At least at one time and maybe still,
there was a decently good living in
applied math within 100 miles of the
Washington Monument in DC.

There early in my career, once I sent
some resumes and in two weeks went
on seven interviews and got five offers.

Big topics were scientific engineering
programming, numerical analysis, especially
numerical linear algebra, standard
applied statistics -- hypothesis testing,
linear statistics, analysis of variance,
curve fitting, etc. --
the fast Fourier transform, digital
filtering, power spectral estimation,
deterministic optimal
control theory, linear and non-linear
programming, discrete and continuous
time stochastic processes, Monte-Carlo,
numerical solutions of ordinary and
partial differential equations, etc.

Some of these topics are part of
mathematical EE.

At one time I my annual salary was
six times what a new, high end
Camaro cost. My wife got to
pursue her Ph.D. in essentially
mathematical sociology as part
of her desire to save the world
while we had big times at
Thanksgiving and Christmas,
shopped in Georgetown for high
end French wine and cheese,
were regulars with good tables
at high end restaurants,
went to lots of concerts
and plays, got a good piano
for her and a good violin
for me,
got boxes of fancy French
pastries and sweet, sparkling
dessert wines and
on Saturday nights
pigged out watching old movies,
went to Shenandoah for
vacations, had plenty of
time for trips to families
in Tennessee and Indiana,
did some fancy cooking at home,
etc.

Of course the money was coming almost
entirely through the US Federal
Government, mostly for US national
security, e.g., via the US Navy,
DARPA, etc. But, still, there was
money via the DoE, NIST, and more.

I went ahead and got an applied
math Ph.D. at Johns Hopkins,
research on stochastic optimal control.

My startup has at its core some
applied math I derived based on
some advanced prerequisites I got mostly
at Hopkins. The math is an advantage.
If the startup works, then the math
will have been the key -- except for
the math and the basic business
idea, it's all routine, that is,
the math is the only thing really
special.

Math can be used to say how to
take data that is available and
manipulate it to get data that
is valuable. Now there is a lot
of data and means to communicate,
store, process, and display it,
infrastructure software to make
the rest much easier,
ads to run to get revenue,
etc.

Except possibly for coding theory
and cryptography,
I don't know if there are valuable
applications of algebraic topology,
algebraic geometry, algebraic
number theory, commutative algebra,
etc., but for the topics I mentioned
it would seem that there is some
practical value.

For some of what can be done
with applications, there is
a long dessert buffet
from the Hahn-Banach
theorem and more in
D. Luenberger, Optimization
by Vector Space Methods.
One heck of a toolkit.
Make just one good application
and retire, make a donation
to a university, and get your
name on a building.

Here's another possibility:
Attack integer linear programming
problems in business. Focus
on the problems that can
attack with min cost flows
on networks with integer arc
capacities. Why? Because it is
just linear programming;
the simplex algorithm becomes
really simple in that case;
in practice
the simplex algorithm is
fast beyond belief on problems
large beyond belief;
and get integer programming
for no extra effort --
if start with an integer basic
feasible solution, then the
simplex algorithm will maintain
an integer solution and,
if there is an optimal
solution then will get
an integer optimal solution.
Can use this in various
resource allocation problems.
For more, use it as a linear
approximation in nonlinear
problems and for still more
enhance it with some
Lagrangian relaxation.
Show that P = NP? Nope.
Make money? Maybe.