SERIES · As application deadlines approach, Proofs and Prompts is publishing a series of posts from 19 to 23 October for people considering a PhD, doing a PhD or looking for a postdoc: guidelines, discussions and speculation about what to do and what careers in mathematics will look like. This post is one of them. Each is written independently and reflects only its authors’ views. All posts in the series
To the mathematicians shaping the future of our profession,
I am mathematics PhD student. Up until recently, I fully intended to pursue a career in academic research. I deeply love mathematics, and I entered graduate school because of this. However I have made the decision to leave academia once I finish my doctorate and I am heartbroken; I would like to explain why.
This decision is not because of job security, nor is it because AI can do better mathematics than I ever could. Rather, I am becoming increasingly convinced that this profession is morphing into something unrecognizable, something alien, something I did not sign up for. OpenAI’s paper dump on October 6th only reinforces my conviction. The speed with which a commercial company can alter and disrupt an entire academic discipline is frightening and should concern anyone involved in academia, not just mathematics. However, what has troubled me more is the response from established mathematicians. There are indeed a mix of reactions to October 6th, but seeing mathematicians greet this release of papers with excitement and joy is beyond confusing. Many celebrate the possibility that AI will relieve them of the burden of difficult calculations, technical lemmas, and other supposedly tedious aspects of mathematical research. Have they forgotten what it was like to become a mathematician in the first place?
1. The mathematics I came here for
I love technical work. I love spending days, weeks, months working on a lemma or an idea without success. I love failing at solving a problem, going on a walk to clear my head, sleeping on it and coming up with a new idea, then repeating this process. I love slowly realizing the shape of a solution and why it needed to be that way all along. More importantly, I love the intuition formed from the process of constant failure. These are not unpleasant obstacles that stand in the way of me proving a more interesting result. These are the reasons I wanted to become a mathematician. When mathematicians talk about being relieved from the burden of doing technical work (or mathematicians welcoming a future of no longer doing this work), I cannot help but wonder if they appreciate what this kind of labor represents to someone at the beginning of their career. I viewed this process as an opportunity to develop the skills necessary to become an independent researcher.
This struggle is not incidental to mathematical education. It is the principle way that education occurs. As AI has now become highly capable of performing this kind of work, I see shockingly little from the mathematics community about how this kind of crisis in education will be addressed.
2. Is Math 2.0 really the future you want?
Terence Tao has proposed a vision of a new way of doing mathematics, Math 2.0, where the emphasis moves away from solving open problems and toward a more holistic approach. His vision includes exposition, conceptual understanding, discovering new principles, developing mathematical frameworks, and synthesizing the enormous quantity of mathematical knowledge that increasingly capable AI systems can produce. Obviously these are valuable pursuits and practices that are already important to mathematical research. But I feel like I am asking the obvious question that has not been addressed: What if I do not want to spend my professional life doing these activities?
I did not go to graduate school to organize, interpret, and curate an increasingly vast collection of mathematical results produced by machines. I came here to learn techniques, develop my own understanding, and use these techniques to discover things I did not previously know. There is a clear distinction between understanding an argument and discovering one yourself. There is a clear distinction between curating a research direction and experience the process of producing it. I do not deny that Math 2.0 will accelerate progress in the field beyond anything I can even imagine right now. However, will these activities appeal to the same people who entered mathematics because they love independently solving difficult problems? A profession centered on interpretation, synthesization, and communication of mathematical knowledge will be worthwhile pursuit. But if independent discovery becomes a secondary activity, then it is not the profession I intended to join. Do we disregard the human fulfillment that comes from experience in exchange for knowledge and understanding produced by AI? Preserving mathematical knowledge and preserving mathematics as a fulfilling human intellectual pursuit clearly are not the same thing. As things are going, we will accomplish the former and disregard the latter. I am not claiming that one is inherently better than the other. But what I can say is that the experience of one is fundamentally different than the other.
3. Who will train the mathematicians of Math 2.0?
There is a problem with the proposed future of mathematics, and it is more concerning than my personal dissatisfaction. How exactly do you expect to train the next generation of mathematicians?
Established researchers possess something far more valuable than understanding of existing theorems. You possess the special sauce of intuition, judgment, taste, and an understanding of what questions are worth pursuing. These skills are precisely what makes you capable of using AI effectively. You know when an idea is promising and when it hints at something greater. You know how to formulate new research directions. Where did these skills come from? I doubt they were developed by reading successful proofs or listening to an explanation of an idea. Rather, they were probably developed through years of sustained thought with hard problems. The activities you now want to disregard are what made you who you are. These activities are what taught you to be a mathematician. AI systems will now do that work for you and from the perspective of someone who possesses years (possibly decades) of experience, this might be an attractive offer. Your students do not possess the special sauce. How do you expect them to develop it? How do we acquire good taste and intuition without technical understanding? How do we learn to recognize promising proof strategies if we have never failed at a proof? How do we learn to direct a research program if we have never experienced the difficulty of conducting one ourselves?
