Selected From:

*Concerns of Young Mathematicians*

Volume 3,  Issue 11

Mar. 22, 1995

An electronically distributed digest for discussions
of the issues of concern to mathematicians at the
beginning of their careers.

An E-mail Interview with Jim Phillips at Boeing.

Questions to Jim Phillips

These are questions that young mathematicians,  some applied,
some pure, would like to ask someone in your position.

1.   If you were beginning graduate school in mathematics today,
      what courses would you take to be as valuable as possible
      in the job market a few years from now?

 I find this difficult to answer without talking about a complete
curriculum, and I'm not informed enough to lay such a thing out. A Ph.D.
going into industry needs breadth (a good foundation that gives him/her the
capacity to dig into a variety of areas of mathematics, and to "think
mathematically") and depth in SOME area. In general, most graduate programs
provide both, between preparing students for qualifying or prelim exams,
and the Ph.D. work itself. Beyond that, one needs to develop an
understanding of where applied problems come from, and how one can get a
grip on them and solve them. If you knew you were going into a particular
industry, it would be easier to say what to take to accomplish this.
Lacking that foresight, some solid courses in something like engineering
physics and mathematical modeling would be desirable. To learn more about
common tools to use, a good numerical analysis foundation is a must.
Slightly (but not much) behind this, I would list optimization and
statistics. Since most physical based problems start with a PDE (or at
least an ODE), some good background in those is most desirable. Finally,
some background in scientific computing issues (e.g., basics of data
structures, solving large scale problems on computers) is highly desirable.
I realize that even this basic list is a long one. One implication of it is
that it is hard to take courses in a large number of these things if your
primary interest area does not have a large overlap with them.

2.   What are the mathematical tools that you use most?
        What are the things I should be getting familiar with?
        Is there a particular computer language  or skill that
        is absolutely necessary in a new hire?

   In the environment my group is in at Boeing, numerical analysis is
probably the toolbag used most. I listed desirable "things to get familiar
with" in 1. above. There is no particular computer language or skill that
is an "absolute" necessity. The overall requirement, however, is that you
have experience using modern computing tools to solve non-trivial problems.
That might be done in different contexts, but the most common one today
(from my perspective) is a Unix environment, and experience with both "C"
and Fortran. Someone with a reasonable computing background can generally
pick up other computing skills as needed.

3.   Suppose you are talking to a brilliant, new math Ph.D. with a
      "pure" background who really wants to get a job in industry
      in the next year or so.  What minimal re-education path
      would you suggest?

Find a way to get involved in some real world problem solving, then work
your tail off to fill in the background you need to solve the problems at
hand. A post-doc at a national lab or industry would be one such
possibility. Another possibility if you are at or near a university: start
spending time talking to colleagues in engineering or the sciences, and get
involved (by volunteering, if necessary) in solving the mathematics-related
problems that come up in their research. While you are in limbo before
finding such a position, work you way through some good books or journals
that focus on engineering or physics applications, then develop computer
tools (mathematical models, algorithms, computer program) to re-solve some
of the problems discussed there-in. Of course, if you are at a university,
you can also sit in on courses and seminars that are helpful, too. But I
think the key thing is: Get involved in problem solving. Industrial
mathematics is neither a spectator sport nor one that you can experience by
reading books or understanding more theoretical mathematics.

4.   How many Ph.D.'s from mathematics are in your employ? 
     How many statisticians?  Physicists?

PhDs: Math, 33; Statistics, 8; Physics, 2; Engineering, 6. 
MS: 29 total.

5.   How many hours per week does the average industrial mathematician

40 is the standard expectation. Many work more, either because that is
their professional style, or perhaps because they are carrying their work
further on their own so they can get a paper or conference presentation
from it.

6.   How is the work structured?  Do they just hand you a project
     and say,  "This is your baby;  get it done in 10 weeks?"
     Or do you always work in a group?  How big are these groups?
     Is there always a deadline,  or do some groups work on a
     more open-ended timetable?

There is a great deal of variety here. I think that it is accurate to
say that most mathematicians in industry are part of groups dominated by
folks with engineering or science backgrounds. As such, the mathematician
is part of a team working on a project of interest to their employer. The
"mathematical part" is generally thoroughly entwined with the other issues;
it cannot be easily separated. In particular, it is rare that the
mathematician will be handed a problem, sent off to solve it, and asked to
bring back a solution on a platter. (When that does happen, the experienced
mathematician will immediately start asking questions, because he/she will
immediately suspect that the problem they were asked to solve is not the
REAL problem that needs solving.) A team working on any particular problem
may vary from one to perhaps six or eight. There is often a hard deadline;
it depends on whether the problem under consideration is part of a schedule
driven project (e.g., getting a new product to market by a target date), or
whether it is part of longer term research and development. In the
environment I am in, the mathematicians often are working as consultants
around the company. Their customers may contract to have the mathematician
support them or their project at, say, a half-time level for a given period
of weeks or months. Whether the support is continued beyond that depends on
the state of the project and the need for further mathematical help with

7.   How do you find the mathematicians you hire?  Is there 
       a bulletin board where openings are posted?

Unfortunately, we have not been able to hire any for about 4 years due
to the recession in the industry. However, our usual sources of advertising
positions are ads in SIAM News, and announcements to e-mail distribution
lists such as NA-Net, a network of people interested in numerical analysis
issues. (Does the Young Mathematicians network list such openings in your

8.   Suppose you are looking to hire an expert in P.D.E's and
       after taking a look at the market and realizing you have
       a hundred people to choose from,  you start thinking about
       what other attributes you want this person to have.  What's
       on that list?

Experience in, and a real interest in, solving real world problems.
Ability to interact with people and work in teams. Good communication
skills, both verbal and writing. Mathematical breadth, with depth in the
PDE area (since that is what you hypothesize that I am looking for). The
depth would include knowledge and experience in solving non-trivial PDE
problems numerically, and a good understanding of some class of physical
problems (e.g., fluid dynamics or electromagnetics) that gives rise to

9.   If you could form your own applied science department to train
       future employees,  what would you put on the curriculum?

This gets back to question 1., or at least my answer to it. That is
really a tough question, because it is so tempting to list every
theoretical and applied area that one might use in his/her career. But in
actuality, the details of what one takes formally are not as important as
gaining the breadth overall, and depth in one area that I mentioned before.
After that, the interest in, and experience with, solving real world
problems, and the attitude toward real world problem solving that one
brings to the job, outweigh specific curriculum requirements. Finally, if I
were forming the department, the faculty hired would all recognize that
their graduates can have interesting and fruitful careers in non-academic
settings, and that such careers are in no way second class or less
desirable than academic careers. They are simply a second career option.