MMA is a fantastic bit of software. It's my secret weapon for lots of tasks, including prototyping algorithms, data manipulation (it absolutely excels at this), visualisation and all sorts of miscellaneous investigatory tasks. I'd love to use it at work but as a Home Edition user my license prohibits this. Were I to accidentally start it at my day job, I'd use it for converting data between various formats, processing it, manipulating it and writing it back again, like a gigantic and insanely powerful interactive awk replacement. Since I maxed out the RAM on my laptop I now have it run at startup so it's always there for back-of-the-envelope stuff.

I used it extensively in designing my side project synth[1], where I used its visualisation capabilities to figure out everything from panning algorithms to delay lines. It earned its keep most often late at night when I was tired and trying to figure out daytime-simple-but-nighttime-hard routines. The Manipulate[] function is really good for this, as it shows you the output of a function as you drag the inputs up and down. I also used it for turning mathematical formulae into C code - the CForm[] function does this very well.

It's also a great way to experiment with functional programming, since that's how it mostly likes to operate.

I reckon there's a lot of places you could use it, but it's too expensive to justify. I don't really care if it's open source or not, but I'd like Stephen Wolfram to have an epiphany on pricing and realise he could sell ten times as many Home Edition copies at a quarter of the price. Its adoption is absolutely held up by its sky high price.

Anyone with further interest in it should check out the Wolfram blog[2] and one of the friendliest StackExchange communities out there[3]

[1]http://www.omnivoresoft.com [2]http://blog.wolfram.com [3]http://mathematica.stackexchange.com