# Axiom -- The Thirty Year Horizon

## Timothy Daly (CAISS at City College)

Axiom has existed for over 30 years. It was born as a research effort
at IBM Research, passed through a long development phase, and was
eventually sold as a commercial competitor to Mathematica and Maple.
Axiom is a huge, complex program that involved over 150 people and
over 300 man-years of research. In 2001 Axiom was withdrawn from
the market and released as Free and Open source software. This talk
covers the 30 year horizon into the past, discusses the present
situation, and discusses the view of the next 30 year horizon.

# Symbolic Computation for Fun, Education, and Research

## William Sit (CCNY Department of Mathematics)

Symbolic computation is the art as well as the science of "teaching"
computers to perform mathematical computations that involve symbols
(variables, parameters, unknowns, indeterminates). There are many
commercial as well as open source software systems that can do
symbolic computations. In this talk, we will illustrate how to
"tailor" ("teach", "tweak", "apply", "program") symbolic computation
software to do what we love to do: for fun, education, and research.
The fun part will be using symbolic computation to design and solve
crossnumber puzzles. The serious parts will involve linear and
non-linear differential equations.

Chacun à son Goût!

# An Incremental Approach to Building a Mathematical Expert Out of Software

## Richard Fateman (U.C. Berkeley)

Pick a class of problems, and then simulate, on a computer, an expert
human solving that problem. Or take all the solved problems from all
the books, and use Google to find answers. Why don't these ideas work?
What ideas might work? We address these questions based on some 40
years of progress in symbolic math programs, including some impressive
strides. As time permits, a case study of building an internet expert
on symbolic integration.

# Collaborative Software Development

## Camm Maguire (INTECH)

In recent years, the ease of communication afforded by the Internet has
turned conventional thinking on the prerequisites for successful software
development on its head. That the real world value proposition of
contributing a fraction of ones time and expertise freely to a development
effort staffed entirely by volunteers spread throughout the world could
clearly exceed that provided by the model of paying for a lease on
commercially developed software forms a paradox long familiar to the
world of science, but only capturing the attention of both business and
the general public at large.
# MathAction - Collaborative Mathematics on the Web using Axiom and REDUCE

## William Page (Axiom Wiki Developer)

Among those systems which allow one to do mathematics on the
computer, Axiom is notable for being concerned with the accurate
representation of mathematical concepts such as formalized in
category theory. Developed over a 30 year period by IBM, NAG and
others, Axiom pioneered several new programming concepts including
a strongly-typed object-oriented design which has yet to be fully
exploited by any other computer algebra system. Axiom is now open
source and can be freely installed on desktop workstations. Axiom
can also be accessed over the Web through an experimental
collaborative interface called MathAction that enables LATEX and
Axiom commands to be entered online. Computer generated output
is displayed in standard mathematical form on web pages that can
later be edited and updated by others. This web interface is easily
extended to other packages and now also includes REDUCE - a computer
algebra system widely used in mathematical physics and of similar
vintage as Axiom. Several examples of using MathAction for
collaborative research in mathematical physics will be presented
including Clifford algebra, exterior differential forms, exact
solutions of partial differential equations and for graphical
visualizations in quantum mechanics and general relativity.