NEW YORK, United States — OpenAI has rattled the quiet world of mathematics by using artificial intelligence to solve a major, century-old problem, raising the question of what role mathematicians will play in scientific research going forward.
Earlier this month, thousands of its AI agents worked together to solve the Navier-Stokes equations -- which generations of mathematicians have tried to tackle -- in a matter of four days.
UCLA professor Terence Tao, who has won the elite Fields Medal recognizing the world's most esteemed mathematicians, told AFP: "I am currently completely overwhelmed with an existential crisis in my field."
The recent shake-up to the field is the latest in a series of instances of AI making mathematical breakthroughs this year.
"If they did choose to study the questions that we find interesting in research, they would be very easy. They could solve those problems easily," said Steven Strogatz, a Cornell University professor for the public understanding of science and mathematics.
Antonio Auffinger, a Northwestern University math professor, said that just a year ago, "hallucinations were happening all the time," but nowadays, "AI can produce long chain arguments," without wandering off course.
In January, Elon Musk -- the world's richest man and an AI chief himself through SpaceXAI -- predicted mathematics would be "crushed," saying "math is going to be extremely trivial for AI" on a podcast.
Yet, while Northwestern University math professor Benjamin Antieau said there is "awe and amazement" for the feat, "in this particular case, they were following in the footsteps of other mathematicians who'd been developing this programmatic approach to this particular class of problems for many, many years."
In this case, the AI mainly followed two Spanish researchers, who were also the inspiration for mathematicians Tristan Buckmaster and Levent Alpoge -- who claim they came close to the solution before OpenAI's breakthrough and are now questioning if their work was plagiarized -- a charge the AI tech giant denies.
'Leaps of creativity'
That's not the only issue with OpenAI's calculations.
"The flag is captured, the goal scored, and the problem is solved; but at the cost of lessons learned, insights gained, collaborations formed, and new targets located," Tao wrote on Mastodon.
Tao was among 25 Fields Medal laureates who signed a letter last Friday to warn of a potential "destructive effect" by AI on the field of mathematics.
To boot, Stanford University professor Mohammed Abouzaid said the technology's lack of imagination is apparent.
"We are still not seeing the kind of leaps of creativity that really involve creating new mathematics, and maybe the labs are going to make that their next target, and that would be very interesting to see," Abouzaid said.
Anima Anandkumar, a Caltech professor working at the intersection of mathematics and AI, succeeded with her team in solving a simplified form of the Navier-Stokes equations (known as Euler equations) using an AI model that did not rely on prior works from researchers.
This AI was not like the ones powering ChatGPT or Claude, but rather a physics-informed neural network (PINN) model, which combines data with the laws of physics.
"So, you could think of OpenAI as being more reliant on humans than we are in some sense," she said.
However, Anandkumar notes that the model still had to be designed and tested.
Auffinger said he does not foresee a time when AI tools "would be able to provide answers for any questions that you ask" and that human mathematicians will continue to "play a huge role because it's not about how to go from point A to point B."
"It's about asking the questions that will help society as a whole," he explained.