FOM: golden opportunities

[Stephen G Simpson]

Martin Davis writes:

 > I think in both cases the terminological dispute had only the most
 > tenuous connection with the substantive issues yyou raised.

OK Martin, fair enough.  Let's forget about the terminological
disputes and focus on the substantive issues.  For instance: (1) Is
categorical foundations the best thing since sliced bread, as McLarty
says?  (2) Is recursion theory in a mess, as Harvey says?

 > "Golden opportunity": this is a strange notion of how
 > mathematicians operate.

Really?  Haven't you ever operated in this way?  It seems to me that
there are opportunities in mathematical research, just as in every
other field of human endeavor.

Around 1980 I had a golden opportunity to switch from alpha-recursion
theory (boo!) to reverse mathematics (yay!).  I seized that
opportunity, and now my book on reverse mathematics is about to be
published.  I am hoping that my book will have a substantial positive
impact on f.o.m. research.  Do you think I made a good move?

 > Would you tell someone working on complex variable theory in many
 > dimensions that they have missed or are missing a golden
 > opportunity to work on numerical methods for PDEs?

I don't know enough about complex variables and PDEs to answer this
specific question intelligently.  Instead, let me give you a generic
answer.

Suppose that X and Y are subjects.  Suppose that X is an isolated
backwater, while Y is tremendously exciting and of general
intellectual interest.  Finally, suppose there is an opportunity for
X-ists to broaden their horizons to include Y.  Then I would say, yes,
that would be a wonderful thing for the X-ists to do.

-- Steve