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Weierstrass, Karl Wilhelm Theodor

analysis mathematical function mathematics

viy ershtrahs] (1815–97) German mathematician: introduced rigour into mathematical analysis.

Pressed by his overbearing father, a customs officer, to study law, Weierstrass spent 4 unsuccessful years at Bonn, learning little law but becoming a skilful fencer and reading mathematics. Emerging in disgrace, he was sent to Münster to prepare for the state teacher’s examination and had the good fortune to be able to pursue mathematics under the guidance of C Gudermann (1788–1852), whose enthusiasm at that time was that power series could be used as a rigorous basis for mathematical analysis.

Weierstrass developed this approach during his stint of nearly 15 years as a teacher in the small Prussian villages of Deutsch-Krone and Braunsberg, completely isolated from contemporary mathematical research. In 1854 he published in Crelle’s Journal a paper on Abelian integrals that he had written 14 years earlier. The quality and importance of this work, which completed areas that had begun, was immediately recognized, and he was appointed a professor at the Royal Polytechnic School and lecturer at the University of Berlin in 1856.

  The significance of Weierstrass’s work was that he gave the first rigorous definitions of the fundamental concepts of analysis; for example a function, derivative, limit, differentiability and convergence. He investigated under what conditions a power series would converge, and how to test for this. Above all, he made great contributions to function theory and Abelian functions.

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