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I love Mathematica and I use it a lot. It's like what happens if you take Matlab, R, or Python (ie any programming language primarily used for math), and turn it into a real functional programming language. It's not irreplaceable at all, but it's a lot nicer than the alternatives.

It's generally pretty nice for any sort of mathematical programming, from designing control systems to statistics to simple graphing. It's also a pretty good language for basic scripting and data manipulation. Most of the mathematical work on my blog is done in Mathematica.