A German mathematician (1815-1897), who was responsible for the rigorous definitions now in use in analysis for such things as limit, continuous, differentiable, and convergent. One of his main fields was the use of power series for complex functions.

Karl Wilhelm Theodor Weierstrass was born in Ostenfelde on 31 October 1815 and studied law in Bonn, but then became a schoolteacher. He did research in mathematics on the side, and came to prominence in 1854 with a paper on Abelian functions, after which he achieved a professorship at Berlin.

One of Weierstrass's pupils and collaborators was the renowned Russian mathematician Sonya Kovalevskaya, who achieved brilliant results with him despite her inability, as a woman, to be accepted for the normal path of study and teaching. He intensely disliked the idea of female students, and gave her a big bunch of dead hard sums to get rid of her, but realized her talent when she returned to him with answers.

He died in Berlin on 19 February 1897. He was a talented fencer, and disliked music. He disputed with Kronecker, a constructivist, because his arithmetic formulation of analysis sometimes used non-constructive proofs: once friends, this issue caused a serious rift between them.

Karl Weierstrass was born on October 31, 1815, in the rural Prussian town of Ostenfelde. His father, Wilhelm Weierstrass, was a cultured man employed as a customs officer for the French; all that is really known about his mother is that she seemingly disliked his father. Karl had four siblings, none of whom ever married: his two sisters apparently had nothing better to do with their lives than devote themselves to his welfare.

As a youth Weierstrass was unusually quick. He finished high school in a year less than the usual time, won a multitude of prizes, and kept himself in spending money by bookkeeping for a local businesswoman. His father noted the boy’s talent and made detailed plans for a career for him in government administration: Karl, he decided, should study finance, economics, and law.

And so in 1834 Weierstrass headed off to the University of Bonn, where he spent the next four years devoting himself “almost exclusively to fencing and the mellow sociability that is induced by nightly and liberal indulgence in honest German beer.” (Bell, 411) He was an expert fencer; no one ever touched him during a match, and according to Bell, he could probably hold his liquor excellently as well. In any event, he attended very few (if any) lectures, but found time to read Laplace’s Celestial Mechanics in between drinking and fencing bouts.

After four years of partying Weierstrass returned home, without a degree. On the advice of a neighbor, the despairing Weierstrass family agreed to let Karl study at the Münster Academy to prepare for a career in secondary school teaching. Weierstrass was amenable to this, mostly because he wanted to study under the Academy’s Professor of Mathematics Christof Gudermann, who was to spark Weierstrass’s lifelong interest in elliptic functions.

After a year at the Münster Academy Weierstrass took his teaching certificate examination. One problem was on elliptic functions, which Gudermann wrote was “in general far too difficult for a young analyst” but had been expressly requested by Weierstrass. The problem earned him a special certificate recognizing his “original contribution to mathematics” (Bell, 415). Weierstrass passed his oral and written tests, obtained his certificate, and went off to teach secondary school.

During the day, Weierstrass taught mathematics, German, geography, handwriting, and gymnastics at Prussian secondary schools. Often in the evenings he would socialize with the “landlords, advocates, and young officers” around him (Prasad, 227). And at night, he worked on his mathematics, reading and rereading Abel. He was completely cut off from all mathematical publications and intellectual life and could not even afford the postage for academic correspondence, but this only helped him develop an original outlook.

In 1854, he published a memoir on Abelian functions in Crelle’s mathematical journal, and found himself immediately famous. The University of Königsberg presented him with an honoris causa doctorate. German mathematicians schemed to get him a university appointment; by 1856 he was an Assistant Professor at the University of Berlin. However, the stress of his new life soon gave him a nervous breakdown, and he collapsed in the middle of a lecture. After his recovery, he would never trust himself to write equations on the board, but instead would lecture sitting down while a student took dictation.

Weierstrass was always kind, considerate, and genuinely interested in his students, who loved him dearly. He was particularly fond of the Russian mathematician Sonja Kowalewski (because the University would not admit women, he tutored her privately) and they formed a friendship which lasted for forty-one years, until Sonja’s death.

Although Weierstrass’s immediate pupils were sincerely fond of him, students in low-level calculus sequences may cheer or revile him as the founder of epsilon-delta proofs. He did a great deal with power series, and always prided himself on having a sound logical basis for his work. And so let Karl Weierstrass, slacker, boozehound, and brilliant mathematician that he was, serve as an inspiration for all of us in college calculus.

Bell, E. T. Men of Mathematics, 1937.
Prasad, Ganesh. Some Great Mathematicians of the Nineteenth Century, Vol. 1, 1933.
Varberg, Purcell, Rigdon. Calculus, eighth edition, 2000.

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