OpenAI Releases Solution to Navier-Stokes Equation
OpenAI has released a solution to the Navier-Stokes equation, a Millennium Prize Problem that has remained unresolved for about 90 years. This mathematical challenge explores whether smooth three-dimensional fluid motion can experience failure (i.e., whether solutions can develop singularities in finite time).
It has been disclosed that this proof was collaboratively completed by a group of AI agents, utilizing a model that significantly surpasses the previously known GPT-6 Astra, belonging to a next-generation model that has not yet been officially released. This indicates that OpenAI possesses stronger reasoning capabilities internally than those available in public products.
The Navier-Stokes equations are a set of partial differential equations that describe the motion of viscous fluids and are widely used in fields such as aerospace, meteorology, and ocean engineering. The "existence and smoothness" problem of solutions has been listed as one of the seven Millennium Prize Problems by the Clay Mathematics Institute, with a reward of $1 million. Among the previous seven problems, only the Poincaré conjecture was proven by Russian mathematician Grigori Perelman in 2003.
OpenAI's method of announcement was to directly release the solution rather than submitting it to academic journals or preprint platforms for peer review, as is customary in the mathematics community. This release path has drawn attention, suggesting that the correctness of the proof currently relies mainly on independent verification by the mathematics community rather than confirmation through traditional peer review processes.
According to the Clay Mathematics Institute's criteria for Millennium Prize Problems, a proof typically needs to be published in an academic journal and undergo at least a two-year verification period before it can be formally recognized as a solution and awarded the prize. This means that even if OpenAI's solution is ultimately confirmed as correct, formal recognition will require a lengthy time frame.
From an industry impact perspective, if this proof is ultimately validated by the mathematics community, it will mark the first time an AI system has independently solved a top unresolved mathematical problem, potentially significantly enhancing market expectations for the reasoning capabilities of OpenAI's next-generation models. This could have a ripple effect on subsequent financing valuations, corporate client collaborations, and even the research investment directions of competitors such as Google DeepMind and Anthropic. However, until the proof is verified, the market is likely to adopt a wait-and-see attitude, with related speculation and skepticism expected to coexist.
Source: Public Information
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OpenAI's path in demonstrating its mathematical and research capabilities has been laid out previously—between 2024 and 2025, both OpenAI and its competitor Google DeepMind achieved near-gold medal levels on International Mathematical Olympiad (IMO) problems using their reasoning models. Google DeepMind's AlphaProof and AlphaGeometry have previously made phased achievements in formal mathematical proofs. OpenAI's direct challenge to the Millennium Prize Problem is a further extension of this competitive path.
OpenAI continues to invest substantial computational power and R&D resources into training next-generation models with stronger reasoning capabilities. The solution to the Navier-Stokes equation was completed by an internal model that "significantly exceeds GPT-6 Astra," indicating that the company is using top scientific problems as a litmus test to validate the capabilities of its unpublished models. Such demonstrations often serve to reinforce its narrative position in technology during negotiations with corporate clients, research institutions, and new rounds of financing.
This is similar to the logic of IBM's Deep Blue defeating world chess champion Garry Kasparov in 1997 and AlphaGo defeating Go champion Lee Sedol in 2016—leading tech companies choose the highest symbolic challenges of human intelligence as public validations of their technological capabilities. The generative AI industry is currently at a transitional point from "proving capabilities through exam-like benchmarks" to "directly tackling top scientific problems that remain unsolved by humans."
Essentially, this represents an extension of the logic of technological substitution into the realm of fundamental scientific research—if AI systems can independently complete proofs that human mathematicians have been unable to solve for 90 years, it suggests that the path to overcoming complex frontier scientific problems is shifting from "relying on the long accumulation of top human experts" to "relying on continuous investment in computational power and model capabilities." The core mechanism is that when the model's reasoning capabilities surpass a certain threshold, research processes previously seen as requiring human inspiration and intuition may also become amenable to engineering and large-scale solutions.
ABAB News · Cognitive Laws
When computational power begins to tackle Millennium Problems, the moat of human genius shows cracks.
A proof without peer review is just an unliquidated bill.
Whoever first conquers the unsolvable problems will redefine the standard of "intelligence."