Craig
There seems to be an increasing number of definitions of "research" in
mathematics these days. You might start by describing what you mean by
"research"--in particular, you'll need to state the sort of goals you
are looking for (publication, student research, teaching?).
It's fun!!!
Also, I enjoy helping others.
Also^2, I like acting as a filter and passing on information to others
that I think they could use (although sometimes they say "Stop!").
I think this may give some insight to a particular problem space and
gives some nice reasons.
http://primes.utm.edu/notes/faq/why.html
Here is another worthwhile read: http://www.maths.nuim.ie/research/why_pure_mathematics.shtml
And yet another: http://www.esotericka.org/pomona/whymath.html
I would also say that mathematics research is unique from the sciences
research because the only lab you need is typically in your house. For
example, the proof of Fermat's Last Theorem was basically done at
home.
Also, how exciting to discover something (and it does not matter how
small or large) it is.
The quest to answer the questions of beauty, symmetry and logic in our
universe with our universal and abstract language is just thrilling.
I hope that helps provide some insights.
~A
I like solving problems, both real-world, and conceptual (theorem-
proving).
Very flat, Norfolk.
--
I can't go on, I'll go on.
No, I've worked in non-linear structures as well.