In the last few months, OpenAI has stunned the mathematical community with the publication of hundreds of math findings. Many of these proofs, which span number theory, theoretical computer science, and logic, had stumped the world’s best mathematicians for decades, or centuries.
The reaction from the math community has been a mix of indignation, astonishment, and sorrow. “Tuesday night, I cried and it woke up my daughter,” said Hugo Duminil-Copin, the recipient of the 2022 Fields Medal, after OpenAI’s October release. “They have annihilated my field of research.”
“I literally cried when I spoke to Wired a few weeks ago,” said Steven Strogatz, a mathematician and author at Cornell University. “People are using language like ‘they’re strip-mining our subject’ or ‘they’re nuking the landscape.’ The feeling is disorientation. I’m discombobulated some days. I’m exhilarated some days. And there is enormous grief.”
I wanted to talk to one of the mourners to understand their technological grief. I wanted to know if theirs was a familiar case of bruised ego or disappointment—akin to, say, a boy who spends an hour building a tower out of blocks and watches his big brother smash the thing to smithereens—or something stranger and more profound.
To be honest, I also wanted to know what it might feel like for me. Today, the mathematicians are weeping, because the machine smashed their tower first. But tomorrow, it may be the physicists, the economists, the illustrators, or the writers who weep over their fallen blocks. I am not one of those AI people who believes that hundreds of millions of jobs will be wiped clean from existence in the next five years. But I am a realist who recognizes that a rapidly improving technology whose output is intelligence is destined to make violent contact with a modern sensibility that prizes human intellect and often equates it with purpose, dignity, and self-worth.
I wanted to know our future. So I called Steven Strogatz.
To prepare you for where my conversation with Steven went, I want to step back from math to ask a question that feels a bit embarrassing in its bigness: What makes humans special?
Some might say intelligence and sociality. We are the smartest creature and Aristotle’s “social animal.” But we share each quality with other species. Crows solve multistep puzzles. Ants congregate and specialize. Elephants appear to mourn their dead.
What sets humans apart is the way these two capacities multiply each other. Human intelligence is unusually suited to imitation and iteration. We imitate our parents and peers with uncanny fidelity, and then we tinker. We copy, and we create. Our sociality spreads this copying-and-tinkering process across groups and generations, so that one discovery becomes the floor for the next. Chimpanzees in West Africa have cracked nuts with stones in the same way for 4,000 years. In roughly the same period, humans went from Babylonian clay tablets to space rockets to machine intelligence. What makes us special, it would seem, is this capacity to compound. Other animals craft and converse, but only humans blend craft and conversation into a culture that builds on itself.
Science itself is both a craft and a conversation. As a craft, science is a mode of thinking; a special way of paying attention to the world; a lens that regards phenomena as something more than mere appearance. To the scientist’s eye, the universe is akin to a cosmic attic of treasure chests, each filled with hidden gemstones that can be pulled into the light if we ask the right questions, find the right keys, turn the right locks.
But science is not a solitary treasure hunt. It is a social experience, akin to a game. Like many games, it is both collaborative and adversarial. Newton famously compared his achievements to “standing on the shoulders of giants,” and a part of science is extending that human pyramid infinitely upward. Feynman preferred to describe science as “the belief in the ignorance of experts”—which is to say, a game of giant-slaying. In both cases, science is a relationship to other people. Whether we’re asking “why, professor?” or insisting “no, that’s not quite it, Mr. Big Shot,” science is not just an act of discovery but a relation to fellow discoverers. Science is a conversation.
When I called Steven to ask why he cried, he said he wanted to tell me about Archimedes.
Two thousand years ago, the Greek mathematician Archimedes calculated the area of curved objects and pinned down the value of pi by measuring the areas of dozens of tiny polygons that filled out a circle. Writing to the mathematician Eratosthenes about his work on curved shapes and infinity, he wrote that “there will be no lack of discoverers to add to the number of theorems which have fallen to our share.” To Strogatz, this sentence contains the essence of mathematics. I could hear his voice break even as he told this part of the story. “I feel like Archimedes is writing to me, or to people like me,” Strogatz said. “Archimedes is saying, ‘I can’t solve these things, but maybe you people in the future can stand on my shoulders.’ That is a very emotional, existential thing. There’s this feeling that we’re in this together, questing for something beautiful and transcendent and sublime.”
A hard-boiled tech optimist might tell Strogatz to get a grip. Math doesn’t care about your feelings, scientific reality is indifferent to your tears, and so forth. He knows it, too. “We’re being derided as guild protectors: Your guild is getting wiped out. Boo-hoo. This has happened to other people before. Suck it up.”
I know why the mathematicians weep. Yes, some are crying about bruised egos, the feeling of wasted years, a creeping sense of status obliteration, the frustration of an unfair competitor, the indignation of feeling cheated and mistreated, and uncertainty about the future. But they are also mourning, because they think something alien and disembodied is setting fire to Archimedes’ letters and dancing in the ashes. Humanity is being stripped from human science. When OpenAI publishes several hundred proofs that end several hundred treasure hunts, it is succeeding brilliantly along the craft axis of science, but it is interrupting the thousand-year conversation. The machines and their architects are saying: From here on out, it’s our turn to speak.
And what if OpenAI is right? What if we ought to treat math mostly as a quest, rather than as a conversation where feelings matter as much as discovery?