When AI Proves Theorems: What Is Left of the Mathematician's Profession

Google DeepMind and OpenAI have built systems that can solve olympiad-level math problems and publish original PhD-level research. The mathematical community now faces a question that seemed absurd just five years ago: what is left for humans when a machine proves theorems?

AI Takes Olympic Gold

In summer 2024, systems from Google DeepMind and OpenAI reached the level of the world's best high school mathematicians for the first time, winning gold medals at the International Mathematical Olympiad. The annual competition asks participants to solve six very hard problems in a limited time, spanning fields from number theory to combinatorics.

An even more significant result followed: DeepMind's experimental system Aletheia independently produced publishable PhD-level results in arithmetic geometry. And an OpenAI system disproved an important conjecture in combinatorial geometry, a result worthy of a leading mathematics journal. Leading specialists called it a milestone: for the first time, AI demonstrated independent, original thinking rather than mere reproduction of known methods.

At the same time, LLM-based systems learned to automatically translate human proofs into formal code for verification tools such as Lean or Isabelle. This labor-intensive process used to take months. The Gauss system independently formalized, in two weeks, the proof of the sphere-packing theorem in 24 dimensions, for which mathematician Maryna Viazovska received the Fields Medal.

Three Positions and Existential Dread

At the Heidelberg Laureate Forum in September 2025, young mathematicians confronted a frightening picture of the future. Speakers on stage forecast superhuman AI systems that would formulate conjectures, build proofs and check results without human involvement. Yang-Hui He of the London Institute for Mathematical Sciences said humans risk becoming "priests at the oracles."

"I felt that everyone around was worried; they simply hadn't thought that far ahead. It was like a big bomb," says mathematician Jessica Randall of Google Developer Groups. "We started to realize that AI is able to replace us."

Three positions have now emerged in the community:

• AI as a tool: understanding stays with the human; AI is an advanced calculator
• AI as a partner: humans and machines jointly solve problems neither could solve alone
• AI as an oracle: what matters is getting the answer, no matter how or by whom

Fields Medal winner Terence Tao, who took olympiad gold at age 11, sees the future in "big math": large-scale decentralized collaborations in which humans take the creative parts and AI handles the technical grind. "A hundred years ago, almost every paper came out with a single author. In the future, I may not even know whether it was a human or an AI."

Risks: Motivation and Atrophy

The first threat is motivation. If AI covers most of the path on its own, why spend years slowly and painfully struggling toward understanding? Fields Medal winner Akshay Venkatesh of Princeton admits: "There were times I spent years slowly working my way to understanding. If a computer takes over big chunks of that work, will you have the motivation to dive as deep?"

The second threat is the next generation. Students who skip the struggle with a problem in favor of a quick answer do not build their own mathematical intuition. Over time, mathematicians risk losing the ability to think outside the AI-based approaches they were trained in. That is why the community is already organizing workshops, writing essays and drafting rules for using AI in research and publication.

"Mathematics teaches you to think logically and rationally, and that helps in every aspect of life," says

Jessica Randall.

What This Means

AI is not "sucking the soul" out of mathematics. It is forcing mathematicians to answer honestly why they do it. The answer, it seems, is not in being the first to find a result but in the journey toward understanding itself: a joy that no algorithm can replace or automate.