Interesting Comment re Mathematica vs Everybody Else

On Mon, Nov 19, 2007 at 07:55:52AM -0800, Richard Fateman wrote:

> I tend to disagree about most (not all) mathematicians.
> They don't want to use a killer-app in their specific field.
> They want to write a journal paper about an algorithm, and in
> order to do so they pick a subset of the problems space
> that is so restricted as to be uninteresting to anyone else.

This sounds suspiciously accurate... 

> Unfortunately, nested definitions of algebraic structures, as
> possible in Axiom, does not make for a selling point for most
> people; in fact it seems to get in the way. 

I found Axiom unusable because its notion of types was far too
restrictive. It just got in the way of doing what I wanted...

> I agree that the most prevalent application for CAS seems to be
> in education. 

This is true, but I think this thread has not yet acknowledged another
area of importance... applied math.

Mathematica is extremely popular with physicists, and many of the
poorer ones have been convinced to try maxima. In engineering, there
are some hybrid solutions like Mathcad that are very popular, and
Matlab has included some CAS related functionality in recent versions
(via Maple, I believe). Excel still dominates of course, but largely
because many engineers are ludicrously ignorant about computers.

In my applied work I use two main computer tools, maxima, and
R. Maxima has been very helpful for some straightforward applied work,
such as solving DEs and PDEs, cranking out the algebra to set up an
approximate differential equation, and solving linear systems for
steady state problems like heat and water vapor flow through a wall
assembly. I even had some success in using it to correct a survey
traverse using maximum likelihood methods.

The fact is that CAS systems ought to be the scratchpad/pocket
calculator of choice in applied fields. Using them as such means that
they must be do-what-i-mean enough. Maxima seems to have started out
with this in mind, and it makes it very successful. The recent work of
the maxima team has made it even more useful in this realm.

-- 
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan