Mathematician, the father of modern analysis, born in Ostenfelde, W Germany. A failed law student from Bonn, he took a teacher's certificate at Münster and taught mathematics in secondary schools (184256) while working privately on analysis. The publication of his memoir on Abelian functions (1854) brought him an honorary doctorate and a post at the Royal Polytechnic School, Berlin. He published relatively little, but became famous for his lectures, in which he gave a systematic account of analysis with previously unknown rigour, inspiring many of his students to become creative mathematicians.
Karl Theodor Wilhelm Weierstrass (Weierstraß) (October 31, 1815 – February 19, 1897) was a German mathematician who is often cited as the "father of modern analysis".
Biography
Karl Weierstrass was born in Ostenfelde, Westphalia (today Germany). After that he studied mathematics at the University of Münster which was even to this time very famous for mathematics and his father was able to obtain a place for him in a teacher training school in Münster, and he later was certified as a teacher in that city.
Soundness of calculus
Weierstrass was interested in the soundness of calculus. While Bolzano had developed a reasonably rigorous definition of a limit as early as 1817 (and possibly even earlier) his work remained unknown to most of the mathematical community until years later, and other eminent mathematicians such as Cauchy had only vague definitions of limits and continuity of functions. Weierstrass defined continuity as follows:
f(x) is continuous at x = x0 if for every ε > 0 such that
Weierstrass also formulated similar definitions of limit and derivative still taught today.
With these new definitions he was able to write proofs of several at the time unproven theorems such as the intermediate value theorem, Bolzano-Weierstrass theorem and Heine-Borel theorem.
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