I am glad that the article mentions the Stone-Weierstrass approximation theorem [1], an analogous result for polynomials from 1885.
More recently, there's now "Chebfun" [2], an open-source Matlab library for working with highly accurate 1- and 2- dimensional polynomial approximations to arbitrary continuous functions.
More recently, there's now "Chebfun" [2], an open-source Matlab library for working with highly accurate 1- and 2- dimensional polynomial approximations to arbitrary continuous functions.
Approximation theory: pretty useful, pretty well-established, under-hyped.
[1] https://en.wikipedia.org/wiki/Stone%E2%80%93Weierstrass_theo... [2] http://www.chebfun.org/