I’ve been recently following some interesting debates about the future of mathematics in the age of AI. I think many discussions about how AI is “disrupting” or “changing” (pure) mathematics tend to conflate, or at least fail to distinguish between, three interlocked interpretations of mathematics:
(1) Mathematics itself, as a body or domain of ideas and concepts living somewhere at the intersection of knowledge and art.
(2) Mathematics as a vocation, as the human practice of acquiring knowledge, understanding, and clarity about structure, guided by a sense of aesthetics.
(3) Mathematics as a profession, as the academic practice that exists in institutions and systems, and includes universities, publications, teaching, recognition, competition, etc.
The first is very hard to understand or define, and I lack the proper philosophical foundations to discuss it eloquently. I suspect it is also importantly different from science and perhaps close to something like theology.
The second is the human practice through which we access the first. By “mathematics as a vocation” I mean doing mathematics as a calling or way of life, rather than as an occupation. It exists individually and/or in community and, like other artistic endeavors, is often in tension with political and societal structures. This kind of practice is utopian: there is a sense of authorship without ownership, a particular sharing economy, and it is not bound to market forces. For many of us, participating in this vocational practice is what being a mathematician means; it is at the core of our identity. Figures like Poincaré, Grothendieck, Erdős, Gödel, and Thurston, to name a few, exemplify this practice.
The third is easier to explain. It depends on politics, systems, markets, biases, trends, diplomas, funding, prizes, etc. Teaching mathematics as a service to science and engineering students, as well as training PhD students, also belongs to this domain. It is what many of us choose as a job because, so far, it is the most comfortable way we can get to (2) without renouncing the benefits of societal structures.
I don’t think it makes sense to discuss AI “disrupting” (1), because technology can only disrupt the practice of mathematics, not mathematics itself.
AI will certainly disrupt (3), and I have some concerns about the direction the professional practice, already quite imperfect, may take. For instance, I think the AI industry might push (3) further away from (2), because the dependence of (3) on the market may become heavier and take a different form. Even if the technology itself is a useful tool (modulo its ethical implications) that, if used correctly, can enhance communication and writing, find counterexamples, and help navigate the literature, there is also a high price to pay: enormous amounts of nonsense and slop, together with widespread misuse by students and early-career mathematicians. But again, the economic and institutional forces surrounding AI – the industry – may alter the profession (and society in general) in ways that are much more consequential.
While I do worry about how (3) is going to change, and about the broader societal and ethical implications of AI, I don’t think (2), the practice of understanding structure through creative means guided by aesthetics rather than market forces, will fundamentally change. Some people might argue that (2) is healthier without tools like AI; others suggest we should somehow “own” the technology and incorporate it into our vocational practice. I don’t know. In any case, for many of us, the incentives for devoting our lives to mathematics do not come from (3), the domain where most changes are expected. This vocational practice is where many of us are centered, and there is a community of friends, not colleagues, built around it that I believe no industry can destroy.
Received 23 August 2026.
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