The presentation of Python as a tool for applied mathematics got highlighted at the 2008 annual meeting of the american Society for Industrial and Applied Mathematics (SIAM). For more information, read this blogpost and the slides.
Wolfram Alpha is a web front-end to huge database of information covering very different topics ranging from mathematical functions to genetics, geography, astronomy, etc.
When you search for a word, it will try to match it with one of the objects it as in its database and display all the information it has concerning that object. For example it can tell you a lot about the Halley Comet, including where it is at the moment you ask the query. This is the main difference with, say Wikipedia, that will know a lot about that comet in general, but is not meant to compute its location in the sky at the moment you enter your query.
Searches are not limited to words. One can key in commands like weather in Paris in june 2009 or x^2+sin(x) and get results for those precise queries. The processing of the input query is far from bad, since it returns results to questions like what are the cities of France, but I would not call it state of the art natural language processing since that query returns the largest cities instead of just the cities it knows about and the question what are the smallest cities of France will not return any result. Natural language processing is a very difficult problem, though, especially when done in the open world as it is the case there with a engine available to the wide public on the internet.
For more examples, visit the WolframAlpha website, where you will also be able to post feature requests or, if you are a developer, get documentation about the WolframAlpha API and maybe use it as a web service in your application when you need to answer certain types of questions.