This book was first published in 1970 and reprinted four years later, but since then it has sold out. The helpful comments of my colleagues have strengthened my con viction that some changes and corrections were to be done in the third edition. These are summarized below, supplementing a nearly unaltered part of the piace to the original edition. Any work on the history of science spanning a considerably long period of time has to satisfy a great number of criteria as the discipline under scrutiny has to be examined as it evolved, embedded in the intricate network of relations in the national and universal history of culture. Ta compound the problem, the rise of mathematics out of backwardness in Hungary was fraught with relapses instead of leading in a straight line to today's heights. To begin with, the author of a book on science history encounters the problem of what material to include and how to treat it. To stretch the point a little, one might say that as many authors and reviewers, as many opinions. It is almost impossible to coordinate all the divergent points of view and expectations.

A glorious period of Hungarian mathematics started in 1900 when Lipót Fejér discovered the summability of Fourier series.This was followed by the discoveries of his disciples in Fourier analysis and in the theory of analytic functions. At the same time Frederic (Frigyes) Riesz created functional analysis and Alfred Haar gave the first example of wavelets. Later the topics investigated by Hungarian mathematicians broadened considerably, and included topology, operator theory, differential equations, probability, etc. The present volume, the first of two, presents some of the most remarkable results achieved in the twentieth century by Hungarians in analysis, geometry and stochastics. The book is accessible to anyone with a minimum knowledge of mathematics. It is supplemented with an essay on the history of Hungary in the twentieth century and biographies of those mathematicians who are no longer active. A list of all persons referred to in the chapters concludes the volume.

As an historiographic monograph, this book offers a detailed survey of the professional evolution and significance of an entire discipline devoted to the history of science. It provides both an intellectual and a social history of the development of the subject from the first such effort written by the ancient Greek author Eudemus in the Fourth Century BC, to the founding of the international journal, Historia Mathematica, by Kenneth O. May in the early 1970s.