Mathematica and its associated Wolfram language may be making the news headlines at the moment, but Sage is an open source system for doing math that might be more useful now that it has a free cloud option.
Sage  System for Algebra and Geometry Experimentation  is a Python based system which integrates a number of other math software packaged into a single system. All you need to know is a little Python to make use of packages that do algebra, calculus, group theory, graph theory and so on. Being open source you have always been able to download and use Sage, but now there is Sagemath Cloud that lets you do the same work in a browser.
As well as Sage you can also make use of IPython workbooks and work books. At the moment the IPython part of the system is a little slow and flaky but it is early days and this is still a beta.
The key points are:
 Worksheets: Sage, R, Python, Cython, GAP, Macaulay2, Singular, and much more
 Latex editor with inverse and forward search
 IPython notebooks
 Cloud IDE: write, compile, and run code in most programming languages
There are currently 288 cores, 1.2TB RAM and 50TB disk space dedicated to the Sagemath Cloud cluster and currently this is a free service of the University of Washington, to encourage the usage of open source mathematical software.
Its creator William Stein made it clear on a Reddit discussion what the objective was:
"It's free due to some significant grant funding I've been able to obtain to increase the use of SageMath which I used to purchase a cluster of 19 computers, and also a gift from Google (there are several Sage developers and enthusiasts at Google). Also, I get unlimited free bandwidth and cheap hosting from the University of Washington. There will always be a free version, but at some point people will also have the option to pay for more dedicated compute power "
It certainly seems like a step in the right direction, although I have to say that it doesn't have the integrated feel of say Mathematica at the moment. It is more like a doitall Swiss Math Knife...
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