Weierstrass, Karl Wilhelm Theodor (kärl vĭlˈhĕlm tāˈōdōr vĪˈərshträs) [key], 1815–97, German mathematician. From 1864 he was professor of mathematics at the Univ. of Berlin. His development of the modern theory of functions is described in his Abhandlungen aus der Funktionenlehre (1886), which was compiled largely from the lecture notes of his students. He was one of those chiefly responsible for the modern, rigorous approach to analysis and number theory, and he did much to clarify the foundations of these subjects. He demonstrated (1871) a function that is continuous throughout an interval but that possesses no derivative anywhere in the interval.