Sage, the free and open source analog to Wolfram Research’s Mathematica, is now SageMathCloud. Thanks to collaboration with Google’s cloud services, Sage is now in a position to draw more mathematicians to its community.
In a blog announcement of the collaboration, Google throws down a gauntlet against claims of ownership of mathematical truths by the likes of Wolfram:
Modern mathematics research is distinguished by its openness. The notion of “mathematical truth” depends on theorems being published with proof, letting the reader understand how new results build on the old, all the way down to basic mathematical axioms and definitions. These new results become tools to aid further progress.
Why does Google take a philosophical position on mathematical processes? It may be to take Wolfram down a peg.
The Problem With Mathematica
Wolfram is arguably the world’s dominant mathematics software provider. Since its release in 1988, the company’s flagship Mathematica software has become the “definitive system for modern technical computing” around the world, as its website says. Mathematica contains libraries of mathematical functions, computational tools for practices such as machine learning and data mining, and even free-form linguistic input for English-language queries.
But Mathematica was conceived in a pre-internet era. Although Wolfram has very cannily moved onto the web and into social media through Wolfram|Alpha, that engine is perhaps still less of a go-to math tool for average users than Google Calculator. As of October 2014, Wolfram|Alpha’s global Alexa rank was 2,868, while Google’s Alexa rank was—and continues to be—1. Of course, it’s not entirely fair to suggest a one-to-one comparison of Google Calculator to Wolfram|Alpha, because both quantitative and qualitative differences exist between them. Google may be the top site in the world, but Google Calculator on its own is not; and Google Calculator pointedly lacks the functionality, range of tools, “graphy-ness,” and intuitive (linguistic) input of Wolfram|Alpha. In other words, one tool is fit for the exploration of the Moore-Penrose pseudoinverse matrix, and the other is fit for simply adding 1 + 9 + 9 + 0.
Wolfram (like Google) is a for-profit enterprise (Mathematica’s prices are here), and as such, it is keen to protect its software and even its software’s calculations. Wolfram holds the position that because the information generated by its software is novel, the results of its calculations may be subject to copyright by Wolfram.
As Richard Stallman points out on the GNU website, there is much confusion surrounding the issues of copyright, copyleft, open source, and free software. Mathematica users themselves have been wondering for at least a couple of years whether there is a free and/or libre “open source implementation” of Mathematica language and what exactly that would mean for mathematics. Is the mathematics field, as Google claims in its blog post, inherently dependent on “openness”?
Due to the cost and closed nature of proprietary software such as Mathematica and MATLAB, many “open” mathematics software projects have indeed begun to appear. Since the 1990s and the advent of BSD licenses and the promulgation of the GNU Lesser General Public License, a number of numerical and statistical software suites have been developed and have become widely known. OpenFOAM, R, Maxima, GNU Octave, FreeFem++, Euler Math Toolbox, and AD Model Builder (ADMB), almost all of which had origins or initial releases in the 1990s or earlier, have been followed by a number of new tools—many of which have only just appeared in the last 2–3 years. Some are overt about their aims; Mathics, for example, “is a free, general-purpose online computer algebra system featuring Mathematica-compatible syntax and functions. It is backed by highly extensible Python code, relying on SymPy for most mathematical tasks.” It does indeed appear that SageMathCloud has come along at just the right time and that Google and Sage together will take advantage of a new open source moment in the mathematics community.
Marshall Hampton, associate professor in the department of mathematics and statistics at the University of Minnesota–Duluth, is an advocate of open math who uses R in his bioinformatics work. He says, “I use the free, open-source program/environment Sage in all of my work; I encourage you to try it and contribute to it if you can.” R is part of Sage, and “Sage includes many independent open projects that I find helpful, such as Gfan and Biopython. The typesetting language LaTeX is another open tool I use daily.” Hampton expresses a critical view of the idea that Wolfram or anyone else can copyright math: “I think any claim of copyright on a calculation is pretty ridiculous.” He concedes that graphical or interactive output, although not the content of a calculation, could be copyrightable.
With advocacy by the likes of Hampton and his peers and students, the new open-licensed and open source languages have quickly gained ground. Julia, SALOME, ScicosLab, X10, Scilab, Chapel, Gmsh, Fortress, and FreeMat are all available under GNU-compatible licensing. By using the Google Cloud Platform, Sage is in a powerful position to lead in the realm of open source mathematics projects; and Google, a for-profit corporation, is clearly facilitating the growth of potential not-for-profit and free/libre competitors to Wolfram.