A dropout schoolteacher who also taught gymnastics became the father of modern analysis
Karl Weierstrass left university without a degree and spent years teaching mathematics, botany and gymnastics in small Prussian towns. From there he published work so original that he won an honorary doctorate and a Berlin professorship, and his epsilon-delta definition of continuity still sits at the heart of calculus courses.
He was born on 31 October 1815 in Ostenfelde, a Westphalian village, to a Catholic family; his father was a government official. Mathematics caught him at school in Paderborn, but his father sent him to Bonn to study law, economics and finance for a civil-service career. Weierstrass largely ignored the syllabus, studied mathematics on his own and left without graduating. He then trained as a teacher in Münster, where Christoph Gudermann's lectures drew him to elliptic functions.
His first classroom, in 1843, was at Deutsch Krone, a West Prussian town; five years later he moved to a lyceum in Braunsberg. Despite a long illness after 1850, his papers made his name. Königsberg gave him an honorary doctorate on 31 March 1854, a Berlin technical institute appointed him in 1856, and in 1864 he became professor at the university in Berlin.
His great cause was rigour. Calculus in his day rested on vague ideas of limits; even Cauchy had wrongly claimed that a limit of continuous functions must be continuous. Gudermann had noticed uniform convergence in 1838 without pinning it down; Weierstrass defined it and used it everywhere. His precise definition of continuity, where for every tolerance epsilon there is a distance delta that keeps the function within bounds, gave him firm proofs of results such as the intermediate value theorem, and he rebuilt the calculus of variations on the new foundations.
In 1870, at 55, he began privately tutoring Sofia Kovalevskaya, whom the university would not admit. He considered her his best student, helped her gain a Heidelberg doctorate without an oral defence, and wrote to her until her death in 1891, after which he burned her letters; about 150 of his survive. Immobile for his last three years, he died of pneumonia in Berlin on 19 February 1897. A lunar crater and asteroid 14100 carry his name.
Source: Karl Weierstrass
