August 12, 2026
Welcome to the second episode of my Retreat in Lozère series. Today I want to talk about a question that is becoming uncomfortable for us mathematicians: what will remain when AI becomes better than us at doing mathematics?
What will remain once large language models (LLMs) become better than us at proving theorems?
This may have sounded strange a few years ago, when LLMs were sloppy and failed at high-school problems. But the line keeps moving. First high-school problems. Then undergraduate problems. Then graduate problems. And now AI is starting to help prove conjectures that humans could not solve for decades.
A recent example in my field of numerical analysis is the proof of Crouzeix’s conjecture by a neurosurgery resident, with help from GPT-5.6 Sol.
So what will be left for mathematicians?
A proof is a sequence of logical steps. It is also a social compact. When I write a proof, I do not define everything again from zero. I give enough details so that another mathematician can follow the argument. I also trust the reader to fill in standard gaps.
This is normal. Without this compact, papers would be impossible to read. Every proof would have to start from the foundations of mathematics. Nobody wants that.
But it also means that many proofs are not checked line by line. If the author or/and the institution is trusted, and if the paper looks correct at first sight, many people will believe it. This includes reviewers.
Of course, this is different for a major theorem. A very important result will be checked carefully by experts. But most papers are more modest. Only a few people will read them in detail. Often, the reviewers will not check every line either.
Sometimes I feel that academic mathematics works like an old gentlemen’s club. Once you have a seat at the table, people trust you more. Your papers look serious because your name is on them. Your mistakes are more easily forgiven. You review your peers, your peers review you, and everyone protects the same system.
Of course, trust is necessary. Mathematics cannot work without trust. But this trust can also become a privilege. It can make people accept papers they have not really read. It can make complicated writing look deep. And I think AI is about to change this.
I would bet 100 dollars that if you pick a math paper at random and run a strong model on it, it will find at least one mistake. Try me!
Most mistakes will probably be small. They can often be fixed. But sometimes the problem is more serious.
The more technical the paper is, the easier it is to make mistakes. If the writing is also hard to read, fewer people will check it carefully. So the author gets less help. The mistakes stay hidden.
I also think that, in twenty or thirty years, people may be surprised by how we used to do mathematics. They may ask how we could publish so many formal arguments without automatic assistants. They may also discover that many published proofs contained small mistakes.
Recently, I tried a small experiment. I took a very technical draft that I found almost impossible to read. To my surprise, some people around me had the opposite reaction. They said the draft was deep and impressive. But when I asked more questions, it became clear that almost nobody had really read it carefully.
Complicated writing can create the impression of depth. A dense proof can make the writer look serious. It can also make the reader feel that the result must be important. And sometimes the reader also wants to sound smart by saying that they understood it.
Then I ran a strong language model on the draft. It found many mathematical problems. Not only style issues. Some serious gaps. The main result may actually be wrong.
I will not give more details, for obvious reasons. My provocative posts are not always appreciated by the community, and this one may hurt a bit.
In the future, it may become much harder to hide weak mathematics behind complicated writing. And I think this is a good thing.
If machines become very good at checking proofs, then clear mathematical writing will matter even more.
One possible answer is formalization. We can write proofs in Lean or another proof assistant. This is extremely useful because it checks whether a statement really follows from the previous ones.
But formalization is not the same thing as understanding. A Lean proof may certify that a result is true. It does not necessarily explain why the result is natural, where the idea comes from, or how one should remember it.
This is why I think the human role may shift toward exposition. We may spend more time reading long AI-assisted proofs, understanding what they really say, and rewriting them in a form that humans can use.
A good proof is not only correct. It should also be readable. It should tell the reader where the difficulty is. It should explain the main idea before the technical details. It should make the result feel less mysterious after reading it.
Hopefully, there will still be room for completely unexpected ideas. Maybe humans will remain better at asking strange questions and making bold connections. Maybe not forever. I don't know.
But even if machines become better theorem provers, I think mathematicians will still have an important role.
We will need to digest complex proofs. We will need to shorten them, sharpen them, and explain them. We will need to find the right analogy, the right example, and the right picture.
We will also need to communicate mathematics to students and colleagues. This is not only about correctness. It is about transmitting the love of science, the taste for rigor and critical thinking, the joy of human discovery, and everything else we find beautiful in mathematical thiking.
“The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful.”
—Henri Poincaré, Science and Method