Future

So, what lessons for the future might a
young person draw from this history?

(1) Science. Off and on, some amazing
science, especially physics, played a huge
role. Maybe that will continue.

(2) Information. The desire for
information, create it, transmit it,
store it, use it, etc., seems nearly
unlimited.

(3) Logic. Want something done? Well,
describe the work in clear steps. For a
lot of work done manually in offices over
the past 100 years, such a description is
now usually fairly routine. Then with
such a description, fairly routinely can
write software to do the work. So, can
automate a huge range of old, manual work
of office workers. That's a lot of what
for some decades made IBM successful.

(4) Social. People are highly social
animals. Or to paraphrase E. Fromm, The
Art of Loving, "For humans, the
fundamental problem in life is doing
something effective about feeling alone."
In more detail, since humans are also
thinking animals, we see that alone we are
at risk, that is, vulnerable to, say, the
hostile forces of nature (earthquakes,
blizzards, tornadoes, floods, wild fires,
disease) and society (war, crime, economic
depression). Knowing that we are
vulnerable, we are worried (have
anxiety) and seek security. We feel
more vulnerable when alone so want to do
something about being alone. From Fromm
again, the first recommended solution is a
good romantic relationship. Next is a
good version of religion -- get all
wrapped up. Next is membership in a good
group -- get acceptance and approval, a
feeling of belonging. Next, not
recommended, is what some college students
try -- get drunk on alcohol, high on
drugs, and go to an orgy. So forget about
the worries until recover (but have more
worries).

So, to do something about the worries, we
want security, financial and emotional,
don't want to be lonely, do want to be
loved, want a romantic relationship, want
to belong, etc.

More generally we will want to form good
families and be in good communities.

We will be using computing and the
Internet for all they are worth for such
things.

(5) Economic Security. Likely second only
to love, and maybe more important than
love, and maybe essentially a prerequisite
to love, people want economic security,
and for that there is a famous one word
answer "more".

The drive to use logic, software,
computing, the Internet, etc. for "more"
will remain powerful for decades, maybe
centuries.

(6) Information. Now one of the keys to
more in economic security, "more", is
information, and the drive for that will
also continue for decades, etc.

For information, we take in available
data, process it, and report the resulting
information. This processing is
necessarily mathematically something,
understood or not, powerful or not. Then
clearly one approach to more powerful
processing and, thus, more powerful and
valuable information, is to use
mathematics to determine how to do the
processing.

E.g., how to look for oil? Okay, often
oil collects in pockets in the
subsurface layers. So, let's map the
layers and look for pockets. How to do
that? On the surface, have something go
"boom". Sound waves go into the ground,
and they get reflected off the layers so
that there is a convolution. So, to find
the layers, take the resulting signal and
do a deconvolution -- Enders A.
Robinson, 'Multichannel Time Series
Analysis with Digital Computer Programs'.
The fast way to do deconvolution? Sure,
the fast Fourier transform.

Once get the oil out, over here have all
that oil, from Texas, the Mideast,
Venezuela, Canada, etc. -- typically it's
all different. Over there know what can
sell -- methane, propane, gasoline,
Diesel, heating oil, motor oil, etc.

So, how to take the available input and
sell the output and make the most money?
That's a math problem, in particular in
optimization. Long the first-cut approach
was via linear optimization (programming
in the sense of operational planning).
At one time, IBM had fun selling
mainframes to Houston for just this work.
But linear programming is not quite the
right stuff. So, want some non-linear
optimization. Well, for more details, see
the work of Christodoulos A. Floudas in
chemical engineering at Princeton.
Houston does know about Professor Floudas.

There's much more to do. Right: Likely
not a single VC in the country says that
they want to see some especially valuable
software based on some especially powerful
mathematics. Hardly a one. And they are
not comfortable backing something they
understand so poorly. So, right, a lot of
confused and unhappy VCs (they so richly
deserve it!) but: Presto, bingo,
opportunity. Besides, the main raw
material into original mathematics is
paper, pencils, and coffee, and how
expensive are those?

Almost inevitably, there will be only a
few people going that way with the rest
heaping ridicule, etc. Not nearly new:
Think of the Mother Goose story The
Little Red Hen.

Secret: It turns out, no matter how much
advanced and/or original mathematics you
use, nearly always a lot of the actual
computations will boil down to linear
algebra and there, numerical linear
algebra. So, take linear algebra,
elementary, intermediate, advanced,
applied, numerical, and related subjects
such as linear programming, non-linear
programming, multi-variate statistics,
ordinary and partial differential
equations and their numerical solutions.
For more, study the leading
generalizations of linear algebra,
functional analysis, e.g., Hilbert and
Banach spaces.

(7) Niches. One of the standard ways to
make money is to have close to a monopoly,
and one of the standard ways to do that is
to have a niche of some kind and where
the monopoly is protected by, say, a
geographical barrier to entry, an
especially good product or service, some
crucial, core, defensible technology or
know-how, a good customer list, some
network effect, etc.

So, go for it!