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Eduard Weyr 1852–1903. (Czech) Zbl 1076.01508

Dějiny Matematiky / History of Mathematics 2. Prague: Prometheus (ISBN 80-7196-024-1). xxiv, 196 p., open access (1995).
The second volume of the series History of Mathematics represents the first of the monographs (partially published, partially planned) devoted to the important personalities of Czech mathematics. This one concerns the life and work of Eduard Weyr, professor of mathematics at the Czech Technical University and Charles University in Prague.
The character of the two initial chapters of the book, written by J. Bečvář, is purely biographical. The first one describes the family of Eduard Weyr, especially the life story of his father František Weyr (1820–1889), professor of mathematics at the German Realschule in Prague, and the older brother Emil Weyr (1848–1894), the important mathematician and professor of the Technical University in Prague and the University in Vienna. The second chapter depicts the life of Eduard Weyr.
The third chapter contains an analysis of geometrical works of Eduard Weyr. Its author, Zbyněk Nádeník, discusses the particular groups of publications from this domain: conic sections and quadrics; projective and synthetic geometry; geometrical affinities; differential geometry of curves; differential geometry of surfaces; algebraic curves; books on projective geometry. The description of individual results is combined with their subsuming to the world context and with critical notes showing the wide range of subjects as well as the levels of writing. Besides interesting geometrical results, Weyr’s merit for the stabilization of the Czech terminology in projective and differential geometry is appreciated.
The fourth and fifth chapters are written by J. Bečvář and they deal with Weyr’s algebraic works. The fourth chapter gives a description and evaluation of Weyr’s publications on linear algebra and the theory of hypercomplex numbers and shows their place within the Czech and world mathematics. One of the remarkable results concerns bilateral equations, where Weyr generalized certain Sylvester’s investigations of the solution of unilateral equations. Another noteworthy issue is Weyr’s study of matrixes \(e^M\) and \(\log M\), where \(M\) is a second degree matrix, or the theory of characteristic numbers and “typical” matrices based on the concept of the nullity of a matrix. The theory of characteristic numbers is then discussed in detail – and from the modern point of view – in the fifth chapter.
The sixth chapter, based on the notes written by Josef Daneš and Jaroslav Fuka, discusses less numerous Weyr’s works on mathematical analysis. These works can be divided into two groups, corresponding to respective sections of the chapter: the works dealing with infinite series and products, and the works concerning elliptic functions.
Relatively great attention is paid to Weyr’s dispute with Jan Vilém Pexider (1874–1914) awakened by Pexider’s critique of Weyr’s textbook on the differential calculus published in 1901. In the seventh chapter J. Bečvář and Luděk Zajíček describe these historical events and evaluate particular rebukes expressed by Pexider and the respective counter-arguments of Weyr; see also the book by J. Bečvář (ed.) [Jan Vilém Pexider (1874–1914) (History of Mathematics 5, Prometheus, Prague) (1997; Zbl 0989.00008)].
The chapters mentioned above are followed by the concluding reflection and by several supplements: the list of publications of Eduard Weyr, the list of his published reviews and references, the survey of his pedagogical activities, the reprint of the couple of his important papers on linear algebra, [C.R. 100, 787–789 (1885; JFM 17.0109.01)] and [ibid., 966–969 (1885; JFM 17.0109.02)], and the collection of reproductions of photographs and interesting documents.

MSC:

01A70 Biographies, obituaries, personalia, bibliographies
01A55 History of mathematics in the 19th century
01-02 Research exposition (monographs, survey articles) pertaining to history and biography
51-03 History of geometry
53-03 History of differential geometry
15-03 History of linear algebra

Keywords:

Biography

Biographic References:

Weyr, Eduard
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