
1. How many
mathematicians and/or people with math degrees does Aerospace employ?
We have a technical staff (engineers, physical and
mathematical sciences, and others) of about 2400. About seven percent (162) have mathematics as
a terminal degree; about 35 hold PhD’s.
Of the 162, academic mathematicians would recognize few as
mathematicians  about 20. A recent
listing of open positions included 70 for which a math degree was included as a
prerequisite. Another 30 positions did
not explicitly request mathematicians, but involved highly mathematical
activities. All Aerospace technical positions require a security clearance that is
dependent upon
2. Why does
Aerospace hire mathematicians or people with math degrees?
We recognize that mathematics training provides excellent experience in critical thinking skills. When mathematicians start at Aerospace, they join an engineering team and apply their analytical skills to solving engineering problems. Mathematicians are valued for their ability to adapt to new problems and their ability to grasp underlying principles. Space system complexity requires people with broad skills and flexibility to analyze and solve problems. Many mathematicians may start by performing mathematics, but many evolve over the years into systems engineers  people who understand how to build entire systems, which in our case are space systems: satellites, launch vehicles, and their ground support.
3. What does
Aerospace look for in a mathematician applicant? Essential qualities?
We hire many kinds of mathematicians and have extremely high standards. We require mathematical maturity  the ability to deal with any kind of mathematics problem, regardless of the person's formal training. We value mathematicians with PhD’s because they generally show both creativity and flexibility in their approach to problem solving. Mathematicians are not hired simply to pursue their own specialties, but to solve practical and complex problems. We do not require an applied degree  the Program Manager for a surveillance system did his dissertation in ring theory  and have algebraists, gauge theorists, and combinatorists working alongside specialists in numerical analysis, PDEs/ODEs, and optimization. We also demand excellent interpersonal skills  the ability to work in small, interdisciplinary groups  written, verbal, and aural communications talent, and expect that every employee be computer literate, with word processing, spreadsheet, programming, and tool (e.g., mathematical) skills.
4. Does Aerospace
prefer to hire Ph.D's, master's, or bachelor's?
Our mix is 28 % PhD, 43 % Masters', and 28 % bachelor’s' degrees. We prefer PhDs or else nonPhDs with specialized skills and many years experience, but will accept a master’s degree. Because few new employees are trained in space systems, we provide inhouse classes and phased tasks to our employees. We do have a few positions for entrylevel (fresh master’s degree) staff, but strongly encourage additional schooling once an entrylevel employee is established.
5. Does Aerospace prefer mathematicians with
a broad background or specialization within one area?
Both. See remark about mathematical maturity in #3.
6. For which of the following is Aerospace
interested in the mathematician?
1) Discipline and logic
2) Ability to recognize a mathematical
problem in a realworld situation
3) Analytic skills
All of the above, but in the order 2, 3, 1. In addition to recognizing the problem in a realworld situation, we expect a solution!
7. Has Aerospace
hired mathematicians or people with math degrees for reasons other than using
mathematics directly?
Certainly. A mathematical background is tremendously
helpful, since many of the engineering problems to be solved require
mathematical sophistication. As
Aerospace employees, mathematicians cannot simply stop with a proof that a
solution exists. They may be asked to
develop a partial solution within an hour or two. Oftentimes, they must also develop the
necessary software needed to implement a practical solution in an efficient and
timely manner. They must be able to
communicate their results clearly and succinctly to a customer who may not have
a great deal of mathematical sophistication, is not interested in how the
solution was developed, only in its cost and schedule impacts, and has little
time or patience for a complete presentation.
8. Do the
mathematicians at Aerospace work more as a separate entity or within groups of
some other discipline?
Although
there are clusters of mathematicians, there is no Mathematics Department. For example, the Navigation and
Geopositioning Systems Department, responsible for estimation theory related to
positioning applications, has mathematicians for 60 % of its staff. It is hard to tell on the surface who is a
mathematician and who is an engineer or physical scientist. Generally, we look for mathematicians who can
adapt their research skills to applied disciplines.
9. Do the
mathematicians at Aerospace conduct research or serve more as a consultant to
other group members?
Aerospace
is structured into two generic organizations:
program offices and support departments.
Employees in program offices are devoted to a single space system 
Delta launch vehicles or GPS satellites, for instance. Support staff members are organized by
technical discipline  radar, controls, or navigation. There is no mathematics department. As program offices require specialized
skills, they contract for services from the support departments. In this respect, mathematicians consult.
There
are only a few Aerospace employees who perform mathematical research as the
academic community recognizes it. On the
other hand, many people develop concepts requiring the same talents as formal
research demands, but their focus is on solving a particular class of
problems. It is not the research per se, but their expertise that is
sought out by others. Excellent
mathematicians recognize the elegant mathematics behind the solutions and
generalize.
10. Do
mathematicians need to be retrained to adjust to Aerospace activities?
