From: kubo@zariski.harvard.edu (Tal Kubo)
Newsgroups: sci.math
Subject: Re: Alleged shortage of mathematicians (was Re: M
Date: 12 Dec 92 02:37:54 GMT
Article-I.D.: husc3.1992Dec11.213755.18417
Organization: Dept. of Math, Harvard Univ.

In article <1401@kepler1.rentec.com>
andrew@rentec.com (Andrew Mullhaupt) writes: 
>>
>>	[a distinction always emerges between those who produce and
>>	 those who consume]
>
>Only when the problem is effectively solved. 

Just because there is some distance between a theory and the intended
application, doesn't mean that interpolating between them is necessarily
mathematical research.  The problem might be difficult and interesting,
and far from solved (as in the problem of a moon landing, circa 1960), but
the nature of the difficulty need not lie in the theory.

>> does there exist a substantial, but largely untapped and
>>overlooked, lode of mathematical employment, outside of the well-trodden
>>paths in academia, available to recent PhD's in mathematics?  

>No that is not the question. You can raise it if you want. The question
>as I see it is "should a  Ph. D. limit himself to employment as a pure
>mathematics research professor?"

The answer to your question is a truism, so it doesn't seem interesting
to ponder it.  This discussion began with some messages noting that 
certain predicted shortages of mathematicians (and consequent job
opportunities) had failed to materialize.  Robert Frey and yourself have
suggested, in effect, that such complaints come from crybabies who are
too narrow minded to avail themselves of the job opportunities available
in industry (particularly on Wall Street).  Several people expressed
skepticism about such employment, or at least its relevance to
*mathematics* job shortages. In light of this, I think that the first
formulation is the more pertinent one.  Another way of asking it is, 
"do industrial positions in mathematics have any bearing on the
shortage of jobs for mathematicians (_qua_ mathematicians)?"  Or if you'd
prefer a less loaded question, "what are the similarities and differences
between industrial and academic mathematics positions?".

>In the case of displacement structure, the point is quite clear. This is
>a bunch of pure mathematics whose express purpose is to arrive at signal
>processing algorithms which can be done in real time and with minimum
>silicon.  [...] 

Could you provide a reference where this program is outlined?

>Do you seriously believe that nobody in the relevant
>industries does effectively the same kind of work as [in academia]?

In essence, yes.  There are some limited exceptions, such as the
research arms of certain big companies, but most positions in industry
are related to mathematics in the same way chemical engineering is
related to chemistry (yes, mathematical engineering would be an 
appropriate term here).  Some relevant differences are:

 1. Less choice of what problems to work on
 2. More emphasis on programming and implementation of algorithms
 3. Mathematical work is viewed as a means to an end
 4. More work in teams
 5. Contact with mathematics is biased toward certain fields (e.g.
    analysis, combinatorics, statistics).
 6. Less opportunity to learn unrelated branches of mathematics.
    Imagine the look on your boss' face when you explain your interest
    in reading set theory, categories and nonstandard analysis on
    company time.
 7. Less exposure to mathematical literature outside the field.

I repeat, there are some exceptions, and of course some people might see
some of the above as features not bugs.  But in general I would expect that
such drawbacks, combined with limitations on publishing the work, would
indeed depreciate one's research credentials as suggested earlier.

>My point is that separating people or mathematics into pure and applied is
>silly. From this I draw the corollary that one is not permanently tainted
>or lost to mathematics if one spends a few years doing a mixture of math
>and something else, and that new Ph. D.'s should consider a broader class
>of sensible employment. What's more, academics should be less obsessed

It's silly in the same way that most such categorization is silly: it
serves no purpose except to put people in boxes. What sort of work
one finds interesting is obviously a matter of taste independent of any
such categories.  However, I think that it is relevant and interesting 
to honestly isolate the differences between different types of
mathematical work, rather than blindly insisting that they are all
the same just because they involve mathematics.

>>>I just want everyone to agree that people who call themselves 'pure
>>>mathematicians' are not the sole progenitors of mathematics.
>
>The idea that there is not a significant chance to produce mathematics
>outside of academia seems to me to claim that there is a difference.

Nobody says that industrial mathematics is nonmathematics, but it's
rather disingenuous to claim that it is identical to the product 
produced in universities.  There are clear differences in the working 
conditions, the style of work, the scope of the work, and the later
ramifications within mathematics.

>It's quite a bit more cynical to count theorems than to count the
>revenue. Counting the revenue is essentially totally objective in
>many cases and agreeable to both parties. [...] I'll take Wall Street
>any day.

This gets back to a point that Allan Adler has made eloquently, about 
the need for objective criteria of job performance in mathematics. I
don't agree, though, that counting the revenue is much more objective,
since profitability depends to a large extent on other people,
circumstances, and various other factors not connected with the performance
of the job.  (I note that you found cause to qualify the second sentence to
"essentially" objective in "many" cases.)  Revenue-counting is agreeable
only in the sense that it's consensual; I can't think of many jobs where
the means of evaluation are negotiable.

-Tal     kubo@math.harvard.edu