Karl Wilhelm Theodor Weierstrass

born: Oct 31, 1815 in Munster, Germany
died: Feb 19,1897 in Berlin

A true mathematician who is not also something of a poet will never be a perfect mathematician.
(Weierstrass)

Poor college student. High school teacher. Superb mathematician.

Weierstrass was the oldest son of a minor customs official, and his childhood is not particularly unusual. He seemed to enjoy school and won numerous prizes in languages and mathematics. At 19 he entered the University of Bonn. His father pressured him to study law and commerce to ensure a secure future, but instead “He devoted his great bodily strength, his lightning dexterity and his keen mind almost exclusively to fencing and the mellow sociability that is induced by nightly and liberal indulgence in honest German beer.”

Four years later he left Bonn without a degree, returned to his angry family, and thought about getting a job. At the suggestion of a friend, he entered the Academy of Munster to study for a teaching certificate. Fortunately, there was an excellent professor of mathematics there, Gudermann, and Weierstrass started to learn research level topics, particularly elliptic functions and power series. At 26 he took his examinations for a teaching certificate and did so well on a piece of original mathematics that Gudermann recommended that he teach at a university instead of a secondary school. The authorities, however, ignored that recommendation, and Weierstrass began teaching at small schools. Besides mathematics, he also taught German, geography, penmanship and gymnastics. During the day he taught children, in the evening he visited the tavern, and at night he did mathematics, sometimes all night. He kept this up for 14 years, and his first paper, Remarks on Analytical Factorials, appeared in a small “program” printed by the school staff.

During the summer vacation of 1853, Weierstrass wrote up another original result and this time sent it to a well-read professional journal, Crelle’s Journal. It appeared in 1854 and caused quite a commotion — a masterful work of original mathematics from an unknown high school teacher! With the support of German mathematicians, he was given several honorary degrees and made Assistant Professor at the University of Berlin where he spent the rest of his life. His research fame spread quickly, and he was also known as a popular and accessible teacher, unusual qualities for a professor in those days. When Sonja Kovalevskaia came to Germany from Russia to study mathematics, she was not allowed to attend classes at the university because she was a woman, so Weierstrass privately tutored her for several years. Later, he kept in touch, worked to help her find a suitable academic position, and was very pleased she won the prize of the French Academy of Science.

Weierstrass’ work had a great influence on 19th and 20th century mathematics, and several of his results are now a standard part of a typical calculus course, for example, the Weierstrass M-test for series and his example of a continuous but nowhere differentiable function. Other results of his are important in more advanced areas.

Condensed from Men of Mathematics by E.T. Bell (1937, Simon and Schuster) and An Introduction to the History of Mathematics, 4th ed., by H. Eves (1976, Holt, Rinehart and Winston). DTH

Last Updated September 22, 2022