Tao himself has already expressed concern about intellectual deskilling and emphasized the importance of preserving productive struggle in education. More needs to happen to address this concern rather than just expressing excitement about new results being proved. Maybe the answer is to preserve independent problem solving in graduate training. To me, this does not appear to be a sufficient answer though. Why would I develop skills through independent technical work and suffering when I can just use AI to solve these problems for me? More importantly, do we really expect students to independently suffer, only to enter a profession in which the skills they suffered to develop are delegated to AI? Even disregarding this though, if the proposal really is independent suffering during graduate training, why should they choose to even undergo this training? Will they be allowed to spend years developing their own ideas when their peers can produce numerous sophisticated results using AI? Will hiring committees and funding agencies value intellectual development that comes from independent research, even when it produces far less tangible results? How do we even deem what a successful graduate student is when AI systems are becoming increasingly capable? If we say that going forward we value organization, interpretation, and curation, why would we assume AI will not be able to do this even a few months from now?
There might be satisfactory answers to these questions, but there has not been an account from any of you as to how this will be addressed. Math 2.0 appears to heavily depend on the accumulated expertise of mathematicians trained under Math 1.0. However, a sustainable profession cannot rely on expertise developed under a system it has abandoned.
4. What kind of students will your future attract?
Let’s suppose we devise an adequate training system for Math 2.0. What kind of people will this profession attract? I entered this field because I love solving hard problems and relish in the problem solving process. If the future consists of interpreting AI generated results, organizing knowledge, and directing automated research, why should I remain in academia? It is entirely possible that Math 2.0 attracts people who find these activities fulfilling, but will that generation possess the same motivations as the mathematicians who preceded them? Will Math 2.0 attract people who are inclined to develop a deep technical understanding of the field for which this future now depends? The training problem and recruitment problem are intertwined. Removing the value of technical problem solving may weaken the process by which we develop expertise and discourage the people who most enjoy developing this expertise. I find this deeply troubling. You seem enthusiastic at imagining what can be accomplished with powerful AI systems. You need an equivalent enthusiasm for understanding what kind of mathematicians you will be breeding under this new profession. You plan the future of mathematics from the perspective of someone who has already become a mathematician, but who are going to be the mathematicians of the future? Are you comfortable with them continuing your legacy?
5. A warning from someone who still loves mathematics
Mathematics is never going to be the same and I recognize that the way I did research and found fulfillment from it are no longer here. I am not demanding you refuse to use these technologies nor am I suggesting that you ignore the opportunities it provides. What I am demanding from you is to recognize that your enthusiasm to use this new technology does not necessarily reflect the aspirations of the people you are currently training. I recently heard a mathematician say that it is “paradoxical” to not want to study a field that is undergoing a scientific revolution in reference to October 6th. This mindset completely misses the point of why I do mathematics, and I suspect this is true for many other graduate students and even other established mathematicians. You may find this future exciting. Some of us find this future discouraging and troubling. You may find it exciting to see that answers to problems you deeply care about are being answered which then allows you to develop conceptual frameworks and interpret massive collections of AI generated results. Some of us entered mathematics because of the very human experience of suffering through a problem ourselves. You may believe that Math 2.0 will usher in an extraordinary period of progress and understanding. Maybe it will. But who will follow in your footsteps? How can you reproduce the expertise you have? How do you know we even want to participate in this new landscape?
I cannot speak for every graduate student, I can only share my feelings and I certainly would not presume to speak for my entire generation. But I can tell you that I entered graduate school fully intending to pursue a career as a research mathematician. The actions of October 6th have reversed this, and I’m probably not the only one. Before ending this letter, I want to emphasize something: I do not want to stop being a mathematician. My love for mathematics is eternal and I am deeply grateful to this field for not only developing my skills as a researcher, but developing me as a human. I do not believe that academics want to keep a space open for the kind of intellectual work that made me fall in love with this subject. I want to pursue discoveries myself. I want to struggle, to suffer, to grow.
I am not asking you to agree with my personal preferences. I am asking you to explain how your proposed future will train its successors, who it will attract, and why that is a future worth pursuing. These are questions that concern generational sustainability of the profession itself and cannot be ignored. I hope you begin treating these questions with the urgency they deserve. Because while you are discussing what your future will be, some of us have already decided that we no longer want to be a part of that future.
—A PhD student
Received 19 October 2026.
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