×

Collected works. Vol. V: Astronomy, optics and probability theory. Edited by J. Bemelmans, Ch. Binder, S. D. Chatterji, S. Hildebrandt, W. Purkert, F. Schmeidler and E. Scholz. (Gesammelte Werke. Band V. Astronomie, Optik und Wahrscheinlichkeitstheorie.) (German) Zbl 1130.01018

Berlin: Springer (ISBN 3-540-30624-2). xviii, 939 p. (2006).
The present volume of Hausdorff’s collected works (for reviews of vols. II and IV see Zbl 1010.01031 and Zbl 0990.01026) contains papers on optics, astronomy, probability. It begins with the editors’ preface to this volume and the list of all Hausdorff publications (those reprinted here are noted with an asterisk), followed by two voluminous parts, annex and registers.
Under the influence of his teacher, Heinrich Bruns, Hausdorff’s first scientific papers were devoted to refraction of light in the atmosphere (Ph.D. theses from 1891 and two other papers), to extinction of light in the atmosphere (Habilitation, 1895), and to infinitesimal mappings in optics where he has found some necessary conditions for the realizability of ideal optic mappings. All these papers are reprinted in Part I (on astronomy and optics), together with two pieces from Hausdorff’s astronomical legacy. The first piece contains his comments on the balance problem of rotating fluid bodies, the second is closely related to the problem (later dealt with extensively by H. Weyl) of uniform partitions of real sequences modulo 1.
Soon after Hausdorff’s interests turned to the philosophy and literature (see the forthcoming vols. VII and VIII), but embraced also the theory of probability, of which here, in part II (on probability) are reprinted two papers, two reviews, and a dozen or so pieces from his legacy.
The two papers deal with a chance of loosing a game. In the first one Hausdorff introduced variance as a measure of risk and applied it to the mathematics of life insurance, obtaining “Hausdorff conditions” in it, and in the other he advanced the concept of conditional probability as a fundamental one, attempted to clarify the Bayesian principle, derived Gram-Charlier series of type \(A\), etc.
Reviewed were the books: of W. Grossmann on insurance and of M. Kitt on “political arithmetic”. And pieces from Hausdorff’s legacy contain a manual on the probability theory, astonishingly modern for 1923 when it was written but never published.
Some other are concerned with the strong law of large numbers and its applications to partitions (one can see here that as early as 1915 Hausdorff defined a system of orthogonal functions which Rademacher reintroduced 1922 and which are now called after the latter, a historical injustice to the former).
And some deal with iterations, a generalisation of Chebyshev’s inequality, and the inequality of Gumbel. Part II is completed by two letters from Hausdorff to von Mises, criticizing the latter’s attempt to axiomatize the theory of probability.
Annex contains two unpublished papers by Christian Huygens on mechanics, which were elaborated and edited by Hausdorff.
Although neither astronomy, nor optics, nor probability belonged to Hausdorff’s main field of interest, one cannot help a feeling of immense richness and originality of his mind.

MSC:

01A75 Collected or selected works; reprintings or translations of classics
85-03 History of astronomy and astrophysics
78-03 History of optics and electromagnetic theory
60-03 History of probability theory
PDFBibTeX XMLCite
Full Text: DOI