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.