Weierstrass, Karl Wilhelm Theodor

Weierstrass, Karl Wilhelm Theodor

(kärl vĭl`hĕlm tā`ōdōr vī`ərshträs), 1815–97, German mathematician. From 1864 he was professor of mathematics at the Univ. of Berlin. His development of the modern theory of functions is described in his Abhandlungen aus der Funktionenlehre (1886), which was compiled largely from the lecture notes of his students. He was one of those chiefly responsible for the modern, rigorous approach to analysisanalysis,
branch of mathematics that utilizes the concepts and methods of the calculus. It includes not only basic calculus, but also advanced calculus, in which such underlying concepts as that of a limit are subjected to rigorous examination; differential and integral
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 and number theorynumber theory,
branch of mathematics concerned with the properties of the integers (the numbers 0, 1, −1, 2, −2, 3, −3, …). An important area in number theory is the analysis of prime numbers.
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, and he did much to clarify the foundations of these subjects. He demonstrated (1871) a function that is continuous throughout an interval but that possesses no derivative anywhere in the interval.
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