From a Math Student in 2026

An uncertain future

Before starting, I'd like to briefly summarize the occasion for this piece. The last few months have been strange for mathematicians. Several longstanding conjectures, including the unit distance conjecture [1], the cycle double cover conjecture [2,3], and the Jacobian conjecture [4], have recently seen major AI-assisted breakthroughs.

I am starting my PhD in math in a couple of months. I'm very privileged to be where I am today, but it is hard to say what the future holds.

Responses among prominent mathematicians have varied greatly, so I suspect no one really knows. Some have chosen not to rely on AI as a source of novel mathematical ideas, while others have eagerly integrated it into their workflows [5,6,7]. Jacob Tsimerman believes that mathematics may soon cease to exist as a profession [8]. However, it is worth noting that he believes all human work might soon be displaced. His concern is therefore not specific to mathematics and should be understood in that wider context.

Note. Tsimerman also believes AI could pose an existential threat to humanity. He recently announced that he will pivot from mathematics to AI safety research at OpenAI [9].

It seems clear that math, and knowledge work more generally, has entered a period of significant change. Mathematical research and the profession may change in ways that many of us find harmful, and it would be dishonest to pretend otherwise.

These recent developments have prompted discussions about what the purpose of math is. Talking to students in math and other disciplines, I find a common sentiment. We want to know that the work we've put in still matters. Rather than speculate about the progress of AI and what will happen, I find myself thinking back to why I am doing math in the first place.

My journey into math

My path here was not particularly linear. I did not always love math. My mathematical education up until the middle of high school was completely standard, and I thought of math as the boring subject in which I did not have to study in order to do well. I loved puzzles and science in general, but growing up, I actually wanted to be an artist of sorts for a long time. Being a first-generation student, I had never considered going into academia.

Frustrated by the pace of ordinary math classes, I decided to skip ahead and test out of all the high school math courses early. I think this gave me a certain arrogance: I believed I knew more math than I actually did. Having never seen math above a high school level, I couldn't imagine how vast the field was.

However, that arrogance didn't last very long. After unexpectedly placing sixth in the national informatics olympiad, I was selected as one of six to represent Norway in the Baltic Olympiad in Informatics. It was inspiring to meet people my age, and sometimes younger, who knew so much more than I did and were extraordinarily talented. I began to wonder whether the difference between them and me was just talent or something more.

I began my undergraduate studies in Norway, majoring in economics and computer science. During my first year of applied math courses, I began to catch glimpses of math as a world much larger than I had anticipated. I remember while taking linear algebra in my second semester, I became fascinated with vector spaces. Eventually I downloaded some lecture notes on functional analysis and fruitlessly tried to understand the theory of Banach spaces. Math is not some dull, trivial subject; it is the culmination of millennia of work and culture. Wanting to learn more about this world, and still wanting to better understand the people I admired, I decided to pursue a bachelor's degree in math in addition to my main studies.

Math and community

In my first official semester as a math student, I took a difficult course in partial differential equations. I was utterly lost. I couldn't do this on my own. Although I still don't always enjoy asking others for help, I learned that I had to ask questions if I wanted to make progress. After all, I loved being asked questions and helping explain things to other people, even if I was sometimes told that my explanations were not the best.

I ended up in “Math Land,” a poorly ventilated part of an old building on campus filled with math students. I remember we would stay until late in the evening, eating pizza and drinking coffee. I still think one of the great unsolved problems of math is how to divide eight slices among three people.

Some evenings, we sat around a blackboard discussing math until midnight. On less productive days, we played table tennis for hours. Before one algebra exam, I claimed that skill at table tennis was inversely correlated with skill in algebra. Occasionally, someone would open a strange website called the nLab, filled with mathematical concepts I had never encountered.

I cannot overstate my admiration for the people I've met throughout my journey. Almost every graduate student I meet understands some area of math far better than I do. I can listen for hours as they explain subjects I know almost nothing about. I'm not sure anything can replace the infectious curiosity of a peer.

