When AI proves theorems: what will be left for mathematicians of their profession

Google DeepMind and OpenAI have created systems capable of solving International Math Olympiad-level problems and publishing original PhD-level research. The mathematical community now faces a question that seemed absurd just five years ago: what will be left for people when machines prove theorems?

AI Takes Olympic Gold

In the summer of 2024, Google DeepMind and OpenAI systems for the first time reached the level of the world's best high school mathematics students, winning gold medals at the International Mathematical Olympiad. This annual competition asks participants to solve six extremely difficult problems within a limited time, spanning various fields—from number theory to combinatorics. The next step was an even more significant result: DeepMind's experimental Aletheia system independently obtained publishable PhD-level results in arithmetic geometry. The OpenAI system refuted an important hypothesis in combinatorial geometry—a result worthy of a leading mathematics journal. Leading experts called this a milestone: AI demonstrated independent and original thinking for the first time, rather than simply reproducing known methods.

In parallel, LLM systems learned to automatically translate human proofs into formal code for verification tools such as Lean or Isabelle. This labor-intensive process previously took months of work. The Gauss system independently formalized in two weeks a proof of the sphere packing theorem in 24-dimensional space, for which mathematician Marina Viazovska received the Fields Medal.

Three Positions and Existential Dread

At the Heidelberg Laureate Forum in September 2025, young mathematicians confronted a frightening vision of the future. The stage featured predictions about superhuman AI systems that will formulate hypotheses, construct proofs, and verify results without human participation. Yang-Hui He from the London Institute of Mathematical Sciences stated: people risk becoming "priests attending oracles." "I felt that everyone around me was worried—they simply hadn't thought that far ahead. It was like a big bomb," says mathematician Jessica Randall from Google Developer Groups. "We began to realize that AI could replace us."

Three positions have emerged in the community today:

• AI as a tool: understanding remains with humans, AI is an advanced calculator
• AI as a partner: humans and machines solve together tasks inaccessible to each individually
• AI as an oracle: the main thing is to get an answer, regardless of how or by whom

Fields Medallist Terence Tao, who won Olympic gold at age 11, sees the future in "big mathematics"—large-scale decentralized collaborations where people take the creative parts and AI handles technical routine. "A hundred years ago, almost every paper came out with a single author. In the future, I might not even know whether it's a person or AI."

Risks: Motivation and Atrophy

The first threat is motivation. If AI completes most of the journey independently, why spend years on a slow, painful struggle toward understanding? Fields Medallist Akshay Venkatesh from Princeton admits: "There were times I spent years slowly building toward understanding. If a computer takes on large chunks of this work—will you have the motivation to immerse yourself just as deeply?" The second threat is the next generation. Students who skip the struggle with a problem in favor of a quick answer don't build their own mathematical intuition. Over time, mathematicians risk forgetting how to think beyond the AI approaches they were trained in.

That's why the community is already organizing workshops, writing essays, and developing rules for AI use in research and publications.

"Mathematics teaches us to think logically and rationally—this helps in all aspects of life," says

Jessica Randall.

What This Means

AI doesn't "suck the soul" out of mathematics—it forces mathematicians to honestly answer why they engage in it. It seems the answer lies not in being first to find a result, but in the path to understanding itself—in the joy that no algorithm can replace or automate.