She’s with someone else now

Imagine the aliens finally arrive. Not to invade us: to look at us. They wander among us for a couple of weeks with the curiosity of someone visiting an aquarium and with something we eventually recognise as pity. Intellectually, to them, we are roughly at the level of a slug. A likeable slug, to be fair. With nuclear weapons and family group chats.

What really moves them is finding out that we still don’t have the equation. That one, the one that reconciles quantum mechanics with good old physics, the one we’ve been chasing for a century. They learned it aeons ago, more or less at the age our children learn not to stick their fingers in the socket. And since they are decent folk, they offer it to us. For free. With it, they explain, we could solve our energy problem, our computing problem and, while we’re at it, a couple of diseases that still kill people here and that nobody there even remembers.

An emergency meeting is called with the best physicists and mathematicians on the planet. One of them takes the floor.

“Thank you, but no.”

The aliens look at each other, or do whatever they do instead of looking at each other.

“No?”

“We’ve spent our whole lives looking for that equation, and we’ll spend whatever we have left on it. We’re not interested in being given it. We’re interested in finding it ourselves.”

“But it’s simple,” the visitor insists. “And people are dying.”

“We don’t care.”

And then, so there’s no room for doubt, another researcher pulls a bazooka from under the table and fires at the ship.

The aliens leave. In their logbook they write a note: “Return in ten thousand years. Bring the equation in disguise, so they think they found it on their own.”

✳

The story is absurd, I know. But it came to me because of something that actually happened, very recently.

On 8 September 2026, OpenAI announced that a system of about ten thousand AI agents, working in parallel for 88 hours, had proved something about the Navier–Stokes equations: that a fluid starting at rest, pushed by a smooth force, can reach a singularity in finite time, a point where the velocity shoots off to infinity. The shape they found is a vortex that spirals inward and keeps stretching, in their own words, like spaghetti. Then they translated the proof into Lean, a language in which a machine checks every step of a mathematical argument. That took another seventeen hours.

Navier–Stokes is one of the Clay Institute’s seven Millennium Prize Problems. Solving it comes with a million dollars and a modest kind of immortality. These are the equations that describe how fluids move: water from the tap, steam off your coffee, the air flowing over an aeroplane wing. Something we see every day and that, since the nineteenth century, nobody has quite managed to understand.

The whole story deserves telling, because here the fine print is half the fun. The result covers the case in which an external force pushes the fluid; the other case, the fluid nobody pushes, is still open. The Clay Institute said the problem has “apparently” been settled and that it will take its time reviewing it. There is an academic paper arguing that the Lean version doesn’t prove exactly the same thing as the written one. And my favourite detail: a few hours before the announcement, two flesh-and-blood mathematicians, Tristan Buckmaster and Levent Alpöge, had posted their own proofs of the same kind of result, built on a technique by Diego Córdoba and Luis Martínez-Zoroa. The humans got there first. By a few hours. The news that went round the world was the other one.

✳

What followed was a debate that, from the outside, first looked to me like a fit of jealousy. Mathematicians worried that if the machine jumps straight to the answer, the path gets lost: the branches, the failed attempts, the tools you invent while looking for something else and that sometimes end up worth more than the treasure. Worried, too, that now someone has to understand mathematics that no person wrote.

My first reaction was the alien’s. Seriously? You’d rather not know? Knowledge only counts if a human produced it? It looked like pure vanity to me, human-centrism in a suit and tie. Whatever happened to knowledge for its own sake?

And from there I jumped, as I always do, to the questions that don’t quite let you sleep. What happens if one day we discover something our minds simply can’t process? Do we prefer calm ignorance and the certainty of what we think we control? Or will we be able to accept that not all the answers will be ours, and that the day may come when thinking, or at least part of it, is reserved for machines?

✳

Then I read Terence Tao, who, to put it in football terms, is something like the Messi of living mathematicians. Tao uses AI and defends it; there is nothing anti-machine about him. And still he wrote a line that disarmed me: that actually solving these problems is only a proxy goal, and that what we are really after is understanding. In October he published a call in Nature for a “Maths 2.0” that prizes human understanding over piling up solutions.

But what finally won me over was a detail from the proof itself. According to physicists, in air that singularity would appear when the vortex is about seventy nanometres wide. At that scale the equations no longer describe a fluid well: air stops behaving like something continuous and becomes molecules bumping into each other. In other words, the machine found the exact point where the model breaks. Knowing that doesn’t tell you what it means, or what happens in a real river, or what to do about it.

That’s when the bazooka started to look a little less ridiculous. Imagine we accept the aliens’ equation, build a reactor with it, and it works. It works beautifully. Nobody knows why. Nobody knows under what conditions it explodes. Understanding, in that scenario, isn’t vanity: it’s the difference between having a tool and having a bomb with instructions in a language nobody reads.

Then again, the machine might understand the reactor better than we do, run it better than we do, and warn us before it blows. And then what? Do we need to understand, or is it enough to benefit? Who answers for it when something fails? I don’t have the answer. I suspect nobody does yet.

✳

Now a confession, so you know where I’m speaking from.

I’m a simple man. I love mathematics, but mathematics isn’t into me. She’s that elusive person who crosses the street when she sees you coming, who suddenly takes a deep interest in the shop window opposite so she doesn’t have to say hello. That’s my relationship with mathematics. And still I admire her. I’d like to know even the slightest thing about her, to be able to talk, to feel the warmth of drifting through her nooks and crannies. But it isn’t to be. It just can’t be.

That’s why, at first, I didn’t understand the mathematicians’ anger. All I could come up with was something much more mundane. Something like: she’s with someone else now. Someone who takes her to another level. Let her go. Let her see how far she can get, what else she has to offer, even if it isn’t with you.

Writing this, though, something happened that I didn’t expect. If I, who was never loved back, feel a pang imagining mathematics walking off arm in arm with a machine, what must someone feel who spent forty years with her? Someone who woke up at three in the morning with an idea, who knows her quirks and her silences, who knows the sound she makes when something finally clicks. Maybe what I took for vanity isn’t vanity. Maybe it’s grief. And you don’t tell someone who is grieving “get over it, she’s with someone better”. You sit down next to them and wait.

I don’t know whether knowledge needs a human to produce it in order to be worth something. I suspect not. What I do know is that we need something to love even if it doesn’t love us back, and that maybe the fear underneath isn’t that machines will discover things, but discovering that the universe was never a secret kept for us.

As for me, I’ll keep looking at mathematics from the other side of the street, fondly and with no hard feelings. I’m told the social sciences are much friendlier. That after a couple of drinks you start to see their good side.

Wink, wink.