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Models as Research Tools: Plücker, Klein, and Kummer Surfaces

In: A Richer Picture of Mathematics

Author

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  • David E. Rowe

    (Johannes Gutenberg-Universität Mainz, Institut für Mathematik)

Abstract

In the late summer of 1869, 20-year-old Felix Klein made his way to Berlin, where he planned to attend the renowned seminar founded by Ernst Eduard Kummer and Karl Weierstrass. Klein had already taken his doctorate in Bonn and he would soon be recognized as a leading expert on line geometry, a new approach to 3-space launched by his mentor in Bonn, Julius Plücker. Just before Plücker died in 1868, he entrusted Klein to complete the classic monograph, Neue Geometrie des Raumes gegründet auf die Betrachtung der geraden Linie als Raumelement. Overall responsibility for this project fell to Alfred Clebsch in Göttingen, which was how Klein first came to the prestigious Georgia Augusta. There he was quickly drawn into the orbital field surrounding this stellar figure, the co-founder of a new journal, Die Mathematische Annalen (Shafarevich 1983). It was during this first brief stay in Göttingen that Klein struck up his lifelong friendship with Max Noether. Their initial encounter also bore immediate mathematical fruit; both found mappings that transformed the 3-parameter system of lines in a linear complex to the points in 3-space, an approach to line geometry that would soon have far-reaching consequences (Klein 1921, 89).

Suggested Citation

  • David E. Rowe, 2018. "Models as Research Tools: Plücker, Klein, and Kummer Surfaces," Springer Books, in: A Richer Picture of Mathematics, chapter 8, pages 81-94, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-67819-1_8
    DOI: 10.1007/978-3-319-67819-1_8
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