Artificial intelligence confronts mathematicians with an "existential crisis.

 

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

Terence Tao, the 2006 Fields Medal winner (the equivalent of the Nobel Prize in mathematics) and one of the most influential figures in the field, described his reaction to AFP, saying, "I've been shaken by an existential crisis in my field."

In less than four days, at the beginning of September, OpenAI's advanced AI system solved the Navier-Stokes equation, whose final form was established in 1845—a problem that had eluded generations of mathematicians.

Since the beginning of the year, major AI systems have successfully challenged several well-known mathematical theories, but this achievement is considered a "seismic shift" in the field.

Cornell University professor Stephen Strogatz believes that "if these systems choose to study the problems that interest us in our research, they might be able to solve those problems easily."

Northwestern University mathematics professor Antonio Ovinger recalls that just a year ago, even the most sophisticated AI models exhibited "constant hallucinations" in their reasoning.

He adds, "Today, AI can formulate long chains of logical arguments" without going off-topic or producing theories that resemble delirium.

While researchers have long relied on this technology, OpenAI's approach differs in that it gives AI the initiative and complete control over the process.

Despite feeling "shocked and amazed," Northwestern University mathematics professor Benjamin Antoh emphasizes that OpenAI's AI system didn't start from scratch, but rather "followed in the footsteps of other mathematicians who have been developing this approach to solve the problem for years."

The reference here is primarily to two Spanish researchers who were also inspired: Tristan Backmaster and Levent Albuque. The latter two maintain that they were close to achieving the solution before OpenAI and question whether their work was plagiarized, an allegation the California-based startup denies.

- Human Creativity -

"This expands the scope of what we can prove, but it doesn't increase the range of ideas we can explore," says Stanford University professor Mohamed Abou-Zeid.

"We don't see a creative leap that will add anything new to mathematics," he adds.

Meanwhile, Anima Anandkumar, a professor at the California Institute of Technology (Caltech) specializing in the intersection of mathematics and artificial intelligence, and her team have successfully solved a simplified version of the Navier-Stokes equations (also known as Euler equations) using an AI model that was not based on previous work.

This model wasn't like those running ChatGPT or Cloud, but rather a model known as PINN (Physics-Informed Neural Network), which integrates data with the laws of physics.

"OpenAI relied more on humans than we did," she explains.

However, the researcher points out that the team had to "design" the model to "make it work," emphasizing that "this requires a great deal of human creativity."

She adds, "In the future, AI may become more precise and capable of grasping finer details, but there will still be a vast range of possibilities available to humans that AI cannot access."

On Friday, 25 Fields Medalists (mathematicians' highest award) warned of a potentially "devastating impact" of AI on mathematical research.

On the social networking site Mastodon, Terence Tao called for AI to be used to serve mathematicians, rather than trying to replace one another.

While Tao believes the goal is the only thing that matters to the model, he writes, "The goal has been achieved and the problem solved, but what's missing are the lessons learned, new perspectives, forms of collaboration, and the setting of new goals."

Antonio Ofinger explains that "even if artificial intelligence could answer all the questions, mathematicians would still have an important role to play; because the issue isn't simply about knowing how to get from point A to point B, but about asking questions that will benefit society as a whole."