From: kubo@boucher.harvard.edu (Tal Kubo)
Newsgroups: sci.math
Subject: Re: Alleged shortage of mathematicians (was Re: M
Date: 17 Dec 92 05:15:24 GMT
Article-I.D.: husc3.1992Dec17.001527.18598
Organization: Dept. of Math, Harvard Univ.

In article <1413@kepler1.rentec.com>
andrew@rentec.com (Andrew Mullhaupt) writes: 

>>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.
>
>Nope. That ain't research all right. However if it's not in the literature
>then even though you may suspect that other people have solved it and not
>published it, it's research.

Huh? The issue of duplicating published work is a red herring. It's
not necessary that all the details needed to solve your problem be
published or even known. There are lots of problems which are not yet
solved, in the literature or elsewhere, whose solution might involve lots
of work and ingenuity and yet fail to generate any really new ideas in the
relevant theory.

>... [students] may not have been well served by their professors. In
>particular, we have heard more than one instance where academics have
>tried to keep the existence of talented students from industrial
>colleagues. We have also heard about academics who feel indignant that the
>industrial people want the best available talent.
>
>I think it's unethical to overproduce students who are not made aware of
>the likely employment outlook in the field they study. It's unethical to
>prevent industrial people from advertising opportunities to students who
>might very well be interested in them. 

Certainly it's deplorable to cut off students from available
opportunities, or to sell them false hopes.  However, when claims are
made such as that conditions "are not a specific fault of the
mathematical job market" or "like it or not, some PhD's will be getting
applied experience ... and the bright ones will make the most of it"
that just sounds like Wall Street types getting on the high horse.

>> ... [there exist exceptions] 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).
>
>Umm, I have doubts about your understanding of the relationship between
>chemistry and chemical engineering. Chemical engineering is not all that
>much about chemistry. In fact large amounts of chemical engineering are
>mathematical engineering.

I should have said, chemistry done in industry, rather than chemical
engineering (which as you point out is sufficiently different to vitiate
the original analogy).  Although industry may be ahead in certain parts of
that field, the situation is in general that new ideas are developed in
academia and optimized in industry. (At least that's the consensus among
chemists to whom I've spoken.)

>But that's besides the point. You seem willing to claim that all the
>stuff I need is already done mathematics. I have a list I would be
>totally happy if you'd look up for me.... Really, nothing would make
>me happier than to find my unanswered questions in the literature
>tomorrow.

Again, I think this misses the point.  Just because the problem hasn't
been done before doesn't necessarily render it an interesting line of
research. Consider, for example, extending certain results from algebras to
superalgebras.  There are lots of cases where even though it's not clear
how to do the proofs, nobody bothers trying because it would amount to an
unrewarding, if difficult, exercise.  One would know more after making the
effort, but would not necessarily be any wiser.

>> 1. Less choice of what problems to work on
>
>There isn't necessarily much of this in academics. I can name at least
>one instutition where you aren't getting tenure without an NSF grant,
>and you aren't going to get one of those for just any old problem. 

There's still plenty of room to choose.  On the other hand, if your
employer wants a particular problem solved during the 67% of your time
under his control, I doubt he would take kindly to a refusal.

>in my present employment, I am _explicitly_ licensed to spend on
>the order of 25% to 33% of my time on [...] whatever I choose,

The 1/3 discretionary time allotment, the Veblen prize winner down the
hall, the offices located on a university campus, and the density of
ex-professors among the staff, suggest to me that your job is hardly a
typical example of what one can expect in industry, even with a doctorate
in mathematics.  The exception proves the rule...

>> 2. More emphasis on programming and implementation of algorithms
>
>I don't think so. When I go over to the local SUNY math lab I see grad
>students hogging the terminals just like when I was a grad student. 

Does this mean anything at all?  The banal caveats on the 
interpretation of statistical samples, etc, apply here. 

>There are a lot of mathematical fields where numerical experiments are 
>as much a time sink as theorem proving. I remember number theory being
>very much a computationally involved field, and this is less and less an
>exception every day that goes by.

Even in computationally intensive fields (e.g. complex dynamics, popular
at some of those same SUNY math labs), a researcher will typically spend
less time on computation than would likely be the case in industry,
precisely because there is also a substantial theorem proving component 
to the work.  Yes, I know there are exceptions, on both sides.

>> 3. Mathematical work is viewed as a means to an end
>
>True. But I contend that this is somewhat observed in the 
>breach in academia, especially in terms of grant proposals.

Fair enough.

>> 4. More work in teams
>
>Not really. I think that where I have been, the collaborations 
>are roughly the same as in industry and academics.... average
>collaboration size is something between 1.5 and 2.5.

My rough impression is that if you look at things published by
people working outside academia, the average length of the author
list is substantially higher than in "pure" publications.  It 
would be interesting to see if any data has been compiled on this. 

>> 7. Less exposure to mathematical literature outside the field.
>
>I get a bigger exposure than before because I now have access to the
>Math Reviews on CD since we moved our offices onto the local State
>University Campus. That didn't exist when I was a professor. I will
>admit that I don't spend as much time reading the journals, but I don't
>spend any time writing grant proposals, either.

I take the above remarks as conclusive proof of my point.  If even in
your exceptional circumstances, with an office on (!) the university
campus to boot, you don't read as much as before, then I wonder how a
garden-variety industrial math job would affect one's "literacy". 

>Publishing is a credential which is good for academic employment. Once
>you consider the possibility of other employment, it isn't the only
>thing any more. I like the quote in the front of Billingsley's book to
>the effect that "... I would rather a man be knockt on the head than he write
>something in mathematics that is not new..." There's publishing to advance
>the field and then there's that other thing.

If you don't intend to pursue a professorship, or to build a public
reputation for other purposes, then clearly ability to publish is
unimportant.  But anonymity can be a drawback in more subtle ways, 
since you might diminish your chances for recognition in the form
of conference invitations, outside consulting work, and so on.

Publications aside, I see this as part of a more general problem with
private employment, where you miss out on a lot of opportunities to meet
people outside your own backyard.  The mechanisms for doing so are much
better developed in academia (visiting scholars, colloquia, sabbatical
leave, conferences, travel grants, etc).  Employers are gradually becoming
more enlightened in this respect, though.

>Remember that I don't teach any courses, and I don't sit on committees,
>and I don't have office hours. When you tot it all up it really isn't
>clear to me that I don't have as much time for research as I did in
>academics. 

It isn't clear to me, either.  Teaching, grant writing and the like 
take up a lot of time, but so do corporate chores like briefings, 
committee meetings, solving in-house technical problems, miscellaneous
firefighting, writing reports to the bosses and clients, and other
mundanities.  Now, your own job might not be fraught with too many of
these distractions, but if anything what I have described is a lot more
representative than the rather peculiar conditions of your employment.

Also, most people simply don't have the capacity to be productive in a
research sense during all of their working hours; how much their other
work duties would impinge on this capacity depends very much on how those
hours are spent. I'm inclined to think that teaching and doing other
research (on the employer's problems, for example) would both be among the
most draining activities.  From what I've heard the best work environments
are not in business or academia, but in independent institutes such as IDA.

-Tal  kubo@math.harvard.edu
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