## Monday, September 17, 2018

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

Scott Aaronson recently won the Tomassoni-Chisesi Prize in Physics (yeah Scott!).
In his post (here) about it he makes a passing comment:

I'm of course not a physicist

I won't disagree (does that mean I agree? Darn Logic!) but it raises the question of how we identify ourselves. How to answer the question:

Is X a Y?

(We will also consider why we care, if we do.)

Some criteria below. Note that I may say thinks like Dijkstra is obviously a computer scientist'
but this is cheating since my point is that it may be hard to tell these things (though I think he is).

1) If X in a Y-dept then X is a Y. While often true, there are some problems: MIT CS is housed in Mathematics, some people change fields. Readers- if you know someone who is in dept X but really does Y, leave a comment. (CORRECTION- I really don't know how MIT is structured. I do know that the Math Dept has several people who I think of as Computer Scientists: Bonnie Burger,  Michael Goemans, Tom Leighton, Peter Shor, Michael Sipser. There may be others as well. The point being that I would not say Sipers is a mathematician because he is in the MIT Math Dept')

2) If X got their degree in Y then they are Y. Again, people can change fields. Also, some of the older people in our field got degrees in Physics or Math since there was no CS (I am thinking Dijkstra-Physics, Knuth-Math). Even more recently there are cases. Andrew Child's degree is in Physics, but he did quantum computing. Readers- if you know someone who got there degree in X but is now donig Y, leave a comment.

3) Look at X's motivation. If Donald Knuth does hard math but he does it to better analyze algorithms, then he is a computer scientist. One problem -- some people don't know their own motivations, or it can be hard to tell. And people can get distracted into another field.

4) What does X call himself? Of course people can be wrong. The cranks he email me their proofs that R(5) is 40 (its not) think the are mathematicians. They are not- or are they? see next point

5) What X is interested in, ind. of if they are good at it or even know any. Not quite right- if an 8 year old  Bill Gasarch is interested in the Ketchup problem that does not make him a mathematician.

6) What X is working on right now. Fine but might change. And some work is hard to classify.

7) If you win an award in X, then you are an X. Some exceptions

Scott is a computer scientist who won the Tomassoni-Chisesi Physics Prize

Ed Witten is a Physicist who won the Fields Medal (Math)

John Nash is a mathematician who won a Nobel prize in Economics.

I want to make a full circle- so if you know other X won a prize in Y then leave a comment and
we'll see what kind of graph we get. Bipartite with people on one side and fields on the other.

8) What they can teach? Helpful in terms of hiring when you want to fill teaching needs.

Does any of this matter? We use terms like mathematician' physicist' `computer scientist' as shorthand for what someone is working on, so its good to know we have it right.

1. the meh sense

2. 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” :-))?

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

4. 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).

5. 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.

6. 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.

7. 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

8. Indeed, all the people you mention are listed on https://toc.csail.mit.edu/faculty 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.