FOM: G.-C. Rota's Indiscretions

[Joe Shipman]

Steve quotes some of Rota's ten "rules" for the survival in Mathematics
Departments.

  1. Never wash your dirty linen in public.
  3. Never compare fields.
  8. View the mathematical community as a United Front.

I'd like to see the other seven!

What disturbs me the most about such attitudes is that it seems to be
dangerous to ignore them and just try to do good mathematics.  How much
of a career handicap is it to simply ignore all such politics and do
good research?  Obviously if one's research is only accessible to a few
specialists it is more dangerous to ignore the sociopolitical issues,
but there are also advantages to doing narrowly accessible research (if
you're on good terms with the other specialists in your field).  There
is also the issue of whether it is valuable to work hard at being a good
teacher and expositor (apparently this can have a negative value in many
mathematics departments even AFTER allowing for the impact of having
reduced time available for research).

Some questions for the professional mathematicians on the F.O.M. list,
from an academic outsider:
(For the purposes of this discussion, "career advancement" means getting
funding, progressing toward getting tenure, or obtaining a position at a
better institution, *not* "job satisfaction")

1. How much pressure is there to continue working in the same research
area?
2. Is any amount of time spent on becoming a better teacher helpful to
one's career advancement?
3. Is any amount of time spent on writing textbooks and other material
for non-specialists helpful to one's career advancement?
4. Is any amount of time spent on popularizing mathematics non-harmful
to one's career advancement?
5. How much does grantsmanship influence the research one works on?
6. What is the minimum degree to which one must respect Rota's rules in
order to avoid hurting one's career prospects?
7. How much pressure is there against tackling "big", hard problems
where there is no guarantee of progress?
8. How much do the other departments of the institution matter?  Can
good relationships and collaborations with them help?
9. Is there a point at which the pressure to publish whatever you have
at the time is counterbalanced by potential damage from publishing
something too trivial?
10. How does the situation differ for pure vs. applied mathematics?

Answers or additional questions along these lines would be greatly
appreciated by those of us considering an academic career!

-- Joe Shipman