Previous (Chronologically) Next Biographies Index Previous ( Alphabetically) Next Welcome page
Karl Weierstrass is best known for his construction of the theory of complex functions by means of power series.
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.
References elsewhere in this archive:
Tell me about Weierstrass's work on set theory and on topology
Tell me about Weierstrass's work on matrices and determinants and on the fundamental theorem of algebra
Tell me about Weierstrass's part in the history of mathematics
References:
Previous (Chronologically) Next Biographies Index Previous ( Alphabetically) Next Welcome page History Topics Index Famous curves index Chronologies Birthplace Map Mathematicians of the day Anniversaries for the year Search Form Simple Search Form Search Suggestions