Mathematician says AI is shifting from scout to oracle in math

Mathematics is entering a phase in which AI delivers results that humans cannot fully explain, according to applied mathematician Steven Strogatz. He made the case in an interview with Ars Technica about Big Math: The Hidden Codes That Run Our World, a new book he wrote with Cornell colleague Alex Townsend.

Strogatz told the outlet that he and Townsend define big math relative to what a human mind can handle. It covers problems with billions of variables or parameters, from medical imaging to spaceflight to the largest language models, which he said now commonly have trillions of parameters. He added that problems which are linear can be scaled up and remain tractable, while large non-linear problems are largely out of reach for rigorous proof, even though computers can work on them.

To explain the philosophical shift, Strogatz described three roles for computers. For decades they were servants that did exactly what people programmed, much like a microscope or telescope extends the senses. In the 1950s they became scouts, sent into unexplored mathematical territory. His example was the Fermi-Pasta-Ulam-Tsingou numerical experiment, in which a simulation of vibrating atomic bonds did not decay into disorder as expected. About 98 percent of the energy returned to the original mode, a result that helped lead to soliton theory.

In that case, he said, humans could still follow the computer and build theories to make sense of what it had found. The newest stage, in his view, is the oracle. AI systems show results that appear to be correct, but they cannot explain themselves, and people do not understand them either.

Strogatz offered two examples. Machine translation performs well, he said, but has not given linguists new principles, or at least cannot tell them what any such principles are. AlphaFold, whose creators won a Nobel Prize in chemistry, can now solve far more protein structures than before. Yet that came from pattern recognition rather than from new physics or chemistry. "It's going to get worse," he said of the gap between output and understanding.

The interviewer also raised concerns in the field after OpenAI released 722 AI-generated math papers, which Ars described as dubbed the "mathocalypse." Strogatz did not address that release in detail in the portion of the interview provided. He did discuss Stephen Wolfram's idea of computational irreducibility, the view that much of nature has no simple, insightful theory and can only be studied by running simulations. Strogatz suggested science may have restricted itself to systems transparent enough for human insight, as in the old story of a person searching for lost keys under a lamppost.

The book's closing passage, quoted by Ars, argues that human beings must insist knowledge serves something larger than itself. Strogatz and Townsend write that the task of this century may be to let power grow "without losing our soul."