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Synthetic and analytic geometry

In: Plane Algebraic Curves

Author

Listed:
  • Egbert Brieskorn

    (Universität Bonn, Mathematisches Institut)

  • Horst Knörrer

    (Universität Bonn, Mathematisches Institut)

Abstract

Human activity and thought are extremely complex historical processes, in which many conflicting tendencies unfold. This also holds for mathematics, in which the unfolding of these conflicts is an important element pushing development forwards. In the process of mathematical research, as well as in the mathematical method itself, dialectical conflicts are of fundamental significance : analytic-synthetic, axiomatic-constructive, exact-intuitive, abstract-concrete, special-general, simple-complex, finite-infinite, regular-singular, algebraic-geometric, qualitative-quantitative. All these conflicts have had a marked influence on many fields of mathematics. I cannot go further into details here, so I shall refer to my essay on dialectic in mathematics [B5], as well as to the article by Alexandroff in the same book.

Suggested Citation

  • Egbert Brieskorn & Horst Knörrer, 1986. "Synthetic and analytic geometry," Springer Books, in: Plane Algebraic Curves, chapter 2, pages 66-102, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-5097-1_2
    DOI: 10.1007/978-3-0348-5097-1_2
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