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Introduction to Part IV

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A Richer Picture of Mathematics

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Abstract

When looking at the early development of relativity theory, one finds an astonishing number of contributions by mathematicians, some of which deeply influenced the work of leading theoretical physicists. Within the context of special relativity, Hermann Minkowski’s writings come immediately to mind (Walter 2008). Klein and Hilbert followed Minkowski’s ideas from their infancy, and both pursued some of their consequences after the latter’s premature death in January 1909. Two other figures with close ties to Göttingen, Max Born and Arnold Sommerfeld, were both instrumental in elaborating Minkowski’s 4-dimensional approach for physicists (Walter 2007). Born had been Minkowski’s assistant for a brief time, and so he was given the task of publishing his mentor’s final uncompleted work on electrodynamics (Staley 2008). Sommerfeld was since 1906 the head of a leading school for theoretical physics in Munich, where he afterward played a key role in promoting special relativity theory in Germany, including mathematical aspects of the theory (Eckert 2013).

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Notes

  1. 1.

    The literature on how Einstein found his field equations is by now vast; see the essays in Renn (2007), in particular (Janssen and Renn 2007). For an overview, see Janssen and Renn (2015) and the references cited therein.

  2. 2.

    The same point can be made for special relativity, as nicely illustrated in Walter (1999).

  3. 3.

    His contacts with Klein intensified during the years leading up to the outbreak of World War I when Weyl was teaching as a Privatdozent in Göttingen. During the winter semester of 1911–1912 he lectured on Riemann surfaces, one of Klein’s favorite subjects, and this course led him to publish Die Idee der Riemannschen Fläche, the book that grounded this theory by introducing the modern notion of a (two-dimensional) complex manifold. Nevertheless, Weyl stressed his indebtedness to Klein’s booklet of 1882, Über Riemanns Theorie der algebraischen Funktionen und ihrer Integrale. According to Weyl, it was Klein’s more general conception of a Riemann surface—in which he replaced the complex plane by an arbitrary closed surface—that gave the modern theory its decisive vitality and power (Weyl 1913, iv–v).

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  1. Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Mainz, Rheinland-Pfalz, Germany

    David E. Rowe

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Rowe, D.E. (2018). Introduction to Part IV. In: A Richer Picture of Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-67819-1_17

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