OpenAI claimed in September that one of its models had solved a mathematical problem worth one million dollars: the Navier-Stokes Problem.
The Navier-Stokes Problem is one of seven “Millennium Prize Problems” proposed by the Clay Mathematics Institute in 2000, each a famously unsolved mathematical problem with a million-dollar prize attached to finding a solution. On Sept. 8, OpenAI announced that an “internal OpenAI system” had solved the Navier-Stokes Problem — news that was followed by shock and uncertainty from mathematicians about how this solution was determined and who should get credit.
Given that artificial intelligence seems to have solved a problem that challenged human mathematicians for decades, the announcement from OpenAI raised broader questions about the role of human researchers and the future of mathematics as AI capabilities grow. To explore these questions, The Sun spoke to four Cornell professors across engineering, computer science and mathematics.
What Exactly Was Solved?
The equations at the heart of the Navier-Stokes Problem describe the flow of fluids and are used across disciplines, from predicting weather patterns to informing aircraft design. Despite these real-world applications, the Navier-Stokes Problem at the center of breaking news is framed specifically as a math problem, not a fluid mechanics problem.
Prof. Brian Kirby, mechanical engineering, explained that distinction.
“It’s a mathematical problem that’s inspired by fluid mechanics,” Kirby said. “It speaks to a physical question that one might have about fluid dynamics, but it addresses that question by going to a range that’s not physical.”
In other words, the Navier-Stokes Problem investigates whether the equations might become unreliable for predicting fluid behavior under certain conditions. Under those conditions, the equations would predict fluids moving at infinite speeds — a potential outcome of the math problem but impossible in the real world.
It remains unclear whether a solution to the Navier-Stokes problem would have any practical applications.
Prof. Donald Koch, chemical engineering, said that while no application of the solution exists at the moment, “there might be eventually.”
“For it to make an impact, there has to be understanding of this result,” Koch said. “All I know at this point is that someone at OpenAI has released 160 pages of stuff and said that this is solving the problem.”
Without a human understanding of OpenAI’s proposed solution, the possibility of the solution’s application can’t be confirmed or ruled out, he explained.
“I’m waiting for the mathematicians in the field to start giving me an understanding [of the solution], and then to transfer those ideas to engineers who will say whether those ideas can be made practical,” Koch said.
Shocking to Some, Expected to Others
While OpenAI’s announcement may have limited implications for fluid mechanics, the reaction within the mathematics community was strong.
Just three days after the announcement, 25 Fields Medalists — recipients of a highly prestigious prize for mathematical achievement — released a signed statement titled “A Severe Misalignment of AI in Mathematics.” They expressed concern over the “misalignment” of AI companies’ goals with mathematicians’ goals in solving math problems, stating that “solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight.”
The Clay Mathematics Institute released its own statement the same day, acknowledging OpenAI’s proposed solution but referring to its process for assessing solutions and awarding the Millennium Prize as “deliberately unhurried.” The Institute’s rules state that a proposed solution must be published and withstand two years of scrutiny before a prize can be awarded.
While AI is increasingly used by math researchers, the mathematician community had been unprepared for what they viewed as a rapid progression of AI’s mathematical capabilities, explained Prof. Steven Strogatz, mathematics.
Strogatz described what the math community's attitude around AI had been earlier in the year.
“Mathematicians [felt] like, ‘Well, still, it can’t really do research that competes with those of us who are near the top of the profession,’ and that was the way that people were talking about it even into the spring of this year,” Strogatz said.
For many mathematicians, the news of the Navier-Stokes Problem was a sudden revelation of just how capable AI had become. That shock has been further compounded by OpenAI’s announcement on Oct. 6 that its AI model solved hundreds of other math problems.
“What’s surprising is how fast they have gotten good,” Strogatz said.
But to Prof. John Thickstun, computer science, these developments are less surprising.
Where mathematicians might see an abrupt improvement in AI’s math prowess, AI and machine learning researchers like Thickstun offer a different perspective. For him, the Navier-Stokes solution reflects a continuous progression of AI’s capabilities, rather than a significant breakthrough.
“We’ve been seeing the development of the mathematical capabilities of these AI systems for several years now,” Thickstun said. “And to some extent, it seemed quite clear that this was a family of problems that was eminently solvable by AI.”
However, these rapid advancements are unexpected on a longer timeline, he said.
“10 years ago, I would not have predicted where AI is today, and I certainly would not have predicted the pace of where it is today,” Thickstun said.
What Remains Human in Research
In the aftermath of OpenAI’s Navier-Stokes announcement, the conversation around AI use in math began to take a new, and broader, shape.
The Fields Medalists’ declaration framed the “misalignment” of AI companies’ goals as an issue “impacting other scientific and creative professions, as well as the whole of society.” Other disciplines, not only mathematics, would have to grapple with the devaluing of human work.
For researchers, this raises a question: As AI’s capabilities continue to expand, what parts of research remain uniquely human?
Understanding, communicating and asking questions were among the responses from the four professors interviewed for this piece.
“The most important part of research is the type of questions that you ask,” Koch said. “As far as I know right now … the human beings are still asking the questions.”
Like Koch, Thickstun emphasized the role of humans in posing research questions, but he also cautioned that the ability to ask good questions is tied to the ability to understand solutions.
“Imagining a world where we’re just going to delegate all the problem-solving work to AI and no one’s going to bother understanding it,” he said. “I think then we also lose our ability to actually steer the work that's being done.”
However, Thickson believes that AI will also introduce new opportunities for humans.
“There will be kinds of AI-enabled work that we don’t really understand yet,” he said.
Kirby took a wider view of the human role in research. He pointed out that previous inventions, such as calculators and the internet, have already been incorporated into the research process without invalidating the human researcher’s role.
“Over time, we keep having things that ... were viewed as high value and achievable only by intelligent things, and then we created a tool that figured out how to do it,” he said. “Whatever is left over is the thing that we then give value to.”
The Future of Mathematics
How much is “left over” as AI advances may vary by field.
“Some aspects of math are sort of self-contained,” said Thickstun. “Empirical scientific progress involves going out in the world and doing experiments.”
He explained that math problems can be more clearly defined and isolated than problems in other disciplines, making mathematics especially compatible with AI systems. That distinction is why mathematicians like Strogatz are now grappling with a rapidly changing field.
In a recent interview with Wired about AI breakthroughs in math, Strogatz cried as he described math’s long history as a human pursuit. Discussing that moment with The Sun, he explained that he sometimes cries “about beautiful things,” math among them.
“[Math] is a very special thing in the story of our species,” Strogatz said, suggesting that the meaning of recent events in that story might depend on how you read it.
“The year 2026 is either ... an annus mirabilis, a miracle year, or annus horribilis, a horrible ... year, [for math],” he said. “I don't know which one it is.”
It’s a tension he explores in his recent New York Times op-ed and in his upcoming book, Big Math. How much of math is the solution and how much is the process? What role will humans have in math if AI can solve problems that advance the field?
Reflecting on the purpose of math, Strogatz said, “If we say [math is] an art and a science, it may be that the art side of it, as a human art, will be what we have left in the end.”
Sofia Romero is a member of the Class of 2028 studying chemical engineering in the College of Engineering. She is a staff writer for the science and technology department and can be reached at scr226@cornell.edu.
