A life of learning in Leiden. The mathematician Frans van Schooten (1615-1660)

Abstract

Frans van Schooten jr. (1615-1660) was one of the most influential Dutch mathematicians of the seventeenth century. He is best known for his two Latin editions (1649, 1659-61) of the Géométrie (1637) of Descartes, which originally appeared in French as an appendix to the Discours de la Methode. This thesis aims to study Van Schooten in the context of his own time and in connection with contemporary developments and practices, both mathematical and extra-mathematical. Van Schooten's ''mathematical life of learning in Leiden'' included his scholarly work, his private teaching, as well as his public lectures at the Duytsche Mathematicque, a program attached to Leiden University. The thesis consists of three parts: a biography of Van Schooten, a case study on his attitude towards Cartesian geometry, and an investigation of his teaching at the Duytsche Mathematicque. The biography is partly based on unpublished archival material and reveals new information on his life and works. For example, Van Schooten's appointment as professor of the Duytsche Mathematicque in 1646 was the result of a well-considered strategy of the Van Schooten family which had its roots in the ten years before. The second part of the thesis investigates Van Schooten's attitude towards Cartesian geometry and the legacy of Descartes by means of a case study of the so-called ''Pappus problem'', one of the key problems in the Géométrie of Descartes. However, Descartes's solution was incomplete and subsequently criticized by contemporary mathematicians with whom Van Schooten was in contact. At first, Van Schooten tried to explain the criticisms away. After this strategy had failed, he contrivedly tried to reconcile Descartes’s original text with the criticisms. Van Schooten identified himself with Descartes to such an extent that he was unable to cope with legitimate criticisms of Descartes's solution. The case study further gives new insights in the way Descartes and Van Schooten employed algebraic notations. A tension between tradition and innovation is seen in Van Schooten's public teaching at the Duytsche Mathematicque, a mathematics program at Leiden University which was taught in the Dutch language. The program had been founded in 1600 in order to train engineers for the army but the audience widened in the course of time and included craftsmen and merchants. Van Schooten's courses at the Duytsche Mathematicque have been investigated in this thesis on the basis of unpublished manuscripts. Hitherto historians have believed that the program was static, but it turns out that Van Schooten made several innovations. He increased the role of theory in his lectures in order to simplify the courses for his students. He revised the existing courses on arithmetic and fortification and he introduced new subjects to the curriculum such as perspective, logarithms and algebra. Van Schooten's algebraic approach to problem solving in arithmetic and geometry was innovative, but he adhered to the old 16th-century algebraic notation and nowhere mentioned the new notation introduced by Descartes. The thesis concludes with a detailed inventory of sixteen unpublished mathematical manuscripts in the University of Groningen Library. Most of these manuscripts are related to Van Schooten and his family.