What should we tell our students?

[This is a guest post by Álvaro Lozano-Robledo. This blog post was initially written in a different file format and converted using AI. — T.] TL;DR: Keep calm and carry on studying math. I would like to give Terry my heartfelt thanks for giving me the opportunity to contribute a post to his blog. After giving much thought to what topic I should write about to maximize impact, I decided to take this opportunity to reach out to the students: particularly to those undergraduate and graduate students who just a few months ago were dreaming of an academic career in mathematics, but their dreams may now seem distant and, for some, apparently impossible to ever become a reality. This post was inspired by a message (quoted below in its entirety, with permission) that I received from a student desperately looking for advice and guidance. This is not the only such message I have received (and I suspect that many of us are receiving many similar requests), but it is perhaps the most heartfelt, and the one that has moved me the most. Please also note the urgency of the message. Students are making decisions now. Hey Prof, I’ve been watching your videos for a while now as a pure math undergraduate who once wanted to pursue a career in math academia. I know you probably have been getting a lot of questions regarding this matter, but I am just completely at an utter loss regarding my career trajectory, and even further, the meaning of life at this point. (I do realize a lot of people have it much worse than I do). I know you have been making a lot of videos lately with the new LLM progress updates, so I thought you might be the appropriate person to reach out to and get a slightly more structured answer regarding this matter. So, to cut to the chase, what I really want to know is: will math academia be big enough and accessible enough for anyone with sheer passion (despite not being the brightest mind in the field) to pursue a career in, or will it inevitably shrink such that it will only really be accessible to the brightest minds? (I do realize the “brightest minds” that I am mentioning here is not well-defined, and in a sense, I am taking it as a hypothesis that this is someone who is “smarter than me”). My second question is, will AI within 5–10 years surpass humans in being able to do pure math research? I’ve just really been lost for a couple of months now and lost in life completely. I don’t mean to make your day more depressing; sorry if I come off in any way of that sort. I would appreciate any advice. The advances in LLMs are disrupting almost all aspects of academic research and education in mathematics and, while there are many aspects that concern me, the one single issue that worries me the most is the very real possibility that we are about to lose an entire generation of mathematicians. Many students are asking themselves whether going for a PhD in math is the right career move at this time. Many of them just a year ago were headed to grad school in mathematics, but they are now changing their mind, and think that a different career (as far from math as Law School) may be the best path given the threat that AI may completely alter the academic math landscape in the coming months. The questions students are worrying about are as follows: Will AI surpass the mathematical research ability of any human? Will research mathematicians become `professional prompters’ and interpreters of LLM output? Will only the `brightest minds’ be able to meaningfully contribute to research mathematics? Will mathematicians be employable? Will mathematicians be needed? Should I pursue a PhD in math at this time? In this essay I will try to address these questions to the best of my ability, but will start with two disclaimers, followed by a brief summary of my own outlook. Disclaimer 1. My answers may “age like milk,” as YouTube commenters love to quip on older videos. I can live with that, because this post expresses how I and many of us in the community around me feel today. Things can change quickly, though (see Disclaimer 2). I also want to acknowledge my privileged point of view as a tenured professor in mathematics — the situation can look much more troubling from the point of view of the job insecurity of a very early-career mathematician. Disclaimer 2. No one has the answers at this time. I want to make clear from the start that no one can know with certainty the answers to any of the questions posed above: not any particular Fields medalist, not any given mathematician, not any particularly vociferous AI expert, and not the frontier model companies. And if someone is telling you with extraordinary confidence what the future holds, then I would immediately distrust the motives of their conviction (anecdotically, almost anyone on X.com that predicts the triumph of AI and the demise of the mathematics profession, is either a self-proclaimed “AI expert” or works for an AI startup). No one has a clear picture because development of LLMs has been so fast (and opaque) that it is almost impossible to predict what is to come. A good piece of advice is to ask the same questions to many people, to hear a (hopefully balanced) range of opinions. To that end, I am collecting interviews with mathematicians in what I call the “Human Mathematicians in the Age of AI” video project. I encourage you to listen to the interviews for some fantastic points. For the record: I do not have the answers either, but I am hopeful and excited for the future. I will explain why below. Who is controlling the narrative about LLMs in math? Overall, the mathematical community’s reactions to the advances in AI have ranged from confusion to anger — but, mostly, confusion about how to proceed. The most dystopian predictions seem to be driven by the fact that the so-called frontier model companies (and other LLM-powered companies) are controlling the narrative in the best of their interests. Unfortunately, the best corporate outcomes for an LLM company could have potential catastrophic outcomes for the math (and scientific) community. It is certain that AI companies want us to believe that their products will imminently achieve “super-human intelligence” and that, in particular, they will be able to autonomously solve any mathematical problem a human could solve with or without the aid of an LLM. It is in their best corporate interest that the public is convinced of the (allegedly) “unlimited potential” of their technology, particularly before their companies’ stocks go public (i.e., their upcoming IPOs: Anthropic in November 2026, OpenAI in early 2027, etc). Thus, they have tried to control the narrative by spending a huge amount of (human and computational) resources in order to find solutions to certain well-known mathematical problems. The proofs are then released in announcements that lead the public to believe that their models can already autonomously solve any problem at all, and swiftly at that. However, this is (currently) far from their true capabilities. For instance, they never discuss how many tokens have gone to the trash bin with no payoff in trying (and failing) to solve famous problems. We do know, for example, that OpenAI invested the equivalent of some $15M to solve (err, scoop) the Navier-Stokes problem, but we are unaware of the surely colossal running cost of the failures to resolve other Millennium Prize problems. My own outlook. Even though I am concerned about the incursions of LLMs into academic mathematics, I am quite hopeful. In fact, I consider this to be the most exciting time in my mathematical career (since the year 2000 say). Truly, this may be the most thrilling moment in mathematics in the modern history of our discipline, and I would be terribly sad to see young people leave academia and miss out on the stunning opportunity to be at the frontlines of the current scientific revolution. And not just sad: I think their absence would have disastrous effects for the field. Undoubtedly, LLMs are already an incredibly powerful tool. If used correctly, and if we set up sensible academic conduct expectations around the use of LLMs, these tools can accelerate progress in our discipline unlike in any previous era. I fully expect that we, the community, will adapt and adjust to this new period, and we will harness these tools to achieve truly great things that just a few months ago seemed far out of reach. And I fully expect that human mathematicians will be front and center in these wonderful achievements to come. I will add reasons that support my optimism below. I also want to add at this point that the day-to-day of a mathematician has not changed much so far! My days are still filled with teaching and joyful conversations about math with colleagues and students, doing research on a number of exciting (old and new) projects, and going to stimulating conferences to learn and disseminate our most recent methods and findings, while spending time with colleagues that make the mathematical community so wonderful and vibrant. Daniel Litt mentioned the same sentiment in a recent tweet. One thing has changed though, I am busier than ever before, because the number of research projects I am involved in has tripled in just a few months. My research horizon has expanded significantly, and I have many more projects available for students to help me with. Now, to the pressing questions: