FOM: Program verification

Matt Insall montez at
Sat Jan 29 00:21:43 EST 2000

Andrzej Trybulec said:

> > Of course I have some ulterior motives:
> > I heard an opinion, not once, that program verification is the most
> > important (the only important) challenge for mathematics in this century
> > and if mathematicians fail, the government should stop cut all money for
> > mathematics. And I would like to get my salary.

Andrej Bauer responded

> Move to a CS department...

You should at least smile when you say that. :-)

> I've heard more than once comments that mathematicians are losing
> prospective graduate students to their colleagues from computer
> science departments. Is this true?

I have seen Mathematics losing prospective graduate students to several
other departments.  However, I switched from another department to
Mathematics myself, and I have seen several students (both graduate and
undergraduate students) move from other departments into Mathematics.  There
is some very interesting Mathematics being done in many of the technical
departments here, and in other universities, but it is my experience that it
is usually not the Mathematics that attracts students out of a Mathematics
department.  It is their own distaste for Mathematics and its Foundations
that seems to DRIVE these students out of Mathematics, and for students who
switch into Mathematics, it seems to be an interest in the beauty of
Mathematics as well as the computations themselves that is attracting.

>Are the bright students choosing
> computer science departments over math departments?

This opens an interesting can of worms.  What makes a student ``bright''?
Are the rest of us somehow ``dull'' just because we choose not to jump for
every dollar?

>Is it just money,
> or has the interesting math moved to CS departments?
> --

I seriously doubt that ``the'' interesting Mathematics has ``moved'' into CS
departments.  The problems of CS have spawned some very interesting
Mathematics questions, and some of these problems have not yet been attacked
by Mathematicians in Mathematics departments.  There are various reasons for
this, not the least of which is that, because some computer scientists do
not formulate the problems they are working on clearly enough, the
Mathematicians are at a loss to understand the problem.  In other cases,
when the problem is carefully stated, it turns out to be some problem
dealing only with proper indexing and ``bookkeeping'', which some
Mathematicians are not interested in.  If the Mathematicians in question are
somewhat impatient, it is easy to decide there is nothing interesting
outside Mathematics, but patient ones see that that is a mistake.  There are
interesting problems available everywhere, both in and out of Mathematics,
but not everyone seems to be able to appreciate the value of communicating
and interacting with people from other disciplines.  The NSF is currently
pouring money into collaborative efforts all over the country, and my
colleagues in Engineering and Computer Science have been inviting me to join
them on projects which need more Mathematics than they have previous
experience with.  I actively pursue discussion with them about teaching and
research topics that interest me and I think will interest them.  As with
anything, when there is not a unity of the form of training, there is a time
period in which the communication must be developed, before very much can be
done, but I think this is the way much future research will be done, in
addition to (and certainly not to the exclusion of) the classical ``lone
problem solver'' sitting at a desk for two or three (or thirty or...) years
reading papers and grinding away at one interesting problem at a time which
is related in some important way to ``the big picture''.

 Name: Matt Insall
 Position: Associate Professor of Mathematics
 Institution: University of Missouri - Rolla
 Research interest: Foundations of Mathematics
 More information:

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