ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

19. History of Mathematics

1991 MS Classification: 01; 03 Mircea Radu, Educational Sciences Institute, Bucharest, Romania Justus Grassmanns Account of Synthesis in Mathematics: between Schelling and Kant Justus Günther Grassmanns mathematical work has been long neglected by historical research. This situation is gradually changing. A recently published volume contains several papers in which some of Justus ideas and contributions are examined (Schubring, 1996). The aim of my paper is to investigate the two concepts of synthesis which can be found in Justus’ work and which have not yet received the attention they deserve. I shall rely on Justus 1817 and 1824 geometry textbooks as well as on a remarkable methodological paper published in 1827 and called “Über den Begriff und Umfang der reinen Zahlenlehre”. I will argue that (1) Justus 1827 account of mathematical or external synthesis is closely related to Schellings concept of construction, and that (2) Justus distinction between mathematical and logical or internal synthesis is reminiscent of Kants dualism between pure intuition and thinking. Selective literature 1. Schubring, G., 1996, Hermann Günther Grassmann (1809-1877): Viosionary Mathematician and Neohumanist Scholar, Kluwer, Dordrecht 2. Grassmann, J., 1827, Ueber den Begriff und Umfang der reinen Zahlenlehre, Stettin