OpenAI AI system solves Navier-Stokes problem in four days, sparking debate

OpenAI’s announcement that its artificial intelligence system has solved the Navier-Stokes problem has reignited debate in the mathematics community about the future of scientific research and the role of mathematicians. The AI system completed the task in less than four days in early September, while 25 Fields Medalists warned on Friday of the potentially "devastating impact" of AI on mathematical research.

The development prompted Terence Tao, the 2006 Fields Medal recipient and one of the most influential figures in mathematics, to describe the event as causing him "severe distress due to an existential crisis in my field," highlighting the profound shift AI capabilities are bringing to complex mathematical problem-solving.

In early September, OpenAI’s advanced AI system managed to solve the Navier-Stokes equation, whose final form was established in 1845 and which had resisted generations of mathematicians’ efforts for decades.

Steven Strogatz, a professor at Cornell University, said the development could greatly expand AI’s ability to tackle mathematical problems, stating: "If these systems choose to study the questions we care about in our research, they might be able to solve them easily."

The debate now extends beyond whether AI can reach solutions, to how it works and what role mathematicians will have in the future. Antonio Auffinger, a mathematics professor at Northwestern University, noted that just a year ago, even the most advanced AI models suffered from "persistent hallucinations" in their reasoning. "Today, AI can construct long chains of logical arguments," he said, without veering off track or producing nonsensical theories.

Although researchers have long relied on such technology, OpenAI’s approach is different in that its system gave AI full initiative and control over the process.

In January, Elon Musk predicted that AI would sweep through mathematics and bring about radical change within a year, saying, "Mathematics will become extremely trivial for AI." He made the comment in reference to his company xAI, later known as Space xAI.

However, the achievement has not ended debate over the origin of the ideas that led to the solution. Benjamin Antieuh, a mathematics professor at Northwestern University, said that while he was "shocked and amazed," OpenAI’s system did not start from scratch but "followed in the footsteps of other mathematicians who had been developing this approach for years."

This discussion is closely linked to two Spanish researchers, Tristan Buckmaster and Levent Alboji, who also inspired this direction. The pair claim they were close to a solution before OpenAI and question whether their work was plagiarized, a claim the California-based startup denies.

Other researchers offer a different perspective on the relationship between AI and human creativity. Stanford University professor Mohamed Abouzaid said, "This expands the range of what we can prove, but it does not increase the scope of ideas we can explore," adding, "We do not see a creative leap that brings something fundamentally new to mathematics."

Similarly, Caltech professor Anima Anandkumar and her team succeeded in solving a simplified version of the Navier-Stokes equations, known as the Euler equations, using an AI model that did not rely on previous work.

The model used was not the type powering ChatGPT or Claude, but rather a "physics-informed neural network," which combines data with the laws of physics.

Anandkumar said, "You could say OpenAI relied on humans more than we did," explaining that her team had to "design" the model to make it work, which she said "requires a great deal of human creativity."

She added that AI may in the future gain greater accuracy and the ability to grasp fine details, but believes there will always be a wide range of possibilities open to humans that AI cannot reach.

As the debate intensifies, 25 Fields Medalists—the highest honor in mathematics—warned on Friday of a potentially "devastating impact" of AI on mathematical research.

Terence Tao, writing on Mastodon, called for using AI to assist mathematicians rather than replacing them, emphasizing that achieving the goal alone is not enough in mathematical research.

Tao said: "The goal has been achieved and the problem solved, but what is missing are the lessons learned, new horizons, forms of collaboration, and setting new goals."

Antonio Auffinger believes mathematicians will remain essential even if AI can answer every question, explaining: "Even if AI could answer all questions, mathematicians would still play a vital role, because it is not just about getting from point A to point B, but about asking the questions that benefit society as a whole."