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. _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-developer
