From: andrew@rentec.com (Andrew Mullhaupt)
Newsgroups: sci.math
Subject: Re: Alleged shortage of mathematicians (was Re: M
Date: 16 Dec 92 00:04:42 GMT
Organization: Renaissance Technologies Corp., Setauket, NY.

In article <1992Dec11.213755.18417@husc3.harvard.edu> kubo@zariski.harvard.edu (Tal Kubo) 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.

>  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). 

Actually, I think the complaints come from students who 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. 

>>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). 

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.

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.

>Some relevant differences are:

> 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. Note
that in my present employment, I am _explicitly_ licensed to spend on
the order of 25% to 33% of my time on 'bootleg' research - i.e. whatever
I choose, although recently I haven't spent this much at all. I am also
encouraged to collaborate with people in universities, but unlike Frey,
I spend somewhat less of my time on this important subject.

Keep in mind that 25%-33% of my time for free investigation is a bit more
than it seems since I don't teach courses or sit on lots of committees.

And for the rest? Sure I work on problems that have come out of my colleagues
work, but that doesn't mean I wouldn't choose to work on it. I have some
amount of say about what is important here too.

> 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. 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.

So yes, there's lots of emphasis here, but there isn't necessarily any less
in some academic fields.

> 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.

> 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. The real team players are the
combinatorialists, but most industrial guys are analysts, (like most
mathematicians unless things have changed a lot) and the average
collaboration size is something between 1.5 and 2.5.

> 5. Contact with mathematics is biased toward certain fields (e.g.
>    analysis, combinatorics, statistics).

Definitely. But don't be surprised when we use anything we find lying
around.

> 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.

In my job I am expected to find out whatever it takes to get it done.
My boss happens to be a famous differential geometer (Veblen prize), and the
other guys more senior to me are from Differential Topology and Several
Complex Variables. It was kind of funny because at lunch once I was
explaining how Birkhoff's theorem on equational presentations can be proved 
entirely from category theory, and they were somewhat amused that as a
nominally 'applied' guy I was more interested in category theory than they
were. But if push came to shove in pure mathematics (outside of stuff
I am interested in like some parts of analytic number theory) I'd _ask_
my 'boss' about it first. 

> 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 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.

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.

>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.

Not clear to me, although I kind of miss teaching... 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.

Later,
Andrew Mullhaupt