original works of authorship” but not the underlying concepts, methods, or ideas that constitute the substance of the resulting scholarship. The result is only a partial solution, one that would be insufficient to protect researchers who lack protectable expression of their work and simply possess the general methodologies or discoveries instead. In the event that a researcher does possess protectable expression, the extent of protection is nebulous at best, with some courts even finding that the use of copyrighted works for model training is fair use. Unfortunately, patent law, too, does little to address this copyright gap, since mathematical formulas and abstract ideas more broadly are generally excluded from patentability.
Conclusion
Though the recent Navier-Stokes controversy and other similar disputes may ultimately reveal no misuse on the part of OpenAI or the other frontier labs, these instances still reveal the open and looming question of platform liability.
Terms and policies are established by the platforms themselves, which may curiously omit consumer protections or expressly allow the internal usage of prompt inputs. Meanwhile, trade secret law, copyright law, and other existing doctrines are simply ill-equipped for closing this gap. Trade secret law generally requires researchers to establish misappropriation of such secrets, and copyright law generally protects the original expression of an idea, while leaving underlying ideas as well as discoveries simply unprotected. Taken together, these limitations may render researchers without clear recourse to determine whether their unpublished work has been used in an internal lab’s operations or to recover damage for such use, especially when a frontier lab’s terms expressly permit it. As with the many other legal concerns involving AI, it becomes apparent that the research community, and society, generally speaking, require rules with more clarity to protect academia and preserve innovation for the AI-driven discoveries to come.