High Quality Content by WIKIPEDIA articles! In mathematics, the Weierstrass function is a pathological example of a real-valued function on the real line. THe function has the property that it is continuous everywhere but differentiable nowhere. IT is named after its discoverer Karl Weierstrass. HIstorically, the Weierstrass function is important because it was the first published (1872) to challenge the notion that every continuous function was differentiable except on a set of isolated points.