XY Han

Here's a secret I've kept for 22 years: When I was in college, whenever I was assigned a difficult math problem that I couldn't solve, I Googled it to look for the answer--and when I found one, I had no qualms about copying it down in my homework. It didn't feel like cheating, because that's never been the part of math that appealed to me. When I found a solution online, I loved reading through it. Seeing the clever ideas that take down a hard problem was almost like watching a slow-mo video of Usaine Bolt running: I enjoyed the aesthetic beauty of seeing something that I could never achieve myself but which I could still appreciate. And I loved zooming in on all the details, delighting in the spectacular power on display. It never felt like cheating because my goal in math was to learn math, and reading solutions I found online helped me learn math, whereas staring at a blank page did not, and trying problems and getting them wrong was often even worse. I was not a good problem solver, so a large number of problems went nowhere for me. On the other hand, I've always been drawn to communication. So when I found a solution online, I tried to translate it into my own words, my own understanding. Was this to avoid getting caught? Perhaps. But it was more than that--I genuinely enjoyed, and learned from, the process of digesting math that was above my level and trying to put my own spin on it. I've been thinking back on this college experience because of what AI is doing to math today. So many people I see online are fretting that AI is solving hard problems, leaving it unclear what humans should do. And saying that AI is undercutting learning because to learn math one must wrestle with problems. Perhaps I'm an outlier here, but I just don't see it that way. I think that by being a poor problem solver my whole life, and by being more interested in story-telling and exposition, I have unwittingly been preparing myself for the AI math singularity for many years! Regarding teaching: I really don't think we need to solve problems to learn math--because that's never how it worked for me anyway. I think we can still teach all the beautiful concepts and theories and tell all the stories than animate math, and even show people how to do calculations and how to solve problems, but then just as I used Google 20 years ago, I think we can let our students use AI however they wish but we should have students verbally explain ideas, concepts, calculations to us--or do so in writing but without access to devices. Let students use AI the way I used Google: to show them mathematics that they can then digest and internalize. Regarding research: Nearly every paper I've published in my career has been coauthored, and in all these collaborations I was largely the one who focused on asking questions, finding examples to illustrate our ideas, and extracting a story from our results to develop into the introduction. My collaborators all helped me with these things too, but they also were way better at calculations and solving problems, so I let them take the lead on those fronts. I wouldn't have gotten anywhere in math were it not for these powerhouse collaborators. What I'm thinking now is that I can increasingly use AI for those functions, while the parts that were my focus are more solidly on the human side of things, for now at least (you can't train for them with reinforcement learning the way you can the problem solving and proving parts of math). So, maybe it's just luck, but I feel like AI is doing the parts of math that I never liked and was never good at, and letting me soar higher into the parts I love despite my limited abilities. I suspect there are plenty more people like me. We needn't be quiet--I'm not ashamed to confess my weakness and disinterest in problem solving. Perhaps by me confessing it, it will be easier for you to do so as well. Regarding the overall feeling of unease and disorientation many mathematicians have been expressing lately, here's my view (apologies in advance for a stretched metaphor). I feel like we have a map of the night sky with hundreds, perhaps thousands, of dark patches, and a telescope was just invented that we can point at these and illuminate many (but not all!) of them. Lots of people worry what will be left for astronomers to do as we've spent thousands of years mapping the cosmos. But many of the images from this telescope are difficult to interpret, so that's one thing for us to work on. And those dark spots that remain dark despite pointing the telescope at them--they take on an increased import and awe, for we must now wonder at why some remain dark while others do not. And with this more complete map of the cosmos we can work toward grander challenges such as uncovering the laws of physics holding this night sky together, contemplating the origins and future of the universe, looking for the larger patterns that we never previously had enough data for. In other words, what's left for us is all the things that I find truly exciting, much more so than the tedious work of filling in missing patches of our map. Above all, there is the incredible, beautiful, challenging, and deeply personal/human act of finding stories in all this space exploration and all this new data. What a wonderful time to be a mathematician!