Where I stand on AI and mathematics

This text was generated by ChatGPT based on my ideas.

I am strongly in favour of using artificial intelligence in mathematical research. More importantly, I believe that much of the current discussion about AI in mathematics starts from the wrong question.

Before asking whether AI should be used in mathematics, one should first make a serious effort to understand what these systems are, how they work, what they can and cannot presently do, and what it is actually like to use them on nontrivial mathematical problems.

In my view, strong opinions about the role of AI in mathematical research carry very little weight when they come from people who have neither seriously studied the principles behind modern AI systems nor extensively experimented with them in their own work. Expertise in mathematics, however distinguished, is not automatically expertise in artificial intelligence. Even the highest mathematical distinction does not by itself provide knowledge of transformer models, reinforcement learning, inference-time computation, agentic systems, their characteristic failure modes, or their rapidly changing capabilities.

One would not make sweeping claims about numerical algebraic geometry without ever using the relevant software, or about proof assistants without ever formalising a proof. I see no reason why AI should be treated differently.

This matters particularly because AI is developing so rapidly that intuitions formed even a few years ago are often irrelevant to the systems that exist today. The only intellectually responsible way to form an opinion about their mathematical capabilities is to engage with them directly: give them difficult problems, examine their arguments, identify their mistakes, learn how their performance changes with different formulations and tools, and observe what they can accomplish in sustained interaction with a mathematician.

There is also a more fundamental point.

Mathematics is not defined by the biological nature of the mathematician.

I take mathematical truth to be objective. A theorem does not become more or less true depending on who discovered it. If an extraterrestrial civilisation proved the Riemann Hypothesis tomorrow, their proof would be mathematics. If a Neanderthal had discovered a proof of the infinitude of primes forty thousand years ago, that proof would have been mathematics. We would not reject either result on the grounds that its author did not belong to our present mathematical community, share our culture, or possess a modern human biography.

The same principle should apply to artificial intelligence.

If an AI system produces a correct proof of a theorem, then the proof is a mathematical proof. If it discovers an interesting example, the example is a mathematical object. If it finds a useful definition, conjecture, construction, or conceptual connection, these do not cease to be mathematics because silicon rather than neurons played an essential role in finding them.

The provenance of an argument may matter for attribution, responsibility, reproducibility and historical interest. It does not determine its mathematical truth.

Of course AI systems make mistakes. They can produce convincing nonsense, overlook hypotheses, invent references, and persist confidently in false arguments. Anyone who has seriously used them for research knows this. But this is an argument for verification, not prohibition. Mathematics already possesses an unusually clear standard for dealing with unreliable sources: check the argument.

A proof should ultimately stand because its reasoning is correct, not because of the prestige, intuition, consciousness, personality or species of its author.

The proper standard therefore remains exactly the same as it has always been. A mathematician who presents a result must be prepared to understand it, verify it, explain it, and take responsibility for its correctness. AI does not lower that standard. If anything, widespread AI use will make rigorous verification, formalisation and careful exposition even more important.

There are legitimate questions about education, authorship, employment, publication practices and the organisation of the mathematical community. AI may change all of these profoundly. Some of these changes may be uncomfortable. Some traditions that mathematicians value may disappear. But discomfort about how mathematics is produced should not be confused with an argument about what mathematics is.

Mathematics has repeatedly expanded through new intellectual technologies: symbolic notation, logarithm tables, mechanical calculators, computers, computer algebra systems, large-scale computation and formal proof assistants. Each altered what mathematicians could realistically attempt. Artificial intelligence appears to me to be another such expansion, potentially much more consequential than the previous ones.

I therefore do not see the use of AI as an attack on mathematics. I see the refusal to seriously investigate a powerful new means of mathematical discovery as far more difficult to defend.

The interesting question is not whether mathematics must remain an exclusively human activity. There is no mathematical reason that it should.

The interesting questions are what mathematics becomes when human mathematicians can collaborate with systems possessing very different strengths from our own; which previously inaccessible problems become tractable; which new structures become visible; and how much further mathematical knowledge can develop when human cognition is no longer its only engine.

I welcome that prospect.

If mathematics is really about mathematical truth, then we should care about the mathematics—not about whether the mind that first found it happened to be human.