I've blogged before about Wolfram Alpha, the search-engine-like product from the creators of Mathematica. Alpha remains a great choice for finding answers to specific questions, especially those related to math or science. Ask it for the mass of the earth? You get one answer: the mass of the earth.
Today, though, Wolfram described a feature that math teachers will either see as a brilliant resource or the bane of their existence. By simply entering the term "solve" and an equation, Alpha will, not surprisingly, solve the equation. This isn't new, but a simple click of the "show steps" button works out the problem step-by-step.
Alpha can handle everything from quadratic equations to polynomial division to limits, showing steps and even multiple approaches for each.
The Wolfram blog entry also serves as a primer of mathematical functions and conventions. "Sqrt(5)", for example, refers to the square root of 5; the function derivative calculates derivatives (I know, this is hardly rocket science, but it's a handy reference for anyone unfamiliar with Alpha's available functions).
According to the post,
The step-by-step programs in Wolfram|Alpha rely on a combination of basic algorithms and heuristics including Gaussian elimination, l’Hôpital’s rule, and Bernoulli’s algorithm for rational integration. These heuristics are a logical formulation of the natural methods used by humans for solving problems. By utilizing Mathematica’s powerful pattern-matching capabilities, Wolfram|Alpha’s developers have morphed these rules into a platform for breaking down and structuring the solutions to complicated problems, which closely mimics the ways by which a human would solve problems of these natures.
Call me a math geek if you want, but that's just plain cool.