This is either going to be a toy, or they're going to limit the amount of computational power (rendering it a toy if you're doing anything intensive like evolutionary computation), or they're going to charge an arm and a leg, or something.

Did you know that I can SSH into my university account and run Mathematica from the command line right now? Revolutionary!

that's harsh. think of how many school kids could get a kick out of this and start thinking about the why's of maths and calculus rather than the tedium of the 'how'

I'm sure this will be great for simple things, but certainly CPU intensive things will be at least an order of magnitude slower in JavaScript?

Mathematica has a command line API. They are almost certainly not porting much of the math functionality to javascript. They'll just run an xmlhttprequest, let the server do its thing, and display the result. The most difficult challenge I see is getting nice 3d renderings, and some of the other more graphically intense features the desktop version has.

Mathematica is no speed demon to begin with. The primitive functions (written in C) are fast and heavily optimized, but the interpreted parts of the language are quite slow.