Dan Spielman on research

Claire: Why are your papers so long? They're sophisticated and ground
breaking, but I don't have the energy or time to read such long,
complex papers.
Dan: I don't want them to be that way. It's accidental that they are so
long. I just don't know when to give up. I keep going further and further
into the problem until some solution comes, and sometimes it takes a
hundred pages and years of work.

Claire: But if many people are like me, then, having papers that are much
longer than the norm, do you really think that that's a good marketing
strategy?
Dan: Probably not. But enough people read them to satisfy me. Anyway, the
way to go if you want to learn about the work I have done is not to read my
papers. I find that the lecture notes format is much more
satisfying. When I write a paper, I feel that somehow I have to state and
prove the strongest result I have. When I teach, I give a weaker version
that has a much simpler, shorter, more understandable proof, and that's
what I put in my lecture notes, so that's what you should read. Also, later
versions are usually quite a bit simpler.

Claire: How do you choose research problems?
Dan: I find that I am attracted to problems that are hard. It's difficult
for me to get motivated unless I have a sense that the problem is
important; that's what keeps me going.

Claire: But among all hard and important open problems, how do you know
which one is a "good" problem?
Dan: It has to be a problem that gives me a lot of ideas, where I see a lot
of possible connections with other areas, other subjects, where there are
many angles that I want to explore, many papers to read and new things to
learn. Then, along the way, I find that I am proving results on the side
that are of interest in themselves. That's how I get a strong sense that
it's a good problem to be working on.

Claire: That seems to require a lot of experience. Is that how you picked
problems when you were a graduate student?
Dan: No, you're right, of course that's not how I worked when I was a
student. Then, I did the usual thing, you know, look around for hot topics
on which there had recently been partial progress and new results had come
out that were begging for improvements, and then I was able to find those
improvements before professors just because I had a lot more time to devote
to research than those professors.

Claire: Do you think that you are a better researcher now than then?
Dan: yes, I think I am better at research. Although, I must admit that I
have a lot less time for research, and, in particular, I no longer have
time to keep up and read an insane number of papers, as I did when I was a
student.

Claire: At this point you're about mid-career. What do you want to do for
the next half of your career?
Dan: That's a scary thought. I'm not really thinking about it. Right now I
have projects that will keep me quite busy for the next few years, and by
then,  presumably I will have learned new things that will drive my
research for the following few years, and so on. I do predict that I will
be doing more and more programming.

Claire: Do you see yourself as a mathematician or as a computer scientist?
Dan: I must say that there are many things mathematicians do that I do not
get, in the sense that I have no clue why they work on those
particular questions. I can read a Math paper and like its content very
much, yet not have any idea why the author worked on that question. Maybe
because someone else asked it before? It's a mystery to me. As for myself,
I come to problems very much from the perspective of a computer science
motivation.