A free alternative to Matlab, Maple, Mathematica and Magma

An open-source tool that allows physicists and mathematicians to solve complex equations, without spending hundreds of thousands on expensive software, has won first prize in the scientific software division of Les Trophées du Libre, an international competition for free software.

The University of Washington-based program, called Sage, faced initial skepticism from mathematical and education communities.

"I've had a surprisingly large number of people tell me that something like Sage couldn't be done — that it just wasn't possible," said William Stein, associate professor of mathematics and lead developer of the tool. "I'm hearing that less now."

Open-source software, which distributes programs and all their underlying code for free, is increasingly used in everyday applications. Firefox, Linux and Open Office are well-known examples.

Until recently, nobody had done the same for the everyday tools used in mathematics. Over the past three years, more than a hundred mathematicians from around the world have worked with Stein to build a user-friendly tool that combines powerful number-crunching with new features, such as collaborative online worksheets.

"A lot of people said: 'Wow, I've been waiting forever for something like this,'"Stein said. "People are excited about it."

Sage can take the place of commercial software commonly used in mathematics education, in large government laboratories and in maths-intensive research. The program can do anything from mapping a 12-dimensional object to calculating rainfall patterns under global warming.

The idea began in 2005, when Stein was an assistant professor at Harvard University.

"For about 10 years I had been really unhappy with the state of mathematical software," Stein said.

Besides being exorbitantly expensive, the commercial programs — Matlab, Maple, Mathematica and Magma — don't always reveal how the calculations are performed. This means that other mathematicians can't scrutinise the code to see how a computer-based calculation arrived at a result.

"Not being able to check the code of a computer-based calculation is like not publishing proofs for a mathematical theorem," Stein said. "It's ludicrous."

Soon Sage will face off against the major software companies in physical space. This January, thousands of mathematicians will gather in San Diego for the joint meeting of the American Mathematical Society and the Mathematical Association of America. In the exhibition hall, Stein has paid the first-timer's rate of US$400 to rent a booth alongside those of the major mathematical software companies, where he and students will hand out DVDs with copies of Sage.

"I think we can be better than the commercial versions," he said. "I really want it to be the best mathematical software in the world."

The Sage project page is at http://www.sagemath.org.