[Amadiro]

Category theory is pretty popular IME, I've seen lots of mathematician talk about it. It seems fairly popular especially with algebraic geometrists and algebraic topologists.

OTOH I've never seen any mathematician use (perhaps with the exception of myself, depending on at what point you start counting a person as "mathematician" and at what point you consider someone to be "using haskell") haskell. I doubt the haskell community actually has any mathematicians, it's mostly just people who'd like to be mathematicians but are too lazy to get a degree.

The overlap of mathematicians who care about category theory (some logicians, algebraic geometrists, algebraic topologists, ...) and mathematicians who program (mostly mathematicians from applied disciplines, numerical methods, computational physics, ...) is pretty much zero.

You probably won't find your algebraic topology professor programming in any language anytimes soon, except LaTeX.

[gjm11]

> The overlap of mathematicians who care about category theory [...] and mathematicians who program [...] is pretty much zero. You probably won't find your algebraic topology professor programming

Well, unless perhaps s/he has some involvement in a project like this one http://comptop.stanford.edu/ ("The overall goal of this project is to develop flexible topological methods which will allow the analysis of data which is difficult to analyze using classical linear methods"; first named person in left sidebar is an algebraic topologist).

Or this one http://www.esf.org/index.php?id=8764 ("Applied and Computational Algebraic Topology"; first named person on steering committee is an algebraic topologist).

Or this one http://munkres.us.es:8080/groups/catam/ ("Computational Applied Topology and Applied Mathematics"; directory is an algebraic topologist).

Or, turning away from algebraic topology as such to mathematics inspired by algebraic topology and involving both category theory and programming: http://homotopytypetheory.org/ ("... new program for a comprehensive, computational foundation for mathematics based on the homotopical interpretation of type theory. [...] currently being implemented with the help of the automated proof assistant Coq"; note that in practice doing nontrivial things in Coq is a matter of functional programming).

For sure there are plenty of mathematicians (in algebraic topology and elsewhere) who don't program, but I think the intersection between people interested in categories and people interesting in programming is bigger than you suggest.

I don't know how many of them are using Haskell, though.

[Amadiro]

Yeah, I'm aware that some projects that apply computer science to pure mathematics (in various forms like Kenzo/CAT, PLEX (not CPLEX, that's for applied mathematics/finance/etc), agda, coq, GAP, ...) exist, but I don't think the claim that they are very very niche with mathematicians is exaggerated.

If you go to your average mathematics department and ask a few professors there that work in logic, algtop or alggeom, I doubt you'll find any that do any programming for their research. You probably won't find that many logicians that use proof-assistants either, although those are probably the least niche category of the things listed (and they are fairly popular with the CS folks)