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Mumbai.OpenAI has claimed that its artificial intelligence technology has solved one of the toughest problems in mathematics, finding an answer to the 90-year-old Navier-Stokes problem in just 88 hours.

The Navier-Stokes problem is among seven difficult mathematical questions selected by the prestigious Clay Mathematics Institute in 2000. These questions are known as the Millennium Problems, with a $1 million prize announced for solving each of them.

Before OpenAI’s claim, only one of the seven problems had been solved. If the company’s claim is eventually established as correct, the number of solved Millennium Problems would rise to two.

First, understand the Navier-Stokes problem

Imagine spilling a glass of water on the floor. The water begins spreading in different directions. Scientists use mathematics to predict where the water will move, how fast it will travel and what its flow will look like.

The Navier-Stokes equations are used to describe the movement of fluids such as water and air. The problem is whether these equations can always provide a mathematically valid description of fluid flow, or whether there could be conditions under which the calculations break down.

The key questions are:

• Can the equations always describe fluid flow correctly?
• Can a situation arise in which the mathematical calculation stops working?

OpenAI says AI solved part of problem

OpenAI said it used a new AI model to work on the problem. The model has not been released to the public and the company has not disclosed its name.

The company described it as an internal model more capable than GPT-6 Astra, which was released on September 3, 2026. OpenAI said the AI did not work as a single system. Instead, around 10,000 AI agents were deployed, exchanging nearly 3 million messages while working on the problem.

However, OpenAI says the AI proved two of the four key parts associated with the problem. This means the entire problem has not been solved. The company also said it would not claim the $1 million prize.

Research theft allegations add controversy

The claim has also triggered a dispute involving mathematicians Tristan Buckmaster and Levent Alpoge, who were working on the same problem and had used AI tools such as OpenAI’s Codex during their research.

They obtained some new results in August but had not made their research public at the time. Buckmaster said he learnt on September 3 that information connected with his research had reached OpenAI, which raised his suspicion.

OpenAI, however, said it had not seen the two mathematicians’ work until it was made public.

Seven Millennium Problems remain major challenges

The seven Millennium Problems cover some of the deepest questions in mathematics:

• Riemann Hypothesis — concerns prime numbers and whether there is a hidden pattern governing their distribution. It has remained unsolved since 1859.
• P vs NP — asks whether problems whose answers can be checked quickly can also be solved quickly by computers. It has remained unsolved since 1971.
• Navier-Stokes Problem — concerns the mathematical description of how water, air and other fluids flow. OpenAI claims progress on it in 2026.
• Yang-Mills and Mass Gap — concerns tiny particles and their energy, including whether there is a fixed minimum gap between certain energy levels. It remains unsolved.

Poincare Conjecture was solved two decades ago

• Hodge Conjecture — asks whether complex mathematical shapes can be explained using simpler mathematical equations. It remains unsolved.
• Birch and Swinnerton-Dyer Conjecture — concerns special mathematical equations and whether their solutions can be determined from their properties. It remains unsolved.
• Poincare Conjecture — concerns three-dimensional shapes and asks whether a three-dimensional object without holes is essentially the same as a three-dimensional sphere.

The Poincare Conjecture was proposed by French mathematician Henri Poincare in 1904. Russian mathematician Grigori Perelman solved it in 2002-03. Although a $1 million prize was announced for the solution, Perelman declined the money.

AI is changing the way maths gets solved

This is not the first time AI has claimed to solve a major mathematical problem. In January, OpenAI said it had solved a mathematical problem posed by Hungarian mathematician Paul Erdos.

AI systems are trained on thousands of mathematical problems and can try different approaches, learning from successful and unsuccessful attempts. Reinforcement learning allows AI to gradually develop methods that increase the chances of finding solutions to difficult problems.

Mathematicians also raise concerns about AI

Many mathematicians are excited by AI’s ability to explore mathematical problems at unprecedented speed, but some have also raised concerns about what this could mean for human understanding.

Mathematician Terence Tao has argued that solving a difficult mathematical problem oneself is important because the process helps mathematicians learn and develop deeper understanding.

He compared it with going to a gym. If a machine lifts a 100-kg weight for you, the weight has been lifted, but your own strength has not increased.

The same concern applies to mathematics. If AI begins solving difficult problems on its own and humans only receive the answers, people could eventually lose some of their ability to understand mathematics and solve problems independently.

At the same time, AI’s biggest advantage is speed. A human could take a very long time to test thousands of possible approaches, while AI can examine a huge number of possibilities in a much shorter period.

Tao has compared this to finding a hidden waterfall in a forest. If a person finds the route themselves, the journey teaches them how to navigate the forest. But if a machine finds the route and simply gives them directions, they can reach the waterfall without understanding how the path was discovered.