Math can mean different things to different people. For mathematicians, it is an act of discovery. Many spend years trying to find new mathematical truths or ‘proofs,’ work that can underpin everything from cryptography and computing to finance and engineering.
Now AI is taking over some of that exploration and the field’s top minds are deeply uncertain about whether that is good or bad.
The answer depends on whether mathematicians can quickly establish new standards for dealing with the technology. With promising developments on that front already underway, the field could create a valuable blueprint for other forms of knowledge work.
An online post went viral recently when a math PhD student confessed to having a “spiritual crisis” over the threat of AI taking away the most meaningful part of his work. While bots discovered new proofs, he warned that mathematicians were becoming mere spectators.
Keith Carne, a retired Cambridge mathematician, says his field is particularly susceptible to AI because the technology can cross-reference many potential connections. “A computer can look at the way 20 different mathematicians have looked at a problem [and get] an advantage over those 20,” he says.
Fields Medal winner Terence Tao, one of the world’s best-known mathematicians, says that AI could shift math from “proof scarcity” to a state of “proof abundance,” essentially putting mathematicians in much the same precarious spot as writers, artists and analysts: The world is being flooded with AI-generated versions of what they normally produce, threatening to devalue the final product.
Professional mathematicians publish a vast number of papers each year, often containing new proofs; i.e., arguments showing how a math rule is true. But the most important breakthroughs unlock entirely new ways of thinking, laying paths for other mathematicians and use cases to follow.
Millennia after Euclid proved there are infinitely many prime numbers, number theory has become crucial to cryptography systems that underpin much of today’s digital economy. Work pioneered by Belgian mathematician Ingrid Daubechies in the late 1980s helped lay the blueprints for modern image compression and how smartphones store photos.
Most math does not seek a final use case but is a quest driven by human curiosity to map out the hidden patterns of the universe. Pure math might find real-world applications decades after a mathematician dies, but it does not have to.
Still, the discipline has long had a ‘publish or perish’ culture, with papers acting like currency that buys you credibility, even though the deeper goal is an increase in collective understanding—an abstract concept that is seemingly impossible to value.
That common knowledge was always the real product, while published theorems and proofs were “residue,” says Benjamin Collas, a mathematics researcher at Kyoto University. AI has simply “called the bluff” of the system, he adds; the risk now is that as software generates more mathematical knowledge, humans understand less of it.
It may take hours to produce a proof with AI, but it can take years to absorb new results into human knowledge. In that sense, the bigger risk is not AI replacing mathematicians, but that universities stop supporting the slow human work that helps them grasp those truths.
This dilemma hangs over fields like writing, where AI generates endless prose while the skill of deciding what is worth saying becomes scarcer. A law firm can churn out reams of briefs and contracts with AI, but the judgement of choosing which arguments to pursue becomes more important for humans and harder to value.
Institutions have historically paid people based on the things that AI is making cheap, from publication counts in academia to billable hours and documents in law. The silver lining to math’s spiritual crisis may be that it forces humans to realize they have been measuring value the wrong way all along.
How do you reward judgement and taste, or smart questions that open new avenues of inquiry? In math, that could mean giving more credit and funding to teaching, explaining other people’s results or building tools like shared databases and math libraries that could help other mathematicians advance, not just publish papers.
That would also reward the very thing that keeps mathematicians in the field. “Going from not understanding something to understanding it. Everything points towards one still-dark part of the landscape, and then it appears with the simplest clarity,” Collas tells me.
As machines make clever outputs ever more abundant, humans should be putting a higher price on knowing which questions are really worth asking. ©Bloomberg
The author is a Bloomberg Opinion columnist covering technology.