Over the past few years, I have had the privilege of working as a teaching assistant. I love being in the classroom, explaining ideas to students and helping underclassmen work through confusion and frustration. I learn something every time I teach. Students often ask questions that make me see something new. At Math Land, someone put up a meme on the wall that says, “Do you need help with math? Ask Torgeir.” It's been there for almost three years now, and part of me hopes that if I visit there one day years into the future, it will still be there. I think that if I could just spend my life teaching, it would not be bad at all.

Doing research

“The product of mathematics is clarity and understanding. Not theorems, by themselves.”

— William P. Thurston [10]

I did not write my first paper in the hope of publishing it. In my bachelor's thesis, I thought I had proved a theorem and submitted the thesis, only to discover that the proof contained a fatal flaw. I still passed, since the theorem was only a small part of a largely expository thesis. Even so, I could not stop wondering what the answer to the question I had asked actually was.

I could not focus on my exams. I simply wanted to know. One sleepless night, I found a proof and wrote it down on my phone while in bed. I discussed it with the professor who had supervised my bachelor's thesis. He said that the result seemed promising, though perhaps marginal: maybe publishable, maybe not. I told him that it did not matter whether other people cared about it. What mattered was that I had answered a question that mattered to me.

I spent the next four months convinced that it was likely of little interest to anyone else. But I accepted that if I learned something new, then something of value was gained, even if it was small. I wrote a small paper and posted it on my old website. I still view writing papers primarily as a way of sharing something that I have learned with the world. Later, this small theorem found its way into the hands of other researchers, who decided that it was publishable, and the paper got refined and expanded.

The meaning of the journey

There may be little comfort to offer in the worst-case scenario. Even before these developments, however, academia was already a difficult and uncertain path. I have met many people who completed master's degrees in algebraic geometry, topology, or other areas of pure math and now work in fields far removed from mathematics. In my own case, I did not begin learning math because I expected to become a mathematician. For a long time, I did not really believe that I had what it took. It therefore seems strange to claim that external developments could render this journey meaningless in retrospect. While I would regard the disappearance of math as a profession as tragic, it would not erase what math has already given me.

When I think about why I keep going, I'm reminded of the path that brought me here. There are still more brilliant minds to meet, students to teach, and questions to wonder about. At least for me, there's enough math left for a lifetime. I don't think I'm the only one who sees it this way, and there are many more reasons why people do math than I have listed. But it's hard not to feel small in the presence of great technological change. I hope we can come together to preserve communities in which we can learn and share our appreciation for the mathematical world.

Sources

1. OpenAI, “An OpenAI Model Has Disproved a Central Conjecture in Discrete Geometry”, 20 May 2026. Accessed July 2026.
2. Jim Geelen, “OpenAI's Proof of the Cycle Double Cover Theorem”, arXiv preprint 2607.15399, 2026.
3. Sang-il Oum, “A Proof of the Cycle Double Cover Conjecture by OpenAI: An Exposition”, arXiv preprint 2607.16356, 2026.
4. Eric W. Weisstein, “Jacobian Conjecture”, MathWorld—A Wolfram Web Resource, 2026. Updated July 2026.
5. Hugo Duminil-Copin, “Publications”, personal webpage, 2026. Accessed 24 July 2026.
6. Peter Scholze, endorsement of the Leiden Declaration on Artificial Intelligence and Mathematics, Leiden Declaration on Artificial Intelligence and Mathematics, 2026. Accessed 24 July 2026.
7. Davide Castelvecchi, “‘The job description is changing’: Mathematician Terence Tao on the rise of AI”, Nature 653 (2026), 16–17.
8. “Jacob Tsimerman on Getting to the Fun Faster with AI—and Worrying About the Future”, Notices of the American Mathematical Society, July 2026.
9. Simons Foundation, “International Congress of Mathematicians: Medal Winners Press Conference”, YouTube video, 2026. Accessed 24 July 2026.
10. William P. Thurston, “Response to ‘What's a Mathematician to Do?’”, MathOverflow, 2010.