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Tuesday, November 11, 2014

Big Numbers: Google Challenges Wolfram to Open Up Math

Sage, the free and open source analog to Wolfram Research’s Mathematica, is now SageMathCloud." reports Brandi Scardilli, Editor,

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.

SMC allows users to interactively explore 3D graphics with only a browser 
Photo: Google Research Blog

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”?


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