Answers at the back of The Book

Sometime during my second year at university, learning math stopped being drudgery and started to feel like visiting fantastic places. I wandered the bonsai gardens of abstract algebra, peered into the abysses of transfinite numbers, and sailed the chaotic oceans of dynamical systems. I would never have reached these places without guides: textbooks, teachers, and fellow students. I climbed staircases polished by the feet of those who came before me.

Math is one of my biggest joys. And according to recent headlines, it’s in trouble.

In August 2026, Daniel Litt warned that OpenAI’s progress might mean the end of mathematics. On September 8th, OpenAI published a solution to the Navier-Stokes Millennium Prize Problem. On October 6th, the company released over 700 manuscripts with new mathematical results.

The response of the math community was mixed. Litt outlined a new beginning for mathematics. Tristan Buckmaster, who used llms to prove the blowup of Euler’s equations, called his experience a Deep Blue-Kasparov moment. Terence Tao, an early advocate of formalization and ai, published a declaration proclaiming A Severe Misalignment of ai in Mathematics signed by 25 Fields Medalists.

Mathematicians are worried that ai produces answers that don’t yield better understanding. Though I agree with this sentiment, I don’t think ai takes away the joy. Transforming answers into understanding is what people studying math do. Why should it matter whether answers come from the back of a textbook or an llm?

Almost all math that humans engage with is solved math. School kids memorize theorems known for millennia. Undergraduates study centuries-old theories. PhD students absorb decades of research before they can meaningfully contribute. International Mathematical Olympiad participants deal with problems that have known solutions.

Professional mathematicians love inventing neater proofs of old theorems. Early in his career, Peter Scholze distilled a 288-page proof by Michael Harris and Richard Taylor to 37 pages. The four-color theorem is settled, yet mathematicians won’t leave it alone until they have a proof that doesn’t involve computers What I would like is a proof without the use of a computer, Thomassen said. And I will never stop thinking about that.
— Gregory Barber, The Four-Color Theorem Gets a Rare New Proof. Casting old math into new shapes gives new insights, as witnessed by Bourbaki, constructivists, category theorists, and, most recently, formalization aficionados.

Knowing that the answer exists is a great motivator. I like to imagine that Fermat’s remark about his Last Theorem, I have discovered a truly marvelous proof of this, which this margin is too narrow to contain, was a clever hoax. It created an illusion that a proof was within reach, pushing generations of mathematicians to try harder. Conversely, progress on the quasi-Riemann Hypothesis stalled for a long time because mathematicians believed it required novel ideas. ai proved them wrong using their own tools contrary to what mathematicians had long expected, the proof didn’t need to introduce any new concepts—it instead unearthed hidden connections between old ones
— Konstantin Kakaes, AI Proved the Quasi-Riemann Hypothesis. What Happens Now?.

Mathematicians stay relevant even in a world where ai can conjure perfect proofs straight from The Book. Mathematics feels like an eternal space independent of human existence, but it comes to life in the minds of people, when a teacher makes a student want to explore it. People care about things that other people care about.

The wonders of math don’t become less beautiful or enjoyable just because a silicon mind found them first and sent you a selfie. You still have to climb there yourself to claim them, ideally in good company. There will never be a royal road.