Karl Theodor Wilhelm Weierstrass
Born: 31 Oct 1815 in Ostenfelde, Bavaria (now Germany)
Died: 19 Feb 1897 in Berlin, Germany
Introduction
After Weierstrass had held several minor teaching positions, his work
became recognised after he published a major paper on abelian functions
in Crelle's Journal. In 1856 he obtained support from Kummer and he was
appointed to the University of Berlin.
His successful lectures in mathematics attracted students from all over
the world. The topics of his lectures included:- mathematical physics
(1856/57), introduction to the theory of analytic functions (where he
set out results he had obtained in 1841 but never published), the theory
of elliptic functions (his main research topic), and applications to problems
in geometry and mechanics.
In his lectures of 1859/60 Weierstrass gave Introduction to analysis where
he tackled the foundations of the subject for the first time. In 1860/61
he lectured on the Integral calculus . In his 1863/64 course on The general
theory of analytic functions Weierstrass began to formulate his theory
of the real numbers.
In his 1863 lectures Weierstrass proved that the complex numbers are the
only commutative algebraic extension of the real numbers. Gauss had promised
a proof of this in 1831 but had failed to give one.
Weierstrass wrote a number of early papers on hyperelliptic integrals,
abelian functions and algebraic differential equations. He is best known
for his construction of the theory of complex functions by means of power
series.
He studied entire functions and functions defined by infinite products.
The notion of uniform convergence is due to Weierstrass. He also contributed
to the theory of bilinear and quadratic forms.
The standards of rigour that he set, defining, for example, irrational
numbers as limits of convergent series, affected the future of mathematics.
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References
Dictionary of Scientific Biography
Biography in Encyclopaedia Britannica
H Behnke and K Kopfermann (eds.), Festschrift zur Ged?chtnisfeier für
Karl Weierstrass (Cologne-Opladen, 1966).
P Dugac, Eléments d'analyse de Karl Weierstrass, Archive for History of
Exact Sciences 10 (1973), 41- .
K Richter, Weierstrass, in H Wussing and W Arnold, Biographien bedeutender
Mathematiker (Berlin, 1983).