Wolfgang Hook

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Wolfgang Haken, 2019

Wolfgang Haken (born June 21, 1928 in Berlin ) is a German-American mathematician specializing in topology (especially 3-dimensional manifolds ), who solved the four-color problem with Kenneth Appel in 1976 .

life and work

Hook studied mathematics, physics and philosophy in Kiel , where he obtained his doctorate on topology under Karl-Heinrich Weise in 1953 . From 1954 to 1962 he worked for Siemens in Munich , where he specialized in applications of microwave technology. He also published work on topology, and his knot algorithm won him an invitation to the University of Illinois , where he became a professor in 1965 (and is currently still professor emeritus). In 1976 he proved the famous four-color theorem together with Kenneth Appel , who at the time, like Haken, was working at the University of Illinois . They worked on the computer proof for about 4 years since 1972. The proof was partially checked in the 1980s, and two errors were found, but they could be corrected. Independent evidence was provided by Frank Allaire (1977, but never fully published) and in 1993 by Paul Seymour , Neil Robertson , Daniel Sander, and Robin Thomas (who only had 633 instead of the 1900 and later around 1400 unavoidable reducible configurations of Appel and Haken ), but everyone used the computer.

In the topology the hook manifolds are named after him and here too he is interested in algorithmic questions. For example, he created an algorithm to decide whether a knot in a closed 3-manifold is “real” or can be untied (with his theory of normal surfaces). Hook also extended Hellmuth Kneser's theory of normal surfaces .

In 1993 he received an honorary doctorate from the Johann Wolfgang Goethe University in Frankfurt am Main . In 1979 he received the Fulkerson Prize for discrete mathematics with Appel . In 1978 he was invited speaker at the International Congress of Mathematicians in Helsinki ( Combinatorial aspects of some mathematical problems ).

In 1990 he became a member of the "Center for Advanced Study" at the University of Illinois, where he a. a. is working on improving its knot algorithm.

literature

  • Donald MacKenzie Mechanizing proof , MIT Press 2001

Fonts

  • Theory of normal surfaces . Acta Math. Vol. 105, 1961, pp. 245-375 (hook manifolds)
  • with Kenneth Appel: Every planar map is four colorable. Part I. Discharging . Illinois Journal of Mathematics Vol. 21, 1977
  • with Kenneth Appel: Every planar map is four colorable . Bulletin AMS Vol. 82, 1976, p. 711
  • with Kenneth Appel: Every Planar Map is Four Colorable . Contemporary Mathematics, Vol. 98, American Mathematical Society, 1989
  • with Kenneth Appel: The Solution of the Four-Color-Map Problem . Scientific American, Vol. 237, No. 4, pp. 108-121 (1977)

Web links

Individual evidence

  1. ↑ MacKenzie Mechanizing Proof , p. 140. Once by electrical engineer Ulrich Schmidt of the Technical University of Aachen in his diploma thesis, the other time in 1985 by H. Enomoto, S. Saeki, University of Tokyo. The program itself was also checked by formal proof verification specialist David Gries, but he only found one error on the safe side, but complained about the unstructured code.
  2. ↑ MacKenzie, loc. Cit., P. 142
personal data
SURNAME Hook, Wolfgang
BRIEF DESCRIPTION German mathematician in the USA
DATE OF BIRTH June 21, 1928
PLACE OF BIRTH Berlin