Lecture Notes taken by Walter Zabel
Minkowski, Hermann, Raum und Zeit, Vortrag, Köln Lecture given in Köln on September 21, 1908, at the 80th convention of the "Deutsche Naturforscher und Ärzte". Walter Zabel copied the text of this lecture from a publication which was out of print at that time as an appendix to his lecture notes of Hilbert's lecture on "Die Elemente und Prinzipien der Mathematik.
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When Walter Zabel attended in summer 1919 the lecture of Richard Grammel on hydro- and aerodynamics, Grammel was a young, 30 years old lecturer four years after his "habilitation" in mechanics. Zabel's notes on this lecture contain dates only from about the middle of the notes onwards. The earliest date is June 26, 1919; the last date July 31.
The theme of the lecture is close to the topics on which Richard Grammel was specialized at that time. His inauguration lecture in Halle in may 1917, when he got his habilitation in mechanics at Tübingen changed into a habilitation in mathematics at Halle, had the title "Mathematik und Aerodynamik". Grammel's lecture in summer 1919, one year before he became full professor at the university of Stuttgart, was divided into four parts, dealing with hydrostatics, velocity potentials, plane stationary potential flows, and turbulent flows. Zabel's notes document all four parts in detail.
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Hilbert announced at the beginning three topics:
- A. Axiomatische Methode
- B. Problem der Quadratur des Kreises
- C. Mathematische Logik
According to the notes of Zabel, Hilbert's lecture focused in the first part on axiom systems, starting with axioms of algebra, followed by axioms of geometry essentially following Hilbert's famous publication. The first part continues with axioms of physics, dealing with mechanics, successively with axioms of mechanics, radiation, thermodynamics, probability, and psychophysics. The part ends with a section on space and time which is a brief account of special relativity.
Hilbert then dropped the second topic for time reasons and provided only an outline taken from his lecture on "Grundlagen der Analysis (und Geometrie)" in the winter semester 1911/12, covering geometrical constructions with compasses and ruler, geometrical constructions with advanced mathematical means, and the problem of the squaring of the circle.
The third part entitled now more precisely as "Das mathematische Denken und die Logik" starts with paradoxes of set theory followed by a more general part on fallacious reasoning. In the following, the lecture dealt with axioms of logic and number and ends with a treatment of indirect proofs using as an example the skipped part on constructions with compasses and ruler.
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According to the lecture notes of Walter Zabel, Hilbert started his lecture with the title "Analytische Mechanik" held in winter 1913/14 with the announcement that he would deviate from the usual outline of beginning with the mechanics of systems with a finite number of degrees of freedom followed by the mechanics of continua. His lecture would rather be the first part of a three-semester course covering the topics classical mechanics, statistical mechanics, and relativistic mechanics and electrodynamics. Zabel's notes cover only the first part of this course.
The lecture notes start with the first session at October 27, 1913, and end with the 29th session at February 26, 1914. The two main parts of the lecture dealt with the mechanics of a mass point and the mechanics of systems of a finite number of mass points. The last two sessions were devoted to the "Neue Mechanik", that is, Einstein's theory of special relativity.
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