Snippets of Pure Applicable Mathematics or
Snippets of Purified Applied Mathematics (SPAM)
Maybe it's time now for a new discipline in mathematical thinking, which is
kind of distinct from Pure Mathematics as welll as Applied Mathematics. I find
that Pure Mathematics has become too abstract, too general and too void of
But I also find that "real" Applied Mathematics has become too much of a hand
waving argument. I'm affraid that Applied has simply thrown away the child
with the bath-water. This leads me to the prediction that its success will be
declining in the future.
- "If Nature can solve its Equations, so can We" (D.Brian Spalding)
The new discipline preferrably shall be called 'Pure Applicable Mathematics'.
('Purified Applied Mathematics' would also be an good calling sequence.)
Snippets of Pure Applicable Mathematics (called SPAM ;-) are characterized by
the following properties:
Having said all this, let's stop talking. Just DoIt !
- All mathematical entities shall have their origin in the Real World. We are
definitely not interested in entities which will turn out to be just
a brain wave of some mathematical genious, and which cannot possibly have a
counterpart in the physical reality around us. Thus Mathematics should be
applicable. Read my lips: applicable. Applicable is not the same as
- On the other hand, Snippets of Pure Applicable Mathematics shall exhibit
a sufficient level of abstraction. Nobody could have
foreseen the enormous practical consequences of a
eix = cos(x) + i.sin(x)
Remember that complex numbers were just a curiosity at that time. They were
not Applied. But they have been Applicable ever since they were invented or
- Let's not give up our rights of being born First, for a mess of pottage!
Example. Mr. Lodewijk has said that pressure drops in a helically
coiled evaporator can be calculated within 50 percent accuracy. Now it's
up to you to prove it. Because otherwise we must do costly experiments.
- Absolute rigour is a phantom. How bout the computerized
proof of the Jordan Curve Theorem? How about the Andrew Wiles' courtroom style proof of
Fermat's Last Theorem? Who is going to check and debug all this?
- Attention shall be paid to issues, which were touched by some researchers,
but have been worked out insufficiently: because of their supposedly low
impact in an Industrial environment. It is emphasized that such issues were
discarded only because of the rat-race for cheap
"results", which is declared here to be irreconcilable with the spirit of
Pure Applicable Mathematics.
- Especially with "demanding applications", details which are interesting
from a pure theoretical point of view (at first sight) tend to be drowned.
Have we forgotten that theoretical results very often have the
potential to become important in practice?
Do not overlook any such "insignificant" details, because any chain is as
weak as its weakest part. And the hand of God is in tiny details,
Not in Generality ;-)
- MultiGrid Calculus (1-D)
Related: Fibonacci Iterations
Extension: TripleGrid Calculus
- Elementary Substructures (2-D)
With a lucid explanation by Gerard Westendorp
together with sources & executable
extensions to 3-D
- Quadratic Splines
- Lie Groups (1-D & 2-D)
- Graph Theory
- Cosine Powers
- Collatz Problem
- Fuzzy Frenet
and Lissajous Analysis
- The Least Squares Finite Element Method
- About the infamous Inside / Outside Problem
- Inverse Perfect Hashing &
Preliminary theory may be found with Google.
Theory as well as practice have been
Chebyshev and stuff (
software & source
Very much related subject:
Important fact is the one-to-one
Polynomial Space and
Is the Euler-Mascheroni constant rational or irrational ?
Really don't know, but anyway, here comes
some research with
software & source