Re: [Axiom-developer] Axiom, FriCAS, forks and teeth

[Bill Page]

On 7/11/07, C Y wrote:
> ...
> THAT is the kind of project I want to work on.  The TeX of computer
> algebra systems.  Am I disconnected from reality?  Possibly.  But we
> have a wide variety of commercial systems and even free alternatives
> like Maxima that are addressing real problems today.  Axiom's codebase
> itself can be forked to a project with different objectives.  MY
> PERSONAL INTEREST is in the long term, TeX-like system that can last -
> can it be done?  What would it take?
> ...

I would say that this goal is certainly very disconnected from
reality. I think comparing computer typesetting (TeX) to computer
algebra (in general) is rather like comparing arithmetic to
mathematics (in general). We know pretty well how to do typesetting
and basic arithmetic by computer. And arguably the technology to do
these things hasn't changed very much in the last 30 years (not
withstanding a few significant innovations in numerical algorithms and
vectorized font systems etc.). But the goals of Principia Mathematica
(a universal treatment of mathematics) has been shown by
mathematicians themselves (e.g. Geodel's theorem) not to be attainable
even in principle. Similarly it seems to me that we just barely have a
few clues about how to use a computer to do algebra and more general
mathematics. We don't really know what programming languages and
systems might or might not be appropriate.

As interesting as Axiom is as a research project, realistically Axiom
(nor any other computer algebra system today) is nowhere near reaching
these goals. If by some miracle we actual had a bunch of energetic
mathematicians and developers working full time on Axiom right now, we
would likely still be scrambling just to catch up with other systems
that have become much more capable while Axiom has slept. But like
Principia Mathematica, I think there is a very real possibility that
Axiom's strongly-typed object-oriented approach is not capable even in
principle of serving as the foundation for a "universal" solution to
doing mathematics by computer. Maybe mathematics is necessarily an
activity that must be carried out in a less structured way and so
computer systems would necessarily have to be designed in a manner to
support this. I just don't know.

Anyway, research and experimentation is necessary at several different
levels and if in the end you decide to spend your time working towards
a goal that seems so far away to me that we can only just barely
imagine it, who am I to try to suggest you do otherwise. ... :-)

Regards,
Bill Page.