The mathematician who left mathematics. What will we leave behind?

On July 23, in Philadelphia, Jacob Tsimerman received the Fields Medal, the most important award in mathematics. It has been granted every four years, for ninety years now, to at most four people under the age of forty. Tsimerman is thirty-eight, and he is the first mathematician from a Canadian university to win it.

That same day, at the press conference, he announced that he was taking a leave of absence from the University of Toronto to join OpenAI's safety team.

He did not resign in outrage. He did not denounce anything. He simply explained, with the calm that comes from conviction, that the mathematical career as we know it will not go on existing in its current form. That he believes that within two years artificial intelligence will be better than mathematicians at doing mathematics. And that, for that reason, he has stopped taking on doctoral students: he doesn't know what profession he would be preparing them for.

Striking, isn't it? A man receives the highest honor in his discipline and uses the microphone to say that his discipline, as he lived it, is coming to an end. A good thought to chew on before we head off on vacation.

Why mathematics falls first

The explanation Tsimerman gives is brutally simple: mathematics is a closed system. It needs no laboratory, no reagents, no clinical trials, no permits, no waiting six months for a culture to grow. It is the epitome of abstraction: all it needs is thought. And anything that needs only thought advances at the speed at which thought can be produced... which is precisely the variable we have set out to scale with hundreds of billions of dollars.

Anyone who has followed this series will recognize the argument, because it already showed up here through another door. When I wrote about the killer app, I pointed out that AI shines at programming precisely because a programming language is a formal system designed to eliminate ambiguity: each instruction means one thing only, and the result is verified in binary fashion, it compiles or it doesn't. On that terrain, "probable" and "correct" almost coincide, and that is why the machine works so well.

A mathematical proof is the extreme case of the same thing. It is either valid or it isn't. There are no nuances, no cultural context, no interpretation. Formal verification systems also make it possible to check correctness without a human having to read anything. Mathematics does not fall because it is hard, which it is, but because it is the only territory where the machine can know whether it got it right without asking anyone.

And the evidence is mounting very fast. In May, an OpenAI model disproved the unit distance conjecture, a result that specialists consider publishable in top-tier journals. Quite a contrast with just a year ago, when these same systems got stuck on high school olympiad problems. This August, the conversation among mathematicians is no longer whether AI is useful, but what is left to do once it produces proofs at a pace no human can read, let alone understand.

That, by the way, is a problem almost nobody has framed in business terms: what happens when the capacity to generate knowledge far outstrips the capacity to absorb it. But that's a whole other article.

First, Manhattan

Leonard Cohen sang it in 1988 with a coldness that still sends a shiver down the spine: first we take Manhattan, then we take Berlin. It is, almost word for word, the story the industry wants to sell us. That the fall of mathematics is merely the prologue, and that everything else will follow under its own weight, in order, without resistance and with no date up for negotiation.

But before buying the ticket, it's worth looking at the map. Mathematics is Manhattan: compact territory, explicit rules, a verifiable victory beyond any possible dispute.

Berlin is something else. Berlin is law, medicine, negotiation, people management. Places where there is no compiler to tell you whether you got it right, where the criterion of truth is supplied by human beings who disagree with one another, and where the gap between "probable" and "correct" opens up again until it becomes dangerous. I have spent months arguing in this series that this gap is architectural and that scaling does not close it.

So yes: Manhattan has fallen, and it would be foolish to deny it. But it does not follow that Berlin is two years away. What follows, rather, is that the order of conquest is not arbitrary, and that figuring out exactly where your profession sits on the map is probably the most profitable exercise you can do this summer.

How, to our way of thinking

When I read the story, the first stanza of Manrique's Coplas came to mind, I'm not quite sure why. The bit that goes: "How swiftly pleasure flies away / how, once remembered, / it brings pain. / How, to our way of thinking, / any time gone by / was better."

Manrique wrote that around 1476, as a tribute to his dead father. Five and a half centuries later we still quote him because he names something permanent: the feeling that what is leaving was better than what is coming. And in Tsimerman's case, the nostalgia is well-founded. He knows with mathematical precision what is being lost.

What is being lost is a way of life that consisted of spending years, sometimes decades, sitting in front of a problem that probably had no solution, failing systematically until you developed an intuition for where the difficulties lay. He tells how his thesis advisor gave him impossible problems, not so that he would solve them, but so that he would learn to recognize what makes a hard problem hard. Tsimerman would come back every few months saying he had made no progress, and his advisor would reply "great" and hand him another one.

