> Or are you saying that
those are not "mathematically"
technical?

Right. They are overwhelmingly
merely heuristic.
The methodology is to guess, with
heuristics, and then try it and find out
(TIFO method) on real data, maybe adjust,
and use it when it appears to work.
There's next to nothing in theorems
and proofs before hand that show that
the manipulations will be powerful
or yield valuable results.

There is a long history of good
applied math where, once the theorems
are proved, there isn't a lot of doubt
about how the real world application
will go. E.g., (1) GPS, (2) the earlier
version for the US Navy, (3) error
correcting coding for, say, satellite
data communications, (4) phased array
passive sonar, (5) optimal allocation of
anti-ballistic missiles to incoming
warheads, .... There's much more
making good applications of math, e.g.,
Wiener filtering, the Neyman-Pearson result
in advanced radar target detection,
in cases of engineering where,
once the engineering is done,
there's not a lot of doubt about
how good the practical
results will be. No guessing.
No TIFO. Low risk. High payoff.
E.g.,

http://iliketowastemytime.com/sites/default/files/sr71_black...

As designed, unrefueled range 2000+ miles,
altitude 80,000+ feet, speed Mach 3+,
never shot down. Just as planned. Just
as clear from the engineering, based
on quite a lot of applied math.

Uh, for (5), really don't want to
have to use the TIFO method!
Instead, want to know with high
confidence before someone pushes
a big red button.

> So applied math researchers
aren't expensive?

For evaluating the cost of a startup,
commonly pay the founder $0.00 per year
until there is revenue or at least funding.
:-)! Sorry 'bout that.

E.g., I worked in artificial intelligence
at IBM's Watson lab. Part of the work
was to monitor the health and wellness
of server farms and their networks.
No theorems. No real guarantees
of the power of the data manipulations
or the value of the results. I did
an upchuck, derived some new math,
and published it. The math says that
we know in advance the false alarm
rate. The AI work didn't. The usual
approaches to machine learning don't
do such things because they don't
approach the work as assumptions,
theorems, and proofs.

For Ph.D. applied mathematicians
(I am one) at Google, once Google
ran a lot of recruiting
ads, and I sent them a resume and
got a phone interview.

They asked what my favorite programming
language was, and I said PL/I. Apparently
the only acceptable answer was C++.
It was clear enough that my
answer of PL/I essentially
ended the interview.

Why PL/I? It has some
total sweetheart scope of names rules.
The exceptional condition handling
is super nice (get an implicit
pop of the stack of dynamic descendancy
with just the right clean up).
The data structures are nearly as powerful
as classes and much faster in execution.
Threading (tasking)
in the language. Pl/I does
really nice things with
automatic storage -- C doesn't.
And there's more.

C++? We know the history: Unix
was a baby Multics, on an
8 KB DEC box. C was a dirt simple
language, no runtime. All function
calls for every little thing, e.g.,
string manipulations -- the first
version of PL/I was like that, but
the later versions compiled such
things and were much faster.
PL/I does just wonderful things
with arrays, but C doesn't really
have arrays.

Then C++? That was, along with Ratfor,
an example of Bell Labs liking
pre-processors. So, C++ was a
pre-processor to C. Instead, PL/I
was carefully designed.

My selection of PL/I over C++
was not wrong.

Google laughed at my naming PL/I.
The laugh is on Google. Uh, Linux
is a version of Unix which was
a baby version of Multics which was
written in, may I have the envelope,
please (drum roll), right, PL/I.

It was clear that my Ph.D. in applied
math and experience were of no interest
at all. None. Zip, zilch, zero.
C++? Sure. Ph.D. in applied math?
Nope -- worthless.

Okay. It was
Google's decision. But,
now I get to make a decision:
I'm not
impressed by the power of the role
of math at Google. At QUALCOMM,
maybe. At Renaissance Technologies,
sure. At Google, nope.

I still prefer PL/I to C++. Sorry
'bout that! But I wouldn't want
to use either language in production
now.

Now I program on Windows, not Linux,
and on Windows I use the .NET Framework.
To do that, for a language, I have
just two leading choices, C# or the .NET
version of Visual Basic (VB). The
difference is mostly just the flavor
of syntactic sugar, and I prefer
the more verbose flavor of VB.

For FB, I never applied -- it
seemed totally hopeless.

I'm doing my own startup, right,
based on some applied math
I derived as in my post here.

A few weeks ago I got
all the code running I first planned
to do. Now that the code is running,
I see a few tweaks. Then I will load
some initial data -- have been
having fun collecting some. Then
on to alpha test, beta test,
going live, getting publicity, users,
ads, and revenue.

Hopefully people
will like the results (from the
math, although users will not be
ware of anything mathematical);
if so, then I stand to have a nice
startup.

Much of my confidence in the work
is the theorems and what they say
about the power of the data manipulations
and the resulting value of the
results.