Certainly  How many
academic mathematics departments know how to build a satellite? More important, there is a culture here at
Aerospace (and in industry in general) that must be absorbed. We cannot have mathematicians or chemists or
computer scientists who live in isolation and work pure problems within their
domains. Instead, we must understand how
everything is connected. A numerical
integrator used within a launch vehicle guidance algorithm must not only pass
all the tests (stability, convergence, truncation, ...),
it must also be packaged in such a way that it will be robust under a wide
variety of initial conditions. Further,
it must be presented to the customer as an efficient and costeffective method
worthy of consideration in light of competition from other algorithms that have
been used for years and years. The
integrator must be tolerant of other vehicle systems which may not know exactly
what time it is, which way is up, or where the vehicle is. Heady stuff!
11. What are the strengths and weaknesses of
mathematicians in contributing to Aerospace?
Mathematicians
frequently provide fresh and innovative approaches to complex and unusual
problems. Mathematicians provide a
sanity check on the assumptions that engineers make. 99 % of the time, the assumptions are right,
but one chance in a hundred with a billion dollar satellite is one chance too
many. Mathematicians may also think in a
manner orthogonal to those of other academic persuasions. Some employees (mathematicians included)
never make it off the ground following their hire because they cannot relate
their (academic) skills to the reality of the workplace. We see employment application after
employment application in which the applicant offers us the opportunity to
support his/her research in some discipline.
Sorry  when you work for Aerospace, you have to solve Aerospace
problems. If you can find a
researchlevel topic hidden in more mundane work, you can often find support
for a limited time in an investigation to extend your result past its initial
use for future application. In the end,
Aerospace shares a limited military budget and cannot expend effort on tasks
that do not advance its clients’ needs.
12. What are the opportunities for mathematicians or people
with math degrees at Aerospace?
Because
of our profession's focused reputation:
Here's to Uncle Albert E
Pundit of relativity
You'll know him by his shaggy locks
And by his utter lack of socks!
mathematicians
start work at a disadvantage. As
problems get harder and harder (the world is not linear!), they are being
appreciated more and more. The
recognition process is twoway. The
company must recognize the excellence of the results mathematicians produce and
the mathematician must understand what the company desires. For these reasons, Aerospace takes great care
in placing mathematicians into the right internal organizations to achieve
their greatest potential.
13. What areas of
mathematics are applicable to Aerospace activities?
Our
prime areas are applied disciplines:
numerical analysis, probability and statistics (assuming this is
accepted as mathematics), applied linear algebra, optimization, and discrete
mathematics (filter and coding theory).
We also do a bit of harmonic analysis (signal processing),
combinatorics, and differential equations.
Be warned that mathematics at Aerospace is practiced by a lot of people,
many of whom are not mathematicians.
Some of our best mathematicians are engineers and some of our best
engineers are mathematicians.
14. What kind of
mathematical problems does your company face?
Just about every kind of applied problem. This includes
practically every technique in numerical analysis, from linear algebra to
numerical solution of initial value problems to least squares; computational
geometry (Voronoi cells); optimization (nonlinear
with constraints); harmonic analysis (signal processing)  the list seems
endless. We deal with both continuous
and discrete mathematics. Consider the
problem of a satellite tasked to look at a large number of ground targets. It must find as many targets as
possible. Each target has a importance
score, different viewing geometries with each satellite flyby, and different
update requirements (once per day, once per week,...). Steering the satellite sensor adds to the
problem complexity, as does the time the sensor must spend pointed at the target.
This is a combinatorial optimization problem worthy of study. Clustering theory plays a role in signal
processing and logic is applied to computer security applications.
We
must deal with solutions known to be partially correct. Oftentimes, a client will request an answer
within an hour and is willing to accept incomplete answers under time pressure.
15. At what stages
of the product cycle is mathematics used most frequently?
At
all stages, but its primary application comes early in the cycle, before all
the complications of an operating satellite system so compound the problems we
face that mathematical abstraction gets lost in the constraint details. On the other hand, mathematically based
reasoning, creativity, and flexibility can be applied to diagnose problems,
analyze data, and maximize the utility of limited resources at any stage of the
product cycle.
16. How has mathematical work benefited
Aerospace?
Primarily in the application of numerical techniques. Aerospace has
employed a number of wellknown folks  including Conte, (Herb) Keller, Osgood  and has gotten great help from them. While there is excellent mathematical work
being done at Aerospace, it is hard to isolate it from other disciplines. For example, we have a strong group in
optimization that applies the theory to finding the best launch
trajectories. Generally, we are
interested in orbiting as much payload weight as we can, since that extra
weight usually comes in the form of propellant used by the satellite in attitude
control. The more propellant, the longer
the satellite can be used. Even ten
pounds can last for a year, well worth the effort for a billion dollar bird.
17. Are other
professionals at Aerospace well trained in mathematics?
Yes! See #13. However, note that knowing mathematical tools
and thinking like a mathematician are two different matters.
18. Where is
mathematics likely to have the greatest contribution for Aerospace in the next
few years?
We
foresee no change in our usage of mathematics and mathematicians.
For
further information, contact:
Dr.
Gary B. Green M4/944
The
Aerospace Corporation
Los Angeles, CA 900092957
(310) 3368761
Email: gary.green@aero.org