Why do mathematicians want AI to do math?

An opinion from just another mathematician

Recently, OpenAI's new o3 model scored fairly highly in a complex mathematics task. Some mathematicians are quite excited about this and want to pursue AI-assisted mathematics to the edge. But you know, as a mathematician myself, I really don't understand the motivation that many mathematicians have at getting AI to do math.

To me it seems that one of the best aspects of mathematics is that it is a human endeavor that requires struggle. What would happen to the field in 50 years if AI gets so good that it can essentially do all research math extremely well and we just have to type in questions such as “classify finite simple groups”. What is the end value for us?

This photo is not only valuable for its aesthetic features, but it also represents an experience: I was once walking through the forest and I found these mushrooms on a cold day in November. Photo © Jason Polak

Even if AI will still need guidance, the idea of using it to do research by filling in large gaps of routine theorems with humans only needed to spot the most beautiful connections is contemptible. Moreover, after AI has mastered the entirety of a basic graduate school curriculum, I wonder if students themselves will feel the same magic in learning the material when an AI can do it so much better. So what is the end value?

Is it that we can now just browse through the most beautiful results and talk about them? Is it just for the sake of producing more research that still requires human help? I mean, what is the end goal of mathematics, after all? It makes no sense to transform mathematics into a product to be made on an assembly line.

As a pure mathematician myself, I always thought the goal of mathematics was to create beauty and find truths in the world that are meaningful precisely because these truths come from a journey of a human being. Yes, we have added some technical tools along the way, but pure mathematics so far has been a surprisingly old-fashioned discipline. Most of it is still done by hand, because pure math involves reasoning with concepts.

In my opinion, AI is merely about getting more final results faster, and the value of mathematics decreases significantly once it only becomes about the final result. The fact that AI has been embraced by many mathematics reflects the already deteriorating nature of the subject. It seems to me quite analogous to the situation in photography, where one can produce a photorealistic result with AI, but that result is rather meaningless because it doesn't represent a human experience.

I've read many beautiful proofs over my time, but an integral part of my enjoyment of them was that it was like a shared journey with the author. AI takes that away. Look at Lee Sedol—he quit Go because he was discouraged by the machine. He said after his loss with AlphaGo, a Go-playing AI, that

Even if I become the number one, there is an entity that cannot be defeated.

People working on these initial stages of such things must find this AI stuff exciting, but what of the mathematicians that are born in a hundred years? I suspect far fewer of them will have the same romantic awe once AI proves the Riemann hypothesis. Instead, they are more likely to say, "yeah, AI did that. Why do we have to study this, again?"

When I was a mathematics graduate student, some of my most enjoyable moments were going to other students or even professors and showing them a neat proof that I had come up with. The joy of that moment was precisely because I had done it. Often such results were just well-known facts that didn't have any proof written down that we could find. The fact that there was a mystery and that it was up to the human spirit to conquer it made it special, not the fact that the answer existed. Now instead, students will be querying ChatGPT the moment they don't understand something. It's just human nature. Yes, new things will be required from human beings, but those things will be necessarily of a more mechanical, irrelevant nature.

That we now place all the emphasis on the existence of the answer, which is the spirit of AI, saddens me. It truly shows the soulless nature of the technophiles who create AI. They have buried themselves so deep in a pile of technology that they have forgotten the meaning of being alive. Their artificial intelligence is creating a world that changes the role of human intelligence from a thing that can express beauty to an assistant on an assembly line, and that is the apex in the transformation of human beings into automatons.