Artificial Intelligence Puts Mathematicians in the Face of an "Existential Crisis"

OpenAI has made waves in the world of mathematics after its artificial intelligence program successfully solved a major mathematical problem that had remained unsolved for a century, a landmark achievement that raises questions about the role of mathematicians in scientific research.

Terence Tao, who won the Fields Medal—the equivalent of the Nobel Prize in mathematics—in 2006 and is one of the most influential figures in the field, described his state to the French news agency AFP, saying: “I have been deeply disturbed by an existential crisis in my field.”

In less than four days, in early September, an advanced AI system from OpenAI solved the Navier-Stokes equations, which were formulated in their final form in 1845 and have been tackled by generations of mathematicians.

Since the beginning of the year, leading AI systems have successfully refuted several famous mathematical theories, but this achievement is considered an “earthquake” in the field.

Cornell University professor Stephen Strogatz believes that “if these systems choose to study the problems that matter to us in our research, they may be able to solve those problems with ease.”

Antonio J. Karcher, a mathematics professor at Northwestern University, recalls that just one year ago, there were “persistent hallucinations” in the reasoning processes of AI models, even the most advanced ones.

He adds, “Today, AI can construct long chains of logical arguments” without going off track or producing theories that resemble delirium.

Although researchers have relied on this technology for some time, OpenAI’s approach differs in that it gives the AI the initiative and full control over the process.

In January, Elon Musk predicted that AI would sweep through the field of mathematics and bring about a radical transformation within a year.

Musk, who is the head of xAI (later known as SpaceX AI), affirmed that “mathematics will become extremely routine for AI.”

Despite feeling “shock and awe,” Northwestern University mathematics professor Benjamin Antieo emphasizes that OpenAI’s AI system did not start from scratch, but rather “followed in the footsteps of other mathematicians who had been developing this approach to solve the problem for years.”

This primarily refers to two Spanish researchers who also inspired the work: Tristan Bachmester and Levant Albuji. The latter two confirm that they were on the verge of finding a solution before OpenAI, and they question whether their work was subject to intellectual theft, a claim denied by the California-based startup.

Stanford University professor Mohamed Abu Zaid believes that “this expands the scope of what we can prove, but it does not increase the range of ideas we can explore.”

In a related development, Anima Anandkumar, a professor at the California Institute of Technology (Caltech) specializing in a field that combines mathematics and artificial intelligence, and her team successfully solved a simplified version of the Navier-Stokes equations (known as the Euler equations) using an AI model that did not rely on prior work.

This model was not similar to the systems that power ChatGPT or Claude, but was a model known as a “PINN” (Physics-Informed Neural Network) that integrates data with the laws of physics.

Nevertheless, the researcher notes that the team had to create a “design” to “make the model work,” emphasizing that “this requires a great deal of human creativity.”

She adds, “In the future, artificial intelligence may gain greater precision and the ability to grasp subtle nuances, but there will remain a vast range of possibilities available to humans that AI cannot access.”

On Friday, 25 Fields Medalists (recipients of mathematics’ highest honor) warned of the potentially “devastating” impact of artificial intelligence on mathematical research.

While Tao views the objective as the only thing that matters to the model, he writes, “The objective has been achieved and the problem solved, but what is missing are the lessons learned, new horizons, forms of collaboration, and the setting of new goals.”

Antonio Ophoven clarifies that “even if AI could answer all questions, mathematicians would still play a crucial role, because the issue is not merely about knowing how to get from point A to point B, but about posing questions that benefit society as a whole.”