That is what disappears. Not a job but a way of being in the world. Tsimerman can afford to miss it because he practiced it for twenty years at the highest level a living human being can practice it. His Fields Medal attests to that.

But not all nostalgia is equally legitimate.

The other nostalgia

Sabina wrote that there is no worse nostalgia than longing for what was never lost. It is one of those lines that gets lodged in your soul for thirty years without your ever quite applying it to yourself.

For months I have been listening to professionals from every sector lament what artificial intelligence is going to take from them. And in a considerable share of cases, what they describe as their loss is something that, if they were honest with themselves, they would admit they never actually had.

The executive who is outraged because AI writes better than he does has spent fifteen years signing texts drafted for him by someone on his team. The consultant who fears being replaced spent his days repackaging other people's frameworks in his corporate template. The lawyer who complains because the machine summarizes contracts never read the full ones the junior prepared for him. The analyst who champions his irreplaceable judgment built presentations by copying whatever industry report was at hand. None of them is losing a capability. They are losing the alibi that allowed them not to exercise it. And that is embarrassing to admit to oneself.

I have written here before that for years I have been asking my students, instead of an essay, for the URL of their conversation with artificial intelligence. Because everything shows up in that conversation: who has outsourced their brain and who has used the tool to think better. What I didn't say then is that the exercise works just as well outside the classroom. And that much of the anxiety surrounding this technology does not stem from the fear of being replaced, but from the fear that a machine will expose how little there was underneath our position.

It is a noisier nostalgia than Tsimerman's, and considerably less elegant. Above all because it almost always comes wrapped in humanist rhetoric: the spark, the intuition, what only a person can bring. All of that exists, of course. But the spark does not arise by spontaneous generation. Nor in empty, comfortably fed heads. It is the result of having accumulated, over years, enough material for two distant ideas to touch. Whoever has not done that work has no spark to lose. At most, they have access to the same tools as everyone else.

The one who did have something to lose

What is remarkable about Tsimerman's case is not his diagnosis. It is what he does with it.

He could have settled in. He is thirty-eight, has the medal in his pocket, a tenured post at a major university and professional credit for three decades. Nobody would have blamed him for giving lectures on the beauty of mathematics while the world changed around him.

Instead, he decided that, if the most important problem he sees ahead lies in these systems doing things nobody asked them to do, the reasonable thing is to go and work on that problem. Last year he co-wrote with Andrew Critch a paper that systematically classifies the pathways through which artificial intelligence could contribute to human extinction. His argument for choosing safety over capabilities is admirably cold-blooded: capabilities are advancing perfectly well without him, and in safety there is far more work to be done and far fewer people.

That is not nostalgia. That is aim. It is someone who, having every reason in the world to lament, decides that lamenting is not among the useful options.

There is a biographical detail I find revealing. Besides being a mathematician, Tsimerman has been doing improv theater for fifteen years, and he has written a musical. He says improv is the opposite of mathematics: one is about losing control and the other about gaining it. And that he applies a three-second rule in his life: you have three seconds to decide, or you accept that you've chickened out.

I don't know whether that rule is a good guide for running a company. I suspect not. But it is a little enviable to see how many people have already spent three years chickening out.

The August question

His mother, a high school math teacher, told him when he was little something he admits he didn't take too seriously: that he didn't have to be a mathematician just because he was good at it.

Several decades later, the line has turned out to be more than motherly advice. It has become the exact description of the problem in front of us. Because throughout our entire professional lives we have taken for granted that what we were good at was what we had to do, and that doing it for long enough amounted to a career. Now it turns out that the first part of that equation may stop being true with twenty-four months' notice.

So I'm going on vacation with this question hovering around, and I leave it to whoever wants to take it along: when someone says they fear what artificial intelligence is going to take from them, are they talking about something they ever actually had?

And if the answer is yes, what are you doing about it, apart from saying so?

This article is part of a series that began with "Less Wood, It's War!", and continues with "The end of the token open bar, or something more serious?", "What if the Genesis Mission were a huge mistake?", "Where's the pea?", "From packet to token, and back to square one", "Investing in typewriters", "Will the "killer app" arrive in time?", "Are they making room for us?", "Spot the 8 differences", "Will AI end up in a backpack?", "Will Nvidia be the new Kodak?", "Is CUDA Nvidia's magic potion?", "Neither conscience nor consciousness", "Neither Hawking nor Einstein. The true origin of intelligence". To be continued...