We discuss and examine Weierstrass' main contributions to approximation theory.
2000 Academic Press 1. WEIERSTRASS This is a story about Karl Wilhelm Theodor Weierstrass (Weierstra? ), what he contributed to approximation theory (and why), and some of the consequences thereof. We start this story by relating a little about the man and his life.
Karl Wilhelm Theodor Weierstrass was born on October 31, 1815, at Ostenfelde near Mu nster into a liberal (in the political sense) Catholic family. He was the eldest of four children, none of whom married. Weierstrass was a very successful gymnasium student and was subsequently sent by his father to the University of Bonn to study commerce and law. His father seems to have had in mind a government post for his son. However neither commerce nor law was to his liking, and he wasted'' four years there, not graduating. Beer and fencing seem to have been fairly high on his priority list at the time. The young Weierstrass returned home, and after a period of rest'', was sent to the Academy at Mu nster where he obtained a teacher's certificate. At the Academy he fortuitously came under the tutelage and personal guidance of C. Gudermann who was professor of mathematics at Mu nster and whose basic mathematical love and interest was the subject of elliptic functions and power series. This interest he was successful in conveying to Weierstrass. In 1841, Weierstrass received his teacher's certificate, and then spent the next 13 years as a teacher (for six years he was a teacher in a pregymnasium in the town of Deutsch-Krone (West Prussia), then for another seven years in a gymnasium in Braunsberg (East Prussia)). During this period he continued learning mathematics, mainly by studying the work of Abel. He also published some mathematical