Re: Where do mathematical ideas come from?

mzafrullah@xxxxxxx wrote:

> It is conceivable that divorcing Mathematics completely from other
> Sciences would result in other Scientists developing their own
> Mathematics, which has already happened so often. It is also
> conceivable that when Mathematicians try to swallow this half digested
> material they do not have a first hand knowledge of what is going on,
> so their model may not be adequate.

So it has lead to situations where Applied has developed mathematics of
its own. An example is the Finite Element method, as has been developed

by mechanical and civil engineers. Has someone ever read that ugly book

by O.C Zienkiewicz: "The Finite Element Method" ? I would recommend it
to every pure mathematician. As an eye-opener.

In contrast to this, there also exist quite excellent books on
Numerical
Analysis, my absolute favorite being:

S.V. Patankar, "Numerical Heat Transfer and Fluid Flow", Hemisphere
Publishing Company, USA (1980).

This book is an eye-opener as well. Because, contrary to most standard
contemporary writeups in mathematics, it's very much _comprehensible_.

> But should it matter? If there is a
> need there would be someone else who would improve the model.

It's all a matter of efficiency. I find that contemporary mathematics,
as far as its real world applications are concerned, is not as
efficient
and effective as it could have been, given the current state of the
art.

Worse. There exist rather obvious facts which are not generally known
in
the area where they _should_ be known for sure, i.e. Numerical
Analysis.
Here comes an example:

http://hdebruijn.soo.dto.tudelft.nl/jaar2004/purified.pdf

And beware! This is not by far the only example of missed
opportunities.

Han de Bruijn

.

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