Re: Mathematics: art or science?

Herman Rubin wrote:

In article <3a833$46d6753b$82a1e228$4033@xxxxxxxxxxxxxxxx>,
Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> wrote:

It is often the case that mathematicians do what engineers have already
done. (An example is the Finite Element Method in Numerical Analysis)

One should be careful about such methods, [ ... ]

One should be more careful about what _mathematicians_ make out of such
engineering methods. They start formalizing, axiomatizing, theoretizing
without an even moderate understanding of the _real_ thing. Take a look
at the end result of such a process:

http://en.wikipedia.org/wiki/Finite_element_method

Especially read the section "A proof outline of existence and uniqueness
of the solution", where mathematicians have introduced - completely OT -
their Sobolev spaces, claiming that they can "prove" things with these.

Also read the section "Comparison to the finite difference method". And
beware! Because here comes the truth. The abovementioned section is pure
_nonsense_, because Finite Element Methods and Finite Difference Methods
are essentially equivalent:

http://hdebruijn.soo.dto.tudelft.nl/www/programs/suna01.htm

From:

http://hdebruijn.soo.dto.tudelft.nl/www/sunall.htm

Han de Bruijn

.