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David Michael Roberts (Nov 06 2025 at 00:06):Someone asked me recently for an estimate on how many category theorists there are. This is obviously a rubbery figure, because of the overlap between higher category theory and homotopy theory, and then also things like algebraic/arithmetic geometry or K-theory. But I'm happy to consider people who publish a paper on category theory where the application comes second as "doing category theory". Argue it out in your answer.
And the question was also raised about how many people do applied category theory. This one is perhaps even harder to outline, because of what counts as ACT. There's the whole nexus surrounding Spivak/Fong/Topos Inst. ultimately coming from John Baez, but this is obviously far too narrow. Looking at the program committee for the recently-announced ACT (and all the other people in that blog post, a few of the names surprised me. Is Tholen doing ACT? Pronk? Maria Manuel Clementino? Maybe some of the more senior people are pivoting, or perhaps they are there because a more interdisciplinary panel needs people not just at the interface, but also within the different specialities.
David Michael Roberts (Nov 06 2025 at 00:09):The best I could do in a pinch (I was in a rush) was to point to the recent CT20XX and ACT conference page(s). That gave an order of magnitude lower bound, but it's less easy to get an upper bound that's tight. There surely is less than ten thousand category theorists, and less than a thousand applied category theorists. But can anyone either give some kind of rigorous data-based estimate, or a good Fermi estimate argument?
Joe Moeller (Nov 06 2025 at 01:03):I think the question is even more difficult to pin down than your characterization. People doing CT have been pushed into other fields for decades. Category theorists have been thinking about CS applications for a very long time. Obviously not everyone who writes in Haskell is an applied category theorist, but how far back from that do you have to pull to find the CTists? Clark Barwick said that homotopy theory is not a branch of topology, it is the enrichment of the notion of equality. Surely category theory could have had claim to this notion over "homotopy", a notion that originally did specifically refer to a topological phenomenon? If you consider algebraic geometry, commutative algebra, Lie theory, the question begins to look like a cousin to asking who does set theory and counting everyone. This I think is partially why so many people in these fields will insist, up to the point of insult and sometimes beyond, that category theory is _no more_ than a convenient language for doing math.
Joe Moeller (Nov 06 2025 at 01:07):These feel a bit like silly points to be making in response to your question, but I think my point is that you could make estimates by counting attendance at the major conferences, counting recent authors in all the CT journals, etc. but it's probably going to miss a bunch of people doing CT elsewhere, and people on a really fundamental level doing the things category theorists do but just calling it something else, for one reason or another.
David Michael Roberts (Nov 06 2025 at 01:14):Yes, it's not an easy problem to delineate. One of my colleagues who works in mathematics education across the whole university likes to make the point that when you count things (eg doing stats in psychology, or quasi-quantitative methods in the humanities etc) you have to decide what counts as the thing you are interested in.
I have estimates from my interlocutor, but I'd love to see people's guesstimates and rationale, before I put them out there for comparison.
Chad Nester (Nov 06 2025 at 07:22):I don't have an estimate, but I think it's easy to underestimate the number of computer scientists, especially in programming languages and related fields, whose work involves category theory in some capacity. The different incentive structure wrt publications kind of makes it a separate world.
Peva Blanchard (Nov 06 2025 at 08:42):It reminds me Fermi's questions, like "how many piano tuners are there in Chicago".
So we should start with an obvious range (I'm certain there are less than 8 billion category theorists, because not everyone on earth is a category theorist), and then find arguments to reduce that range.
I see 188 topics in the channel "community: our work". So I can update my range to, e.g., .
Ok maybe the 8 billion limit can be reduced :)
I see 500 universities in the Shanghai ranking for maths. I guess there are less than 100 math professors on average per university. So my range is now .
Now, looking at TAC. By eye scanning, I see there are about 30 papers per issue, with about 2 authors per paper. I'd count that as 60 category theorists per issue. So, on a period of 20 years, there are less than 1200 authors at TAC. I would say that, someone who has been active in CT in the last 20 years should appear at least once. But to be more confident, I'll just update my range to .
I'll stop here, but it's a fun game :)