Weierstrass, Karl Theodor Wilhelm (1815–1897)

German mathematician who deepened and broadened the understanding of functions. He demonstrated in 1871 that there exist continuous functions in an interval which have derivatives nowhere in the interval.

Weierstrass was born in Ostenfelde, Westphalia, and trained as a teacher. From 1856 he was professor at the Royal Polytechnic School in Berlin as well as the university.

Weierstrass' breakthrough came with a paper in 1854 that solved the inversion of hyperelliptic integrals. He did much to clarify basic concepts such as ‘function’, ‘derivative’, and ‘maximum’. His development of the modern theory of functions was described in his Abhandlungen aus der Funktionlehre (1886), a text derived chiefly from his students' lecture notes. In the 1890s Weierstrass planned the publication of his life's work, again to be compiled from lecture notes. Two volumes were published before his death and five more appeared during the next three decades.