Math as we knew it is gone.By “math”, I mean all mathematical pursuits. This includes subfields of computer science, physics, engineering, etc. Yet, even as we grieve this loss, we are faced with the prospect that the field, as a human pursuit, may cease to exist entirely.
Mathematics is currently placed alongside science, technology, and engineering in the social consciousness; our courses focus on teaching tools to those who wish to study in technical fields, there is a general understanding that our research, however abstract, will eventually benefit future technologies, and the public views our work as some kind of scientific magic. We have happily accepted, or even promoted, this positioning, and in exchange, we enjoy a relatively high status in the academic hierarchy.
Now, the entanglement of math with these disciplines has become an existential risk to the discipline. It is a real possibility that AI systems will soon produce and communicate mathematical ideas better than any human can, and if this comes to be, it seems broader society has little incentive not to automate the role of mathematics in the pipeline of technological progress.
We are already seeing hints of such a future. In recent months, AI systems have become powerful enough that the community is facing an influx of solutions to problems that human mathematicians had spent substantial effort on. There is a consensus that this is a serious concern.e.g. leidendeclaration.ai; mathandai.org; The fall of the theorem economy. David Bessis. 2026 In particular, the relative ease with which solutions can now be obtained is incompatible with existing incentive structures, raising major questions about infrastructure such as journals and conferences, graduate education, and career advancement. Moreover, whereas proving theorems used to also produce new ideas, techniques, and future problems, the new solutions-centric approach of AI-math seems less beneficial in this regard.
Nevertheless, despite the present shortcomings, it would be disingenuous to take AI’s current proclivity for solutions as evidence that “math-as-a-science” cannot be carried out autonomously. Indeed, until now, the vast majority of effort has been spent on getting AI to solve problems.And solve problems they have! It’s possible that, with a realignment of priorities, AIs will soon be able to produce math in a self-sustaining way, even if humans cannot understand what’s going on. If this comes to be, and “AI math” proves to be equally useful to technological progress, then it seems like that this program will be automated.
Recently, the concept of “human understanding” has emerged as a popular justification for approaches to dealing with the massive number of new results being produced with AI. This shows up in many ways: new journals dedicated to peer-reviewed recordings of research talks are popping up, publication venues are increasing their standards by limiting the number of submissions and adding requirements like video explanation, and there are even efforts to provide readable explanations of large troves of AI-generated math.
On the face of it, a shift towards understanding is a good thing. Our past emphasis on things like the difficulty of a proof or the novelty of a technique made it harder to understand new ideas and inhibited the advancement of the discipline. However, I wonder whether the present approach is simply replacing our previously shortsighted fixation on “proving theorems” with an equally shortsighted fixation on “understanding theorems”.
Specifically, in much of the current discourse on understanding, math is viewed as a collection of universal truths—theorems, definitions, proofs, techniques, and connections between subfields—that somehow transcend humanity.In Thurston’s essay, On proof and progress in mathematics, he takes the position that “what mathematicians are accomplishing is to advance human understanding of mathematics”. This might be the origin of much of the current use of the term “human understanding”. However, I don’t think that what he is referring to is the same think that I’m critiquing here. Indeed, his essay is written in protest of the idea that the purpose of math is to prove theorems, and in arguing this point, he provides a human-centered perspective on mathematics. The quest for universal truth is a noble one, and just as the devout may find meaning in more deeply understanding their faith, the mathematician may find meaning in more deeply understanding mathematics. However, if we limit the value of math to its qualities that exist beyond humanity, and if AI becomes better than humans at explaining math, then it seem the the future of math will be a lonely one.
This summer, AI became capable of doing more-or-less all the research work I’d ever produced. What’s more, it seemed that it was only a matter of time until it exceeded my abilities to contribute to science entirely. This brought about a period of despair. Much of my sense of purpose had been tied to developing new ideas in the service of scientific progress, but future contributions I could envision, like pointing the AI in new directions, or developing “human understanding”, all felt meaningless in the face of powerful AI.
As I sat with this sadness, I began to reflect on how and why I do math. For years, getting an academic job was my main goal, so I had mostly considered these questions in relation to existing institutional structures. This time, though, having secured a job, and armed with the knowledge that all academic norms are flux, I felt free to explore my relationship with math from a new perspective, and in doing so I came to understand something central to why I do mathematics: mathematics provides me a way to explore the human condition.
Math is a collaborative endeavor. In some ways, this is obvious; any institution operating at the scale of research mathematics consists of the collective efforts of many people, each playing some role in advancing the enterprise. Yet, as William Thurston observes,On proof and progress in mathematics. William Thurston. 1994. the way we organize our efforts suggests that “the social setting is extremely important” to why and how most of us do math. We like having “colleagues who share [our] excitement”, and choose what we work on based on human factors, not solely the pursuit of new knowledge and theorems. In other words, part of why we do math is human connection.
