AI Just Did in 6 Months What Mathematicians Couldn't Do in 50 Years. Now 25 Fields Medalists Are Begging It to Slow Down.

When AI starts clearing out mathematical conjectures

In 2026, if you only read headlines, you would think mathematics had suddenly entered harvest season.

In January, GPT-5.2 solved a 45-year-old number theory conjecture. It was the first Erdős problem verified in Lean, and Terence Tao confirmed it. In March, OpenAI's GPT-5.4, Anthropic's Claude Opus 4.6, and Google's Gemini 3.1 Pro took down the hypergraph Ramsey problem using different methods. In May, AlphaProof Nexus solved nine Erdős problems in one go. In early September, OpenAI claimed to have cracked the Navier-Stokes Millennium Prize problem. The same week, a system called Odin verified the Komlós conjecture.

By rough count, in just half a year, more than a dozen mathematical problems that had been open for decades were cleared out in a batch.

The pace is off. Terence Tao and 24 other Fields Medalists issued a joint statement slamming on the brakes.

The statement did not deny that AI is strong or useful. AI can already solve major open problems across several branches of mathematics. What the statement said was: too fast. These solutions are often announced in a hurry. There is no time to write them up as proper papers, no time to extract the new methods and new ideas, no time to cite relevant prior work.

When a human mathematician solves a conjecture, the normal cycle is years of reading the literature, years of trying directions, and then more years of writing and peer review. A Fields Medalist who takes down three major conjectures in a lifetime is considered prolific.

Now these AIs are doing in half a year what would take several generations of human mathematicians.

Tao admitted one thing. Even if the Navier-Stokes equations were solved in an ideal way, the final construction would be extremely complex, impossible for humans to verify on their own. The Lean-formalized proof file could become the largest artifact of its kind.

On September 4, Anthropic announced that Claude had completed the Lean formalization of Fermat's Last Theorem in 11 days: 13 million lines of code, 29,500 intermediate theorems, 6 billion tokens of output. Kevin Buzzard of Imperial College London, one of the reviewers, called it "an extraordinary achievement in autoformalization," with a proof that "depends on no additional assumptions beyond the axioms of mathematics."

But no human can read 13 million lines of Lean code line by line. Human verification has degenerated into running the compiler and seeing whether it errors.

Mathematics first

The reason is plain. Mathematics is the only discipline where verification cost is close to zero.

To prove a theorem, you do not need to build a particle collider, raise white mice for three years, or burn millions of dollars in reagents. You only need to design a formal verification system and let a machine check the proof line by line.

Running a Lean verification takes a few hundred lines of code and a few minutes on an ordinary server.

Next door in biology, verifying a drug's effectiveness costs millions of dollars in preclinical work alone and takes months for results. In physics, verifying a particle physics prediction costs about $1 billion a year to run CERN's Large Hadron Collider. In chemistry, synthesizing a new molecule, or screening a single candidate compound, costs thousands to tens of thousands of dollars.

AI generates ten thousand proof paths, feeds each to Lean, throws out the wrong ones, keeps the right ones, and iterates thousands of times a day.

In other disciplines, even if AI produces a brilliant hypothesis, you still have to go back to the lab and spend half a year verifying it. The entire feedback loop is too slow. It is so slow that AI's learning efficiency gets dragged to death by the response speed of the human world.

Mathematics happens to be the discipline where the fuel is free. The equipment is complete, you can train anytime, and you know immediately whether your form is correct. You do not have to wait six months to find out you trained the wrong muscle.

Mathematics is the compiler

Beyond cost-effectiveness, there is a deeper reason. Mathematics is the compiler for all the sciences.

Physical laws are written in mathematics. Quantum calculations in chemistry are done with mathematics. Protein folding prediction is essentially an optimization problem, still mathematics. Once AI trains its reasoning ability at the mathematical layer, that reasoning engine is ready to migrate upward. Add some formulas, transplant it, and it works.

Players like OpenAI and Anthropic have done the math. Every dollar spent training on mathematics produces reasoning ability that can be reused across physics, chemistry, biology, and everything upstream. Every dollar spent on experiments in those upstream disciplines verifies only one single hypothesis.

The former is platform investment. The latter is single-point expenditure.

It is like training an army. Mathematics is physical fitness and marksmanship. Once the basics are solid, conventional warfare, winter warfare, and guerrilla warfare all become easier.

Mathematical conjectures are only targets. The AI model's reasoning ability is the bullet. When the targets are used up, they can be replaced. Once the bullets are trained, they can be used anywhere.

The next disciplines

Theoretical physics and computational chemistry.

