The AI That Rewrote Math – and What It Means for Every Researcher

The scene evokes not an academic paper, but a nautical chart.

When Levent Alpoge posted the link to his paper on Twitter, he used no exclamation marks. He said the first two pages contain all the core construction data—anyone, if they wished, could skip the hundred‑plus pages of derivation and, starting from that data alone, independently reconstruct the entire manifold. That sentence was more of a signal than the paper itself.

Was he handing his peers a key, or was he saying: I’ve made the key; now you just go and unlock it?

Whether the six‑sphere S6S6 admits a complex structure was pinned down once in the middle of the last century by Borel and Serre: among all spheres, only S2S2 and S6S6 can even possess an almost complex structure. S2S2 is the Riemann sphere, tamed long ago. After the standard almost complex structure on S6S6 was proved non‑integrable, the remaining possibility became like a drawer opened and shut again and again. For more than half a century, the best minds went in, and the best minds came out empty‑handed. Every time someone claimed a construction, the refereeing would reach the later stages, and then some symbol, some topological invariant, some convergence condition would crack like a fine hairline fracture, and the whole wall would come down.

What is different this time, Alpoge himself said: Claude had a lot to do with it.

He said “Claude really contains multitudes,” and the precise meaning of that might be that he himself does not fully know at which step Claude made the crucial move. A construction proof of over a hundred pages, involving degenerations at three special points on a modular curve, each step requiring cross‑checks between homotopy and homology groups. This kind of work used to be years at a desk for one person. Now it is two people, one of whom is not a person.

But what truly unsettles is not that “AI can write a hundred pages.”

It is these three things, all of which are already happening.

First: mathematical discovery is turning into compute‑gacha.

Teams are already running bulk‑scan projects on open problems—thousands of questions fed in, dozens of theorems returned in one pass. The reduction conditions you spent three years thinking up might be just one line in a log file of some run. You couldn’t get your own agent to produce it; switch to a stronger model, and maybe it does. First to the finish line, not by talent, but by cluster.

Second: the journal peer‑review system is drowning.

A major result takes a year to referee. A year later, AI has gone through at least two more iterations. What you thought was “cutting‑edge” when you submitted is, by the time it appears in print, an old version that AI has strengthened countless times. Not to mention the daily flood of AI‑generated papers pouring into submission systems—editors and reviewers stand like people counting leaves in a rising river.

Third: concealment is becoming the rational choice.

If honesty means “giving co‑authorship to AI” and getting no tenure, no grants, no currency in the academic exchange system, then concealment is the optimal strategy. This is not a moral issue; it is an incentive‑structure issue. Human nature being what it is. From now on, when you read a paper, you will never be sure whether the theorem came from a human intuition or from a random seed.

If, by this point, you feel this is a lament that “mathematics is doomed,” then you—like me—have been fooled by your own inertia.

Alpoge did something no previous “AI‑assisted mathematics” case had done. He singled out the core data on the first two pages and told everyone: you don’t need to believe me; you only need to verify this construction. This is verifiability forcing a showdown with incomprehensibility—since the proof is too long for anyone to read through in full, make the construction itself a key and throw it out.

That gesture is more telling than the proof itself.

It hints at a possibility: the core competence of the future mathematician may not be “writing long proofs,” but designing a construction that can be independently verified, and convincing others to verify it. The proof can be handed to AI, but “compressing a proof into two pages of data”—that takes mathematical taste.

From this angle, the anxiety‑ridden question—“Does an AI‑produced result count as a human achievement?”—may have been the wrong question.

The right question is: If AI can solve most open problems of moderate difficulty, and the really hard nuts remain beyond human reach for a lifetime, what can mathematicians still do?

What they can do, in fact, has multiplied—it just no longer goes by the name of “problem‑solving.”

For example: ask a good question. AI is good at finding the optimal path within a given framework, but deciding “whether this framework is worth entering in the first place”—that is a human judgment. For example: cultivate mathematical taste. AI spits out a hundred theorems; which one is deep, which one is trivial, which one points to a new continent—that takes a human nose. For example: redefine “progress.” Progress used to be “proving a new theorem”; in the future it may be “translating an entire field’s problems into a format AI can handle.”

None of these produce papers—or at least, not in the current form of papers.

So what do we do?

No one knows. But at least one thing is certain: the evaluation system that runs on “number of publications” and “impact factor” is failing. Not because it is not good enough, but because what it measures is no longer scarce.

Scarcity has become something else.

It has become whether you dare, after AI hands you a perfect construction, to ask one more question: “But why does this construction look the way it does?”

It has become whether you can endure years without a result, just to re‑ask a single question—more pointed, more primal, more stubborn than the version AI could understand.

It has become two lines of data on a single page, and that sentence in a phone call: “I suggest you start from here.”

Let me end with a scene.

On the night Alpoge’s paper went up on arXiv, in some office somewhere, a graduate student opened those two pages of core data, and copied down the first homotopy‑group calculation onto scratch paper. Beside him, on another screen, an agent was still running through problems. He did not turn it off.

He picked up his pen, drew a line under that line of data.

Then he asked himself a question. Not “Is this construction correct?” but another one. That question he did not write into any paper, nor post on Twitter.

That question was his own.