Person: Scheffers, Georg Wilhelm
Georg Scheffers was a German mathematician specializing in differential geometry.
Mathematical Profile (Excerpt):
- Scheffers studied mathematics and physics at the University of Leipzig from 1884 to 1888.
- When Scheffers started his studies at Leipzig he was taught by Felix Klein, the professor of mathematics, but Klein left to take up a chair in Göttingen in 1886.
- Friedrich Engel, who had been a student at Leipzig, returned there as a lecturer in 1885 and taught Scheffers.
- Sophus Lie was appointed to Leipzig to succeed Klein and immediately had a strong influence on Scheffers.
- Lie acted as Scheffers' thesis advisor when he began to undertake research on plane contact transformations in 1888.
- Lie continued to advise Scheffers as he continued to work on plane contact transformations and complex number systems for his Habilitation thesis which he submitted to Leipzig in 1891.
- Scheffers, who had succeeded Guido Hauck, held the chair of mathematics there until he retired in 1935.
- During the period that Scheffers worked with Lie in Leipzig he used his skill as a writer to assist in publishing Lie's important contributions.
- These were substantial accounts of Lie's basic ideas in which Scheffers decided that it was more important to explain the ideas in a meaningful way even if this meant that the account lacked absolute rigour as a result.
- The first volume of an intended two volume collaboration between Lie and Scheffers was published in 1896 entitled Geometrie der Beruhrungstransformationen Ⓣ(Geometry of contact transformations).
- However, in the year this volume was published, Scheffers moved to Darmstadt and, although the two authors had done some preparatory work on the second volume, they made no further progress and it was never published.
- Even after Lie's death Scheffers produced work which had been clearly strongly influenced by Lie.
- For example Scheffers' most important work was a paper in 1903 on Abel's theorem which still showed Lie's influence.
- Scheffers gave a historical introduction to this topic in his 1903 paper, where he also continued development of the theory.
- Before this paper appeared, however, Scheffers had published one of his most important textbooks, namely the two volume work Anwendung der Differential- und Integralrechnung auf Geometrie Ⓣ(Applications of differential and integral calculus in geometry).
- In 1908 and 1909, Eduard Study, the Professor of Mathematics at Bonn, published two papers in which he criticised the standard treatment of differential geometry in general, and Scheffers' treatment in particular.
- Scheffers reacted very positively to this criticism and incorporated many improvements into his treatment which he published as a second edition in 1910 and 1913.
- Scheffers' book remains one of the best textbooks on the subject; it deals with the material in a very pedagogic way and illustrates it with many interesting examples.
- Scheffers' book contains many historical footnotes.
- One of Scheffers most important textbooks was his revision of Serret's famous book Cours de calcul différentiel et intégral Ⓣ(Course of differential and integral alculus) published in the 1870s.
- It was not this original edition which Scheffers revised, rather it was the second edition of 1897-99 of the German translation which was first published in 1884.
- Scheffers wrote many other books.
- We should also mention Scheffers' contribution Besondere transzendenten Kurven Ⓣ(Special transcendent curves) which appeared in Enzyklopädie der mathematischen Wissenschaften Ⓣ(Klein's Encyclopedia) in 1903, and another of his books which was Lehrbuch der Darstellenden Geometrie Ⓣ(Textbook of Descriptive Geometry) (1919).
Born 21 November 1866, Altendorf (near Holzminden), Germany. Died 12 August 1945, Berlin, Germany.
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive