We’re gonna need a lot more mathematicians
When I was an undergraduate student, I remember talking with several students who felt that the pace at which the top students could understand new math concepts was far too fast for them. They, too, could understand the ideas, but it would take them much longer. Eventually, almost all of these students gave up their dream of pursuing research mathematics and found something else to do. I have been thinking about those students a lot in the last few days.
The research mathematics community consists largely of those of us who either rarely felt that way, or who felt it and managed to overcome it through hard work. We have had the good fortune to find a place in mathematics where we could make progress. But we are now entering a time for humility: a time when all of us are going to know what it feels like to be unable to keep up.
The AI systems I have worked with are already producing beautiful new ideas. They are doing far more than impressive calculations or quickly carrying out arguments that a strong human researcher would already understand. And we probably can’t even imagine the wonderful ideas that future systems will be capable of producing.
When we feel that we cannot keep up, will we take that as a reason to leave research mathematics, like the students I am remembering? As more of us experience this, there will undoubtedly be a temptation to draw the same conclusion as they did: If the machines can move so much faster than us, perhaps we should find something else to do.
For our community to give up the work of understanding would be a profound abdication of our responsibility to humanity. Each of us is entitled to choose a different life. The responsibility I am talking about belongs to us collectively: to build a future in which humans can understand and contribute to the discoveries that will change our world. A future with meaningful human agency.
