AI-era researchers ask whether math is obsolete | Science

In just a few days, AI has turned mathematics upside-down. First, OpenAI disproved a conjecture of Paul Erdős, a renowned 20^th century Hungarian mathematician, which no one had been able to crack since 1946. Soon after, Google DeepMind announced the solution to nine problems, including two that have gone unsolved for 50 years. These incidents are two examples of the impact AI is having on a field as specialized as mathematics.

“It’s a considerable mathematical achievement,” says Jeremy Avigad, a professor of philosophy and mathematics at Carnegie Mellon University, in respect to OpenAI’s take on Erdős. “In contrast to previous results, this problem is well-known, and its solution could be published in the world’s best journals. I predict it will not be the last case, and that we are at a real inflection point,” say Javier Gómez Serrano, a Brown University professor who a year ago teamed up with Google to solve the complex Navier-Stokes equations.

Amid the subsequent uproar, mathematicians have reacted to AI in a similar way to many professions: with fear, indifference, and by writing a manifesto, which in this case is called the Leiden Declaration on Artificial Intelligence and Mathematics, and recommends disclosing the use of AI in scientific articles and confirming their human authorship.

As in many other professions today, across the globe, mathematicians are analyzing the true value of humanity in the advancement of mathematics. One might think that such a refined profession would be safe from AI, but it turns out that may not be the case. In recent weeks, it’s been easy to find articles and posts with titles like “Will AI ruin Mathematics?,” “The meaning of doing mathematics,” and “Is Mathematics Obsolete?”

Underneath those headlines, the conversation is more complex. How could it be that a technology like AI, which until only recently was making errors in simple calculations, is suddenly solving problems that have been untouchable for decades? Is this the end of mathematics as a discipline? There is a general sense that it is not. “Mathematics, both as a discipline and a scientific community, will be affected by these changes,” says Petra Schwer, professor at Heidelberg University in Germany. “It’s hard to say where it is going. But there will continue to be a place for mathematicians. At the end of the day, AI is a tool. Mathematicians have already been threatened by the calculator, the computer, and computer algebra systems,” she adds.

“With these tools, someone with good mathematical training and fluency can get ahead of another who does not use them,” says Gómez Serrano. “But critical thought is necessary. Someone who has the tool without the training would produce trash they won’t even be able to detect, and that is probably what will happen in great quantities. The advantage is not knowing how to use AI; it’s knowing how to use it and being able to tell when it is lying to you,” he adds. Those in charge of creating AI systems know their current limitations, says Demis Hassabis, founder of DeepMind: “Today’s systems are extremely far from what would be a true invention or someone like [Indian mathematician] Ramanujan, no matter how many Erdős conjectures they solve.”

Attention-grabbing headlines

The work of OpenAI, Google, and other startups dedicated to mathematics focuses on solving famous problems, precisely because their solution makes bigger splashes. Each attention-grabbing headline implies attention and potential new investment. In addition to the big companies, there is a startup group centered on models to solve mathematical problems. “It solves mathematics, it solves everything,” is the motto of one of these firms. “Mathematical research can be competitive, but these communities have solid ethical norms,” says Avigad. “It is unacceptable to use someone’s work and ideas without giving them credit, or to work on a collaborative project and then take credit for the result. In academia, skipping over those norms can endanger one’s reputation. In business, it’s harder to follow those norms,” he adds.

As in other professions, being a mathematician consists of much more than solving a half-century-old Erdős problem. “It’s important to consider ‘mathematics’ and ‘mathematicians’ separately,” says Seewoo Lee, a researcher at University of California, Berkeley. “AI helps mathematics progress more quickly. For mathematicians, that’s not always a comfortable advance. The public tends to imagine the mathematician as someone who solves difficult problems, so headlines like ‘AI has solved an old conjecture’ makes people imagine that AI ‘will solve all mathematics.’ That image is erroneous,” he adds. A mathematician constructs theory: they find appropriate definitions and theorems that allow them to solve difficult problems, and help to explain the world around us.

Nor has the pace of advancements and discoveries taken off in the sector. “‘Taken off’ seems too dramatic for the moment. Recently, we have seen some new solutions with AI, but it’s still not a huge leap,” says Thomas Bloom, a mathematician at the University of Manchester who is familiar with the impact of AI, given that he runs a website dedicated to the thousand-plus problems that Erdős posited over the course of his life. It is a living catalogue, and a good barometer for measuring the advancements of AI.

If there has been any growth, it’s still somewhat haphazard and of poor quality, says Sam Livingstone, a mathematician from University College London. “I have heard that the most prestigious journals are seeing an increase of around 20% to 30% in submissions in comparison to two years ago, and that they suspect it could be AI-related, but also that the majority of those additional submissions are not considered good studies.”

For now, AI has yet to arrive at the offices of all renowned mathematicians. “I know several mathematicians who have never touched it,” says Livingstone. “Some use it a lot and others, not at all. Mathematicians, generally speaking, are a conservative group. That could change if it becomes clear that AI is accelerating mathematical discovery, but for the moment that’s the state of things,” he says.

If that acceleration does take place — which could happen if models continue gaining ground — mathematicians will become part of a debate that is plaguing most academic and professional disciplines: what crumbs will be left for humans? Will mathematicians be the new chess players, for whom AI is unbeatable, or will it be like other fields in which AI serves as a sophisticated assistant? “There are far more mathematicians than chess players,” says Avigad. “Mathematics is not just a game; it is an important part of how we give meaning to the world, we reason and discuss with one another. I don’t think that will change. AI should help us to do all those things, but we are the ones who decide how to use it and what to do with it,” he says.

That adaptation will be evident in education as well, according to Gómez Serrano. “It’s important to develop competencies related to modern mathematics in the AI era, and that students be trained in these new ways to work and take advantage of its great potential. For example, connecting apparently distant fields within the world of mathematics.”

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