Absolutely a killer application. For example, http://www55.wolframalpha.com/input/?i=Ibm+aapl I strongly recommend that you get a feel for Alpha and get intimately acquainted with it.

Still haven't used it for a real world application, but it's an amazing tool to use when taking advanced math courses. Their step by step explanation of results will probably change the face of math education drastically in the years to come.

Its not that new, I remember using Matlab or Maple years ago to do symbolic math (check answers). However now its avialable to everybody.

Not sure I understand what you mean. Suppose you type in: <i>y''-y'+y=0</i> http://bit.ly/hii46Z -- you get the solution, but no understanding of the "step by step" thinking involved. I don't see how that helps with "math education" -- it's more of a supercharged pocket calculator, useful for saving time if you already understand the math.

http://www.wolframalpha.com/input/?i=integrate+x^2+sin^3+x+dx click on "show steps" in right hand corner of solution.