Thank you for posting this. It wasn't immediately clear for me what Sage was though, so I'm pasting the project's description from their home page [1] here in case others were confused as well:

Sage is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib, Sympy, Maxima, GAP, FLINT, R and many more.

Access their combined power through a common, Python-based language or directly via interfaces or wrappers.

Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.

[1] http://www.sagemath.org/index.html

This looks more interesting than the (pricey) Wolfram offering, but they certainly have a weird password fetish if you try to open an account. Never found anything so fierce before, and I just wanted to take a look...

Agree completely. For onboarding tentative users just interested in trying out a product, front-ends should be using email-only or even URL-only authentication instead.

In a way the progress of Sage actually does remind me that Mathematica and the new Wolfram stuff are pretty impressive. I think eventually Sage will overtake it, and I personally feel much more comfortable doing science on top of an open-source stack. But Mathematica was pretty ahead of its time with some of the ideas that are now being implemented on the open-source side of things, like the live "notebook" interface (which Mathematica has had since the '80s). I think it had/has a lot of the right ideas about how to build an interactive workbench that ties together a bunch of built in functionality, with both graphical and REPL/language interfaces to it. And I think the Wolfram Language stuff is making the right moves in generalizing that to data-mining/ML, cloud integration, domain-specific things like built-in mapping support, etc. It's less of a revolution than Wolfram wants you to believe, but it's still good, quite well designed.

There are bits of that concept that come from elsewhere, so it's not 100% novel coming from nowhere. E.g. older computer-algebra systems, Matlab, etc., all have bits of the ideas that this particular class of mathematics+data systems is converging on. But prior to the current wave of open-source stuff, I think Mathematica had the best example of integrating it all into a usable system. It might still be the most polished and integrated one out there; parts of Sage still very much feel like libraries with different conceptual/interaction models, glued together with a thin layer of Python glue. Though Sage does have the advantage of being able to add functionality at a more rapid pace, and I assume the integration will get more seamless in the future.