Math Had Heroes Because Ideas Had to Fit in One Mind

In the middle of an essay about machines solving proofs that had stumped professionals for years, writer Noah Smith pauses on a stranger question, why mathematics ever needed heroes at all. His answer, in his words, is that "every idea that got added to the collective ultimately had to be comprehensible by a single human being."

Smith argues that most research was never heroic. It was incremental, often wrong, and yet the enterprise as a whole groped toward truth. In his metaphor, individual people were what technologists now call edge compute, small devices that gather slightly new data and report it back. The central store they reported to, he writes, was not a computer but society itself, the network of universities, companies, governments, and conversations that spread knowledge and coordinated action.

That system, Smith argues, had a narrow channel. A theorem had to be learnable by one graduate student, or teachable by one professor to another. It therefore had to be first conceivable by one person, too. The people who could conceive the nearly inconceivable widened that channel a little, and we called them heroes.

His examples are the familiar giants of mathematical theory. As Smith puts it, "Isaac Newton invented calculus and classical mechanics all by himself." His next case is Grigori Perelman, the Russian mathematician who proved the Poincaré conjecture: "Grigori Perelman, sitting in his little room in Russia, solved a famous math problem that had bedeviled the entire profession for decades." Then, Smith writes, "Andrew Wiles did something similar a generation earlier," referring to Wiles, the mathematician who proved Fermat's Last Theorem after centuries of failed attempts.

Artificial intelligence, in Smith's view, replaces that central store rather than any single worker. It trains on all accumulated human knowledge, so writing a paper or a memo is now, whether intended or not, writing for the AIs. He compares the change to derivatives trading, once done through private phone deals between traders over complex products like CDOs, bundles of mortgage type debt that helped trigger the 2008 crisis, then moved after the crash and Dodd-Frank legislation to central clearinghouses, single hubs that guarantee and track trades. An AI world-mind, he argues, has no single brain limit, so the bottlenecks the great mathematicians once widened have been removed, or will be soon.