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

[C Y]

--- Bill Page <address@hidden> wrote:

> On 7/11/07, C Y wrote:

> > OK.  So then, how DO we work with mathematics? (I don't expect an
> > answer - but it's still a reasonable question, unless one wants to
> > throw up one's hands.  A universal treatment (whatever that means)
> > might not be possible, but what is the best solution (or solutions)
> > that ARE possible?)
> 
> Perhaps the answer lies in category theory as a foundation for
> mathematics and as a model for appropriate formalisms in computer
> science.

Then, in that case, we are ENTIRELY in agreement! :-).  That is
PRECISELY the direction I am interested in exploring.
 
> Seriously, I do not think we are at the stage where we can trust the
> output of any system -- certainly not one that is complicated enough
> to include arithmetic (ref: Geodel's theorem). I agree that the
> marriage of computer algebra and computer aided proof systems is an
> interesting concept but it is still at the very early research stage.

Certainly.  But that to me is a call to drive the research forward - it
won't happen by itself.  Since at the moment funding and programs to do
this seem rather hard to come by, it must be done outside traditional
academic research institutions.  (Although I hope with a quality that
will appeal to them none the less...)
 
> > I would be curious what branch(es) of mathematics you think Axiom
> > will be incapable of dealing with, via one form or another of 
> > extension?  Is
> > there any possible system you feel would be MORE useful?
> >
> 
> Category theory, category theory. Any computer algebra system that
> makes at least a half way attempt to structure things according to
> category theory.

EXACTLY.  I understood Axiom was already relatively close to category
theory, but not quite.  Once a proper non-algebra framework is in place
(i.e. one I can ignore), my next thought is to use Stephen's SPAD to
attempt to implement a CAS foundation which will feel "natural" to
research mathematicians, and begin to include the current Algebra work
in that framework.

> > ...
> > Am I nuts?  Probably ;-).  I don't know if even Tim shares my views
> > in this respect.  I know I'm not a good fit for FriCAS, perhaps I
am
> > not a good fit for Axiom.  But what else can we do in a volunteer
> > project but pursue our interests?  If those are not compatible with
> > the project, I can work on my own - I have no wish to disrupt
> > anything any further than it has already been disrupted.
> 
> Gee, there must be something (bad vibes?) in the air recently ... ;-)
> 
> Certainly you have as much right to be here (or there) as anyone
> else. I do not find any of the work you do or your comments at all
> disruptive.

Thank you for that, Bill.  I very much enjoy the Axiom community, and
admire its members for their skill and willingness to contribute.  My
hope is that we can all settle into where we feel comfortable (Axiom or
FriCAS as interest dictates) and advance the state of the art.

Now, I need to write some actual pamphlets... ;-)

Cheers,
CY


 
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