Sunday, September 16, 2018

What is a Physicist? A Mathematician? A Computer Scientist?


I'm of course not a physicist


Is X a Y?

















  1. Obviously, there is a fuzzy border between Theoretical Computer Science (TCS) and Mathematics. Just look at the Nevanlinna Prize winners. Are they computer scientists or mathematicians (in sheep’s clothing)?
    Also Computability Theory belongs to Mathematics (as part of Mathematical Logic a.k.a. “Recursion Theory”) and Theoretical Computer Science. Just look at the (recent) developments of Kolmogorov Complexity for an example of a full merge. You can publish under this heading pure Recursion Theory in major TCS-conferences and journals. Some years ago the buzzword “Recursion Theory” alone would have placed you out of scope of TCS (with the only but remarkable exception of the small but steady field of “Inductive Inference”).
    The same token more or less applies to Combinatorics in general which belongs to (Discrete) Mathematics, but main parts of Computational Complexity (including “Logic in Computer Science,” e.g., Finite Model Theory) can be considered as a subfield of Combinatorics.
    It is interesting to speculate how this will develop in the future. More specifically, will there be any more homegrown theorists coming from Computer Science proper or will this become a subfield and hunting ground for (pure) mathematicians who are looking for a well-paid job (that they would not get if they stayed in curiosity-oriented research of Mathematics proper without “approved applications” :-))?

  2. X could be a Y and a Z too.

  3. The majority (17/25) of MIT faculty doing theoretical CS belong solely to the MIT
    EECS Department; there are 7 belonging solely to the Math Dept, and only one joint
    appointment (Bonnie Berger) that I know of. All but
    one of these 25 are members of the Theory of Computation Group in the MIT Computer
    Science and AI Laboratory.

    Personally, I think of myself as a Mathematician whose entire career has been
    happily spent in Computer Science departments (at CMU, MIT, Harvard).

  4. I posit that someone who proves theorems is a pure mathematician, but someone who directly uses theorems for something other than proving other theorems is an applied mathematician. Someone who does both is a purple mathematician.

    In conclude that most of the people you talk about are various shades of purple, the exception being cranks.

  5. You can go one step further and ask what (sub)field someone is in. Is someone who works on efficient routing doing systems/networking or algorithms? Is someone who works on cryptography in cybersecurity or theory?

    I personally find it useful here to think in terms of someone's "home conference": the conference they regularly attend (even when they don't have a paper) and probably regularly publish. Some people may have more than one home conference, and one's home conference may change over time, but that is ok.

  6. Who are you thinking of when you say "MIT CS is housed in mathematics"? I find this a very odd claim. Check out the people at the page for the Laboratory for the Theory of Computer Science.

    1. Having read your comment I am thinking, and I made the correction in the post, that I really do not know how MIT is structured and that I am incorrect. What is correct is that there are some people in the Math Dept who are (at least in my opinion) Computer Scientists.

      Thanks for pointing out my error

  7. Indeed, all the people you mention are listed on as having joint appointments, with many more who aren't joint with math.
    The weird thing at MIT Math, I would say, is that combinatorialists are classified as "applied mathematics", which I don't know of happening in any other math department.