Free math

Many years ago, when I was a grad student, I bought a student-discount copy of Mathematica, the symbolic computer algebra system. It was crucial to finishing my doctoral thesis: I pretty quickly got beyond the point where I could safely do the algebra involved in my research by hand without making a fatal mistake somewhere. I knew some people who had superhuman ability at manipulating page-long expressions without screwing up a minus sign, but I definitely couldn't.

Unfortunately, that old copy of Mathematica (for the Mac OS of the time) was soon orphaned by Apple's many major OS and hardware changes, and stopped working long ago. And Mathematica is a really expensive piece of software, especially if you're not buying the student edition. Even the stripped-down "Home Edition" costs hundreds of dollars! There are alternatives, but until recently, the most viable ones (Maple, Macsyma) were all costly commercial products too.

Wolfram improved matters greatly by providing a free public front end in Wolfram Alpha. It's very nice for the purposes that many people will need, especially since it has a pretty good natural-language interface that means you don't really have to learn any special syntax to enter a problem. But it's limited to simple question/answer interactions rather than extended multi-stage calculations, and they often pull advanced features back behind the paywall (they clearly want you to buy a subscription).

In the past few years there have been several efforts at coming up with free alternatives: there's a free fork off an old version of Macsyma (the granddaddy of them all) called Maxima, and a very cool Python library called SymPy that you can use either interactively or scriptedly from within plain old Python, and a number of more specialized projects aimed at specific branches of mathematics.

I've been playing around with Sage lately. It's an interesting system. ( More on Sage... )