This makes sense to me. I work with collaborators not just because they have knowledge that I can benefit from, but also because I enjoy learning about their tastes, their interests, and their goals. I share ideas with friends, not just because I think they will benefit from them, but also because I know they will enjoy hearing them and that their response will teach me more about how they see the world. I go to conferences not just to watch presentations and learn theorems,I actually don’t like this part very much. But I need it for the rhetorical device. but also to experience the wonder of participating in a large community. And, I teach, not just to help students understand mathematical concepts and tools, but also to share with them the excitement, fear, hope, and joy of this formative time of their lives. In all of these ways, I understand better my place in the world.
Math also provides benefits beyond direct interaction with others. As humans, we are naturally driven to push the limits of our bodies and minds, and math provides an outlet for this desire. We play games like Chess and Go, even when we have no hope of beating computers, because doing so provides us enjoyment or satisfaction. Likewise, we find meaning in memorizing more digits of pi, learning a proof, discovering a new way of thinking, or finding improved methods for teaching others. By participating in these activities, we grow as people and are able to exist more fully in society. In other words, as Francis Su writes, “doing mathematics cultivates virtues that help people flourish”.Mathematics for Human Flourishing. Francis Su. 2017.
For me, the most important way math helps me flourish is by serving as the context for creative expression.For instance, this essay. As I try to figure out what I want to convey and to whom, why I’m even doing this, and how to turn vision to reality, I gain insight into my own state of being and the state of the world around me. In doing so, I am connected to the present moment and to an envisioned future in which I might exist. Likewise, when I finally get something “just right”, a sentence or figure in a paper, the arrangement of a talk, or the organization of an idea, I feel a sense of satisfaction and exhilaration that I carry with me into the world. It is the entire process, not just the end result, that provides value.
As I came to understand my motivations for doing math better, I began to develop a sense of optimism about my future in mathematics. I realized what I actually cared about was contributing to the wellbeing of humanity, and that I’d lost track of the distinction through years of working in a discipline close to application. Thus, even in the case that “math-as-a-science” is fully automated, perhaps I could still do math.
As I realize this, I began to imagine a future for human-centered math that I would be excited to participate in. A future in which math is organized under the umbrella of what might be called the mathematical arts: mathematical pursuits centered in ideals such as “creative expression, storytelling, and cultural participation”,en.wikipedia.org/wiki/The_arts rather than technological progress. A future in which these ideals are understood and valued across all facets of society, and in which math is viewed as essential to the human experience.
A future of math as an art.
I feel almost embarrassed sharing this essay. In a sense, I have not really added much to the ideas of Thurston, Su, and the many others advocates of a humanist approach to math. I have published the essay anyway, because I’m worried that such voices are not receiving sufficient attention in this moment. Indeed, faced with the looming threat of a complete structural failure, the response has largely been to patch leaks in the past way of doing math.
It is easy to get distracted with leaks, because they are so visible. However, to truly move forward, we need to take a step back and focus our energy on understanding our “goals, objectives, and values”,Mathematics in the age of AI. Terence Tao. 2026. free of preconceptions of “how math is done”. Indeed, without some idea of where we want to go, it seems we will have a hard time getting there. This essay originated as part of my own attempt to to gain such perspective, and in writing it, I’ve become convinced that repositioning math as an art is a path forward that should be seriously considered.
The arts and humanities struggle financially, and admittedly, positioning math alongside these disciplines exposes us to the same risk. However, maintaining the status quo does not mean that we will avoid this struggle; even if AI stops improving today and “math-as-a-science” is never automated, the role of humans in the process will change substantially. It seems to me that, unless we clearly lay out the value of math outside of this program, we will remain beholden to the current system and its misguided emphasis on technological progress and economic value.
Yet, as much as the current moment is a challenge, it is a chance to shape the future of our discipline and of society. The same factors threatening the future of math are impacting many other professions, and our current struggle has become a flashpoint in the broader struggle for our collective futures. This is both a strategic opportunity and a moral obligation. We already enjoy broad public support, and the concept of “math-as-an-art” is easier to understand than many other explanations of the value of math,Especially compared to narrower/more specific justifications like “human understanding”. making such a transition more palatable to the general public. At the same time, our discipline commands a certain level of respect in society,For example, AI companies have changed their behavior based on the math community’s response. and we should use this to advocate for the rejuvenation of human-centered pursuits at large.
Therefore, as we fight to define the future of our discipline, let us join the chorus of voices calling out for a renewed focus on the dignity and well-being of humans and humanity. Math as we knew it is gone, but math as it will be known is just beginning.