Kursthemen

  • Introductory words

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    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).


  • Origins

    In the process of writing a history of mathematics it appears to be rather difficult to describe the beginnings. From a distant modern viewpoint the various influences and obstacles to long-lasting developments are often almost invisible. In addition, there do not exist sufficiently many sources about ancient researchers and their achievements. Consequently, it is quite difficult, one might even say impossible, to talk about the origins of mathematical thinking. Certainly, one can find in every ancient culture some early thoughts about counting. However, mathematics (as well as philosophy) is believed to have begun with Thales of Milet (who lived around 600 B.C.E.). Different from antecessors he invented the concepts of deduction and proof. His and most of the mathematics of the ancient Greeks was about geometrical objects and numbers. One of the earliest texts in mathematical literature is the Elements of Euclid (from around 300 B.C.E.); they provide us with a rather good understanding about the knowledge at that time and, most importantly, they include the first axioms, another concept that later on played a substantial role, in particular in the foundations of mathematical disciplines.

    In this chapter, we do not aim to give a complete overview about the origins of math but focus on the early cultures of Babylonians, Greeks, Indians, and Chinese, mentioning just some of their discoveries and insights.  

    image/svg+xml more important Symbolgröße middle Location Other Person Events Mathematics Type Symbole wrote contents influence relation (color) all relation (dashing) all relation (thickness) relationale Attribute Network map BEGINNINGS Euclid Sun Zi Aryabhata Hamuraby dynasty first proofs Greek signs sexagesimal system Euclid's theorem clay tablets Pythagorean theorem bronze tablets decimal system Number 0 root extraction diophantine equations Pi tangrams modular arithmetic

  • Renaissance

    The so-called Renaissance was an epoch in the European history from the 14th to the 17th century, connecting the Middle Ages and modern history. The name "renaissance'' reflects the "rebirth'' of culture (and later science), starting in Italy and later in other parts of Europe. The first European universities were founded (in Bologna already in the 11th century, followed by Paris and Oxford in the beginning of the 13th century. In the next decades several further universities in Italy, France, Spain, and Germany started their business; Würzburg University was first opened in 1402, however, it was closed only about a decade later in 1413 due to financial problems and murder of the chancellor; in 1582 the institution was re-opened). At that time, quite a few researchers were working as clerics, e.g., Nicolaus Copernicus was a canon (priest) at Frombork (Poland), where he established his idea of the heliocentric model of our solar system just before his death in 1543, and Pierre de Fermat earned a living as a lawyer in Toulouse, in 1652 being promoted to the highest level at the criminal court. Moreover, there was no clear distinction between different subjects, Galileo Galilei, famous for his work in astronomy, was appointed the chair of mathematics at Pisa in 1589, and Isaac Newton got the Lucasian Chair of Mathematics in Cambridge in 1663; both are nowadays famous with respect to their works in physics.

    Here we shall focus on the mathematicians Rene Descartes, Blaise Pascal, and Pierre de Fermat; the three of them were playing a central role in the development of analytic geometry.

    image/svg+xml most important Symbolgröße middle person Event Person Mathematics Type Symbole approach worked with influence action (color) all action (dashing) all action (thickness) relationale Attribute Network map some progressive actors Fermat Déscartes Pascal problem solving algebraic symbols analytic geometry comprehensive worldview conic sections Pascal's triangle mathematical circle - Mersenne

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