Twilight of the mathematicians

In 2004, during his incarceration, the Unabomber and former maths prodigy Ted Kaczynski received a letter from a high school student. The letter asked him whether mathematics is a worthwhile endeavour. He responded emphatically: “mathematics absolutely is not a worthwhile endeavour!”

In his reply, Kaczynski gave three reasons why someone might choose to study maths: for entertainment; to promote technological progress; and for the sake of their career. He described the first reason as “harmless”, while opining that we don’t refer to mere entertainment as a “worthwhile endeavour”. And he characterised the second reason—to promote technological progress—as “nothing short of criminal”. 

As for the third reason, Kaczynski noted that choosing mathematics as a career would be very risky. Why? “Within a few decades,” he explained, “machines will be developed that will be more intelligent than even the smartest human beings.” And although these machines will replace everyone eventually, “mathematicians probably will become obsolete before anyone else does, because mathematics is more amenable to computerisation”.

More than two decades later, Kaczynski’s career advice looks remarkably prescient. In July of this year, researchers working with AI were able to disprove several long-standing mathematical conjectures—to the surprise of many, who had assumed that such AI-aided discoveries were still some years away. 

Kirwin Hampshire, a mathematics graduate student, related his feelings about the matter in a piece that ended up going viral. “I am suffering a profound spiritual crisis,” he wrote. “The story of human discovery and the triumph of the human spirit will soon be excised from this discipline.” Hampshire even asked whether there’s “something evil” about what AI companies are doing.

Then in September, OpenAI announced that an internal model had solved the Navier–Stokes problem, one of seven Millennium Prize Problems selected by the Clay Mathematics Institute in 2000. 

A controversy immediately arose because Tristan Buckmaster, an NYU mathematician, had stated 12 hours earlier that he and his colleague Levent Alpöge were making significant progress on the problem, and OpenAI had recently become aware of this. What is more, Buckmaster and Alpöge had used OpenAI tools in their own research, so there was a possibility that their prompts had inadvertently helped OpenAI’s internal model find the solution. (OpenAI subsequently carried out an audit and concluded that this would have been “impossible”.)

In any case, OpenAI’s announcement was not well-received by large parts of the maths community. A statement titled ‘A Severe Misalignment of AI in Mathematics’ was signed by 25 Fields Medallists (the Fields Medal being roughly equivalent to the Nobel Prize). While acknowledging that “the mathematical capabilities of LLMs have improved dramatically”, it raised concerns about plagiarism, attribution and violation of scholarly norms.

Any suggestion that OpenAI would heed these concerns was put to rest a few weeks later when the company published a document dump of 722 maths papers, comprising solutions to hundreds of outstanding problems. Alpöge declared, “It’s obviously the most significant moment in mathematical history.” 

Other reactions were far less sanguine, however. In a statement posted on the blog of Fields Medallist Terence Tao, the Association for Human Mathematics again accused OpenAI of flouting scholarly norms. It also stated, in a remark that has since been widely mocked, “mathematicians did not ask for this work to be done”.

That was only the beginning. French mathematician Hugo Duminil-Copin (another Fields Medallist) revealed that upon reading OpenAI’s document dump, “I cried and it woke up my daughter.” Elaborating, he explained that “they wanted to prove they could massacre us” and had effectively “annihilated” his field of research. Duminil-Copin added that his students were “in a state of total panic”.

Across the pond, Cornell maths professor Steven Strogatz had a similar reaction. Appearing on the New York Times’s podcast, he broke down in tears while grappling with the question “what’s the point?” in an era where AI can do maths better than any human. 

Gauging lay reactions to these developments on social media, it’s clear that not everyone sympathises with the floundering mathematicians. One line of criticism is that new technologies always displace humans, and mathematicians are just getting a taste of what numerous other professionals have experienced throughout history—from skilled artisans to film projectionists.

Another line of criticism considers what experts in other fields would do if AI were making ground-breaking discoveries in their areas of specialty. Suppose AI found a cure for cancer. Would medical researchers put out a statement saying, “we did not ask for this work to be done”? Surely not.

As Strogatz noted on the New York Times podcast, there also seems to be an element of schadenfreude—smug satisfaction that the smartest kid in class isn’t quite so special any more.

Creators may lose their sense of purpose; others a sense of connection with their fellow humans

Personally, I am sympathetic to the mathematicians. To begin with, I understand the thrill (or, at least, satisfaction) of engaging in creative work—even if, in my own case, it’s just writing an article that someone finds useful. Second, my son happens to be obsessed with numbers, and it saddens me to know that he’ll never be able to make mathematical discoveries himself. 

Another reason I’m sympathetic to the mathematicians is that I can see the writing on the wall: AI development isn’t stopping here. More and more creative endeavours will succumb to automation. And while this may allow humans to live longer, and may leave us with more GDP to consume, it also represents something tragic. Creators may lose their sense of purpose; others a sense of connection with their fellow humans. 

Most of all, we will no longer be masters of our own destiny. For that torch will have passed to the machines.