Why History of Mathematics? One of several possible answers may be illustrated by the following quotation by George Sarton (1884 - 1956), a renowned historian of mathematics and natural sciences:

''The study of the history of mathematics will not make better mathematicians but gentler ones, it will enrich their minds, mellow their hearts, and bring out their finer qualities.''

These words are taken from Sarton's book entitled The Study of the History of Mathematics, published with Harvard University Press in 1936.

Indeed, mathematical knowledge can be achieved in rather different ways. Besides the well-known phenomenological or systematical approaches (present in most university courses on mathematics), learning the subject (or parts of it) by taking its historical development into account may provide an interesting alternative. The major advantage of such a genetic approach is, of course, its proximity to the origins of mathematical thinking. Although we usually get to know a mathematical discipline in our studies as a streamlined elegant theory, it is in fact the outcome of a difficult and rarely straightforward process of discoveries made by dozens or even hundreds of mathematicians over years, decades or even centuries. As a matter of fact, the historical development offers a much better understanding why a certain definition has been introduced, a mathematical object is studied, and which results play a central role. (These are all obstacles not only freshmen face when introduced to a new theory!)

There are several reasons forcing a mathematical discipline to develop in this way or another. Responsible for historical developments and breakthroughs can be an individual mathematician (or a small group of individuals, e.g., the differential calculus introduced by Newton and Leibniz) or new ideas or methods in a related field (for example, the impact of Cantor's set theory on the development of integration theory). In addition, the community of mathematicians (with their international journals and meetings) and even the society (as a supporting or retarding force) had a strong impact on mathematics, too. However, this perspective is not only of interest while looking back; it may give us a hint how mathematics could develop further in the future... 

Of course, we do not aim at giving a complete history of mathematics here. We restrict ourselves to certain selected topics in order to provide a first overview. Each chapter starts with a short introduction explaining the period or the subject (e.g., Renaissance or the role of Women in Mathematics). This is followed by animated so-called network maps illustrating complex relations and processes with respect to the topic (as, for example, cooperations and disputes around Mathematics in the National Socialist period). These network maps also link to further online sources (namely, the Mac Tutor History of Mathematics Archive at the University of St Andrews, Scotland) as well as essays giving more detailed information (and references to further scientific literature).