Computers have long been the servants of mathematics. Now, according to applied mathematician Steven Strogatz, they have become something stranger: oracles that give correct answers without being able to say how they got them. Strogatz and his Cornell colleague Alex Townsend lay out that argument in their new book, Big Math: The Hidden Codes That Run Our World, and they discussed it at length in an interview with Ars Technica.

The book covers what the authors call “big math,” a term Strogatz said is defined by scale relative to the human mind. A problem can be big even when the numbers are small, he said, if it involves more variables than a person can hold in their head. The lunar module’s guidance computer, for example, had to track only about 20 or 30 variables at a time to steer the craft to the Moon’s surface. No person could do that work unaided.

Strogatz said the book also looks at problems that involve nonlinearity, which he described as the real dividing line. Linear problems can be scaled to enormous size and remain manageable. Nonlinear ones are harder. “If they’re non-linear, you don’t have any hope of dealing with them with pure math,” he said. “You can do them with computers.”

From servant to scout to oracle

Strogatz traced the change in how mathematicians have used machines. For decades, he said, computers were tools that extended human reach, no more threatening than a microscope or telescope. They became electronic computers in the 1950s, and they did exactly what they were told.

The first big shift came when computers started to explore. Strogatz pointed to the Fermi-Pasta-Ulam numerical experiment, in which Mary Tsingou carried out the calculations. The researchers did not know what the machine would show them. Instead of an expected slide into disorder, the system produced a strange echo, with about 98 percent of the energy returning to its original mode. That result helped lead to soliton theory, and human researchers were able to build theories to explain what the computer had found.

Can AI give mathematicians answers they cannot explain?

Strogatz said that ability to keep up is now fading. “What’s different now is that it’s going from servant to scout to oracle, where it’s showing us things that we don’t understand and it’s not articulate enough to explain itself. It seems to be right.” He cited Google Translate, which translates well but has not, as far as anyone can tell, uncovered new principles of linguistics. He also cited AlphaFold, which has solved far more protein structures than before without, in Strogatz’s view, revealing new physics or chemistry. “It just recognized patterns, but it can’t tell us how it’s doing it.”

Could mathematics become a model-driven field like medicine?

Strogatz acknowledged that some systems may stay opaque because of human limits. If that happens, he said, mathematics could start to resemble medicine or engineering. Doctors do not need to know exactly how aspirin works to use it, he noted, and drugs are tested through controlled studies and trials. “If the AI is an oracle, you can still check it by seeing how often it is right.”

What mathematicians may lose

Strogatz said the loss is real. Pure mathematics has long prided itself on proof and certainty. Euclid’s proofs, written around 300 B.C., still hold, he noted, while little from the science or medicine of that era remains accepted. Treating mathematics as a model-driven field like science would be, in his words, a big sacrifice for the purest mathematicians.

Interviewers asked about the emotional side, including the “aha!” moment that comes when a pattern suddenly becomes clear. Strogatz said he has been through what he jokingly called the five stages of grief, and he said younger people feel it more sharply. A 25-year-old who has dreamed of becoming a mathematician may now hear that the subject is over, he said, and some people in the tech community have been cruel about it.

What could mathematicians lose as AI advances?

Strogatz also pointed to the value of struggle, the companionship of working alongside people who love the same problems, and the personal style that mathematicians bring to their work. He said he has cried during several interviews over the past few months. Still, he said, it is not yet clear what will be lost. AI could become a very effective explainer, he said, and people who enjoy math as a puzzle or a workout will still find things to discover, even if the largest discoveries go to machines.

Strogatz described the moment as both hopeful and confusing. He noted that AI systems are not yet good at asking questions, though he thinks they could be trained to do so. Teaching new doctoral students to ask good questions, he said, has always been one of the hardest parts of their training. The book ends with Goethe’s Faust, which Strogatz read as a warning that striving to build something larger than ourselves is “still a very dangerous game that we have chosen to play.”

Cet article a été rédigé avec l'assistance de l'IA.
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