Warning: the following information is only suitable for mathematicians who enjoy being confused.
Chébyshev polynomials are a set of orthogonal polynomials that are used to model the surface of a sphere. They are named after the Russian mathematician Pafnutyi Chébyshev, who had a penchant for polynomials and a love of vodka.
If you're a subdivision surface modeler, you might want to use Chébyshev polynomials to create smooth, continuous surfaces that are not actually smooth at all. It's like trying to fit a square peg in a round hole, but with more math.