"I'm not keen on the hype" says Stephen Wolfram, this from the man whom I once heard exclaim "First there was Euclid. Then there Gödel. Then there was Mathematica". Despite the quote, Mathematica doesn't really help you prove new theorems but I found it quite useful when trying a few simple cases, simplifying messy expressions, optimizing parameters and checking other people's proofs.
But then Wolfram wrote that book that Scott Aaronson read so I didn't have to, and had that silly Turing machine contest. Now he comes out with the modestly named WolframAlpha.
WA is not a search engine, it isn't sure what to do with computational complexity and functionality for P=NP is under development. Good luck with that.
On the other hand it has considerable built in data and calculations. Type in sunset Chicago and I'll get useful information that used to take multiple clicks on Google.
More importantly WA is Mathematica Lite. We have a site license for Mathematica at Northwestern but the convoluted process to download it dominates its value to me. But I can just simplify and maximize directly into WA. solve x=4y^2-7, y=x+5 gives clean solutions. I had a little trouble maximizing probabilities with max p(1-2p) but change p's to x's and everything works fine. It solves all my daughter's homework questions on solving quadratic equations and simplifying radicals (but she's smart enough to know not to use it).
So kudos to Wolfram for producing something useful and free. Hope he keeps it that way.