In theoretical physics, many problems are verified the same way as mathematics, by mathematical derivation rather than experiment. String theory conjectures and quantum gravity framework derivations are essentially mathematical problems wearing a physics skin. The reasoning ability AI trains in mathematics can migrate almost without friction.

Computational chemistry follows similar logic. Quantum chemistry calculations are essentially approximations for solving the Schrödinger equation, playing with partial differential equations, draped in mathematics. The PDE solving, symbolic reasoning, and optimization abilities AI trains in mathematics can be applied directly to molecular simulation, reaction path prediction, and materials design.

The roadmap is roughly this: first digest mathematics, where verification cost is zero. Then digest theoretical physics and computational chemistry, which rely heavily on mathematical derivation. Finally, the experimentally intensive disciplines.

Teams are already building fully automated labs. Robots run experiments, AI analyzes results, and the system adjusts the protocol automatically. Once that path is opened, the feedback loop in experimental science will also be compressed to a severe degree.

By then, biology, materials, and medicine, fields that still depend on wet labs today, will become battlegrounds where AI can iterate at high speed, just like mathematics. Today's mathematical verification relies on Lean. Tomorrow's experimental verification will rely on robots, microfluidics, automated platforms, and AI closed loops.

The brakes from 25 Fields Medalists

The joint statement by Terence Tao and 24 other Fields Medalists slams on the brakes in this sense. They are not opposing AI. They fear that mathematical research will become fast-food-style true-or-false judgments and lose the soil that nurtures new ideas.

When AI mass-produces true-or-false judgments at an ever-faster pace, human mathematicians have no time to digest, no time to summarize, no time to extract new methods and new ideas. Mathematics asks whether a conjecture is true. It also asks why it is true, what relation it has to other mathematical structures, and whether it can inspire new theories. If those steps are skipped, mathematics degenerates into an answer competition.

The deeper worry is transmission. What is passed between mathematicians is not only citations. It is intuition accumulated through discussion, argument, and failure between mentors and students, between peers. A young mathematician grows by solving a lighthouse problem. That path may be interrupted by AI's mass output. When even leading mathematicians cannot understand AI's intermediate steps, the model of accumulating intuition through human exploration seems set to become a bubble.

When Claude completed the Lean formalization of Fermat's Last Theorem in 11 days, producing 13 million lines of code, 29,500 intermediate theorems, and 6 billion tokens of output, human verification had already degenerated into running the compiler and seeing whether it errors. We can trust the compiler. But mathematics means more than a compiler that does not error. The meaning of mathematics lies in understanding, turning the unknown into the known, chaos into structure, intuition into proof. If that process is black-boxed, mathematics loses its meaning as understanding.

From soloist to conductor

Mathematicians will keep working, but their role will change.

The "Human-AI Mathematics Lab" newly established at MIT puts it clearly. Mathematicians will likely go from soloists to conductors. Mathematicians will no longer calculate every step themselves. They will only tell AI which direction to calculate and which lemma is worth digging into.

The way work gets done will change sharply, from manual plowing to driving a tractor. Those open conjectures will likely be turned over like plowed fields and then left behind.

When AI can handle massive derivation and verification, human judgment, taste, and sense of direction become scarcer. Asking a good question matters more than solving a known problem. Deciding which lemma is worth digging into requires more taste than proving a lemma. Outside the intermediate steps machines cannot understand, preserving a bit of human intuition may be the core value of future mathematicians.

The shift from soloist to conductor is a change in role. A soloist needs technique. A conductor needs vision. A soloist cares about every note. A conductor cares about the structure and purpose of the whole work. Future mathematicians may no longer need to prove every lemma by hand, but they need to know which lemmas are worth proving, which directions are worth exploring, and which structures are worth building.

The targets change, the bullets don't

These AI companies are not rolling through mathematics because they are bored and want to show off by solving conjectures.

Those mathematical conjectures are only targets. The AI model's reasoning ability is the bullet. When the targets are used up, they can be replaced. Once the bullets are trained, they can be used anywhere. Mathematics is the gym. Conjectures are the barbells. Today they lift Erdős problems, Ramsey problems, and the Navier-Stokes equations. Tomorrow they will use the muscle they built on physics, chemistry, biology, materials, and medicine.

Researchers who ignore these tools will be working at a different speed. The rest of the field will move on without them.

When AI becomes a general reasoning engine, human value may no longer lie in calculating every step. It may lie in asking better questions, judging what is worth digging into, and preserving a bit of human intuition, taste, and sense of direction outside the intermediate steps machines cannot understand.

The targets change. The bullets don't.

After AI finishes these conjectures, the next task is to ask new questions.

Those new questions are the part that remains ours to ask.