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“I learned how to have fun doing math research when I was a teenager, and that fun continued until my 20s. When I got the option to do a Ph.D, I wanted to keep doing it, because I have so much fun doing math research.
I think the passion and beauty that I see in mathematics is in its simplicity to express ideas that initially appear extremely complicated. I think mathematics is full of philosophical lessons, if you listen carefully. Lessons such as there’s real value in perceiving a problem from a range of perspectives and considering all vantage points before coming to a solution. There’s real value in translating the same idea into a bunch of languages to understand its nuances in the different ways that it can be spoken. There’s real value in building bridges between seemingly far away ideas, bridges across which you can communicate insights from one field into another. The fact that math teaches you these lessons I find beautiful.
The problem is that AI is detracting from the human experience of mathematics, and that makes it simply less fun.”
romain speciel
One of the things I’ve particularly loved about mathematics research at the higher level is its human aspect. It’s social among very anti-social people, because you need to ask each other for help. We never charge each other for the service of teaching ideas to one another. We never have, and as humans we never will.
The problem is that AI is detracting from the human experience of mathematics, and that makes it simply less fun. Here’s the problem: current AI tools know what 99.9% of what most mathematicians know, and so that means that I am no longer incentivized to ask questions to other mathematicians. It’s much, much easier for me to simply talk to the AI to get my answer.
We often say mathematics is not a spectator sport. You can’t watch someone do a proof; you have to at some point struggle through it yourself. If an AI is solving the problems for you and you watch the AI solve it, it’s hard to get a real understanding of yourself, because you don’t struggle through the difficulties. You don’t understand all of the routes that don’t lead you to the correct solution.
There are some things that we actually do want to struggle with because we enjoy it. I don’t drive to the top of a mountain – I hike. There’s no point in getting dropped off there by a helicopter. That’s not the point at all.
On the other hand, you can ask the question, why do we care about having any sort of human understanding at all? If the machines can give us the answers we need, if we’re really looking at mathematics from a practical perspective, eventually it’ll get applied in physics and engineering to solve some real-world problems. What does it matter if a mathematician understands it at all?
So, yes, something is lost when the AI solves math problems. There is no longer a human that understands the proof, but I don’t think that was ever something practical to begin with. The real question we should be asking is, as a society, are we angled on practicality uniquely, or do other things matter as well?
And for mathematicians, that’s how they approach theorems a lot of the time. Having the solution be parachuted from an alien civilization or from OpenAI feels kind of the same way. No one actually hiked to the mountain, you just teleported to the top, and what we were doing to begin with was actually enjoying the hike.”
Romain Speciel is a sixth-year mathematics Ph.D. student at Stanford University.
This profile is one of nineteen featured in the “Humans in an age of AI” portrait series. See more profiles here.
