The History of Approximation Theory

This book traces the history of approximation theory from Leonhard Euler's cartographic investigations at the end of the 18th century to the early 20th century work of Sergei Bernstein defining a new branch of function theory. The main focus is on the St. Petersburg Mathematical School and its interaction with mathematicians in Goettingen. The author presents a mathematical analysis of the subject together with a discussion of the philosophical underpinnings of the differences in approach of the