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 In 2001 Axiom was withdrawn from the market and released as Free and Open source software.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.