Helmut Pulte

das Wesen der reinen Mathematik verherrlichen

Zusammenfassung. C.G.J. Jacobi gehört zu den prägenden Gestaltern der Mathematik in der ersten Hälfte des 19. Jahrhunderts. Dies gilt für seine Forschungs- und Lehrtätigkeit, aber auch für sein Mathematikverständnis allgemein. Mit seiner Konzeption der Mathematik als einer autonomen, reinen, d.h. erfahrungs- und anwendungsunabhängigen Mathematik grenzt er sich insbesondere explizit gegen die zeitgenössische französische Tradition ab. Im Kontext dieser Wissenschaftsauffassung versucht er, Antworten auf die Fragen nach dem Grund des Fortschritts der Mathematik und ihrer Anwendbarkeit zur Beschreibung der Realität zu formulieren. Im vorliegenden Beitrag werden Jacobis diesbezügliche Anschauungen und ihre Veränderungen dargestellt und vor dem Hintergrund der zeitgenössischen Mathematik und Philosophie analysiert. Im Mittelpunkt steht dabei das ausführlichste von Jacobi erhaltene Dokument zum Themenkomplex: eine lateinische Rede, die er zum Eintritt in die Königsberger philosophische Fakultät im Jahre 1832 hielt. Diese Rede wird hier erstmals in deutscher Übersetzung wiedergegeben und ausführlich kommentiert.

C. G. J. Jacobis Vermächtnis einer konventionalen' analytischen Mechanik: Vorgeschichte, Nachschriften und Inhalt seiner letzten Mechanik-Vorlesung

Summary In the history of mathematics and natural philosophy Jacobis contribution to theoretical mechanics is known as a part of the higher calculus in the tradition of Lagrange: accepted as mathematically important, it was denied to have any substantial physical or philosophical relevance. His last lectures on analytical mechanics, given in 1847–1848, three years before his death, and not yet published, show this view to be no longer tenable. These lectures are the most detailed and genuine source on Jacobis views concerning the foundations of mechanics. In particular, his criticism of the principles of mechanics is unprecedented for its time and anticipates some of Poincares views, published about fifty years later. The prehistory of Jacobis Analytical Mechanics, a description of its content in general and an outline of his criticism, are presented in this paper.

Order of Nature and Orders of Science

The role of mathematics in eighteenth-century science and philosophy of science can hardly be overestimated, though it was and is frequently misunderstood. From today’s point of view, one might be tempted to say that philosophers and scientists in the seventeenth and even more in the eighteenth century became aware of the importance of mathematics as a means of ‘representing’ physical phenomena or as an ‘instrument’ of deductive explanation and prediction. According to this view, the rise of mathematical physics is a peripheral aspect of the new experimental sciences, and the mathematical part of physics is a methodologically directed, constructive enterprise that is somehow ‘parasitical’ with respect to experimental and observational data. But such modernising outcomes of logical empiricism are missing the central point, i.e., the ‘mathematical nature of nature’ according to mechanical philosophy. I will start with some general considerations about mathematics under the premise of mechanism before coming to the aim of my paper.

J. F. Fries’ Philosophy of Science, the New Friesian School and the Berlin Group: On Divergent Scientific Philosophies, Difficult Relations and Missed Opportunities

Jakob Friedrich Fries (1773–1843) was the most prolific German philosopher of science in the nineteenth century who strived to synthesize Kant’s philosophical foundation of science and mathematics and the needs or practised science and mathematics in order to gain more comprehensive conceptual frameworks and greater methodological flexibility for those two disciplines. His original contributions anticipated later developments, to some extent, though they received comparatively little notice in the later course of the nineteenth century—a fate which partly can be explained by the unfortunate development of the so-called ‘First Friesian School,’ founded by E. F. Apelt, M. J. Schleiden and O. X. Schlomilch. This situation changed temporarily when Leonard Nelson (1882–1927) arrived on the philosophical stage and founded a second, so-called, ‘New Friesian School’ in 1903. In the following two decades, Fries’ specific transformation of Kantian philosophy gained influence within the vigorous discussions about ‘new’ foundations of mathematics and, thus, also played a role within the Berlin Group surrounding Hans Reichenbach, though his work had no direct impact on the philosophy of physics being expounded therein.

Mini-Workshop: The Reception of the Work of Leonhard Euler (1707-1783)

2007 marked the tercentenary of the birth of Euler, famous as a major figure in mathematics. 16 scholars came together to discuss the influence of his work in some detail. The topics covered included not only pure but also applied mathematics (with engineering), physics and philosophy. Mathematics Subject Classification (2000): 01A50, 01A55. Introduction by the Organisers Quite a number of scholars work on all aspects of Euler, especially in connection with the continuing preparation of the edition of his Opera omnia. But the historical study of the reception of his work during his lifetime and especially after his death has been rather patchy; for example, in the general volume [1] to commemorate the bicentenary of his death and in the recent Euler handbook [2] to note the tercentenary of his birth few articles dealt with aspects of reception in any depth. (This point holds of reception history in general.) In our workshop the reception of Euler’s work was usually considered up to around 1840. After that, it seems that it was ordinarily either used routinely or replaced, or quite forgotten, or was studied historically; a few exceptions are noted. Sixteen scholars came together from eight countries to present their ideas on Euler’s influence in a number of mathematical areas. The selection of topics is indicated in the table of contents; it includes several from applied mathematics, where scholarship is especially limited. We also discussed some examples of Euler’s influence in various countries, but this kind of history is even less well developed than the influence by areas! In addition, we aired other neglected historical questions, 2238 Oberwolfach Report 38/2007 such as: why was there such a small reception of the many papers and other writings that were posthumously published by the Saint Petersburg Academy between 1783 and 1862? The sign ‘En’ in the abstracts below indicates the number n of an Euler writing according to the list that was prepared in the early 1910s by the historian Gustav Eneström. The meeting was a success and we are thinking of building up our efforts into a book on Euler’s influence. References [1] Leonhard Euler. Beiträge zu Leben und Werk (Basel 1983). [2] R.E. Bradley and C.E. Sandifer (eds.) Leonhard Euler: life, work and legacy (Amsterdam 2007).