William Stein

William Stein joined the UW Mathematics Department in 2006 as an associate professor. He received his Ph.D. in 2000 at the University of California, Berkeley, and has since been on the faculty at Harvard and the University of California, San Diego. He does research in number theory and computation, and uses computers heavily in his work.

SAGE: Software for Algebra and Geometry Experimentation

This year the UW Mathematics Department hired William Stein as an associate professor. In January 2005 he started a project called SAGE: Software for Algebra and Geometry Experimentation, whose purpose is to create unified free open source mathematics software. He is currently using an NSF grant, startup funds, and the UW VIGRE grant to involve many UW students in research on theoretical and computational projects related to SAGE.

J. Neubuser described the crucial importance of free open source mathematics software as follows:

You can read Sylow's Theorem and its proof in Huppert's book in the library [...] then you can use Sylow's Theorem for the rest of your life free of charge, but for many computer algebra systems license fees have to be paid regularly [...]. You press buttons and you get answers in the same way as you get the bright pictures from your television set but you cannot control how they were made in either case.
With this situation two of the most basic rules of conduct in mathematics are violated: In mathematics information is passed on free of charge and everything is laid open for checking. Not applying these rules to computer algebra systems that are made for mathematical research [...] means moving in a most undesirable direction. Most important: Can we expect somebody to believe a result of a program that he is not allowed to see?
– J. Neubuser

Both the development model of SAGE and the technology itself is distinguished by a strong emphasis on openness, community, cooperation, and collaboration.

SAGE uses the open source free software GAP, Maxima, Singular, PARI, Macaulay2, Gfan, Python, and other more specialized software, to build an environment for rigorous mathematics computation. SAGE also provides unified interfaces to Mathematica, Maple, MATLAB, Magma, Axiom, and other systems.

The overall goal of SAGE is to create an optimal computational environment for research and education in algebra, geometry, number theory, cryptography, numerical analysis, statistics, and other areas. This involves the creation of software, databases, and web sites. Students at UW have been developing and implementing advanced mathematical algorithms, designing user interfaces, running computations, and giving presentations in seminars and at conferences.

I think the SAGE developers were very bold – maybe even audacious – to actually attempt this. And they are doing it in a largely pragmatic way without attempting to incorporate the more formal and theoretical ideas developed by the OpenMath community.
One might have been tempted to predict an early failure to this effort but on the contrary SAGE seems to be growing more rapidly than any other computer algebra research and development effort.
– Bill Page (one of the main Axiom developers)

The SAGE Days 2 workshop at UW in October was a major success. Over 30 mathematicians, students, and technology workers came from as far as Germany to work intensely on SAGE for five days. UW students participated in the workshop include undergraduates Emily Kirkman, Yi Qiang, Tom Boothby, and Bobby Moretti, and graduate students Josh Kantor, Robert Bradshaw, and Robert Miller.

SAGE development at UW is helping to bring a wide range of mathematicians together, from many areas of pure and applied mathematics. It is also providing long-term research experience for mathematics students, similar to what they might get working in a Biology or Physics lab:

Students at UW did not have any easy way to get started doing mathematics research (no washing petri dishes, etc.). This is something that I have experienced personally and know that many of my math major friends are frustrated about. SAGE is opening the door to advanced mathematics research to many students that wouldn't have this chance otherwise.
– Yi Qiang, UW undergraduate

If you are interested in SAGE, please drop by the "SAGE Lab," Padelford room C-423. Or come to the SAGE Seminar on Fridays at 4pm in C-401. Also, in the Spring 2007, Stein will be teaching an undergraduate number theory course, and a graduate course on the Birch and Swinnerton-Dyer conjecture, and both will use SAGE extensively.

William Stein