This book contains five essays on the complexity of continuous problems, written for a wider audience. The first four essays are based on talks presented in 2008 when Henryk Woźniakowski received an honorary doctoral degree from the Friedrich Schiller University of Jena. The focus is on the introduction and history of the complexity of continuous problems, as well as on recent progress concerning the complexity of highdimensional numerical problems. The last essay provides a brief and informal introduction to the basic notions and concepts of informationbased complexity addressed to a general readership. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in applications. Table of Contents  E. Novak  Henryk Woźniakowski and the complexity of continuous problems
 H. Woźniakowski  Complexity as a new challenge for mathematicians
 J. F. Traub  A brief history of informationbased complexity
 I. H. Sloan  How high is highdimensional?
 H. Woźniakowski  What is informationbased complexity?
