Heinrich Heesch

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Heinrich Heesch (1930)

Heinrich Heesch (born June 25, 1906 in Kiel , † July 26, 1995 in Hanover ) was a German mathematician who dealt with geometry.

life and work

Heesch was the son of a head of the state chancellery and graduated from high school in Kiel. From 1925 he studied (supported by the Studienstiftung des Deutschen Volkes ) in Munich music at the State Academy for Tonkunst (1928 he passed the violin master's examination with Felix Berber ) and mathematics and physics at the University of Munich with Arnold Sommerfeld and Constantin Carathéodory . In 1928 he went to the University of Zurich , where he studied the application of group theory to atomic spectra for his doctorate under Gregor Wentzel . This gave rise to his interest in groups and symmetriesand instead of about atomic spectra he wrote a doctoral thesis on crystallography , with which he obtained his doctorate “summa cum laude” under Wentzel in 1929 ( on systematic structure theory ). In his dissertation he introduced Heesch-Shubnikov groups (called black and white groups by him). The groups were examined in detail by Russian mathematicians around Alexei Wassiljewitsch Schubnikow (1887–1970) in the 1950s (in particular by Nikolai Wassiljewitsch Below , who gave them their name and classified them) and initially called Shubnikov groups - but Shubnikov corresponded with them as early as 1929 Heesch. They added a fourth parameter to three-dimensional space groups, which can assume binary values ​​(such as spin direction or black and white). You have applications e.g. B. in crystal chemistry and the theory of antiferromagnetism .

Also in Zurich he derived the 80 two-sided surface ornaments after he had learned from Andreas Speiser (who had solved the corresponding problems with ribbon ornaments in the plain) that the question was still open. But Carl Hermann and Leonhard Weber got ahead of him here. Heesch also derived a new representation of the room groups in Zurich and made friends with Speiser, with whom he regularly played (Heesch on the violin, Speiser at the piano).

In 1930 he went with Hermann Weyl from Zurich to Göttingen as his assistant . During his time as Weyl's assistant, he solved the regular tiling problem of the level.

In 1933 he witnessed the National Socialist purges among university members, and many mathematicians and physicists (including Weyl, who had a Jewish wife) left Göttingen at that time. Since he was not ready to join the National Socialist German Lecturer Association, as was requested, he resigned from his position at the university in 1935 and worked as a private scholar in his parents' house in Kiel until 1948. During this time he did research on tiling and, at about the same time as the Russian mathematician Boris Delone, found a way of specifying the totality of all plane fundamental tiling (his full proof was not published until 1968). He indicated 28 fundamental areas . Many of these tiling were also "discovered" intuitively by MC Escher in his graphics. Heesch himself, who was a private citizen and lived with his parents, tried to come into contact with the industry in order to market his parquet floors and was partly successful (gift paper manufacturer, tile manufacturer Villeroy and Boch). During World War II, his mathematical methods were used to reduce sheet metal scrap in the war industry.

Heesch began to be interested in the four-color problem during his time as Hermann Weyl's assistant in Göttingen . At that time, Ernst Witt , who was a friend of Heesch, thought he had found proof, which he also presented with Heesch Richard Courant while they were accompanying him on a train ride, but without being able to convince him - on the return journey Heesch found a mistake. Heesch continued researching the problem in the 1940s and estimated the number of unavoidable reducible configurations to be investigated at around 10,000 in lectures he gave in 1947 and 1948 ( Wolfgang Haken was a student at Kiel University).

In 1955 Heesch began teaching at the Technical University of Hanover and worked on graph theory . In 1955 he became a lecturer, after his habilitation in 1958 private lecturer and finally associate professor. During this time, Heesch pioneered the computer-aided solution of the four-color problem. He was the first to use the "unloading" method, which became a fundamental part of the 1977 proof of the four-color theorem . Between 1967 and 1971 Heesch traveled to the USA a few times , where larger and faster computers were available and where he worked with Wolfgang Haken and Yoshio Shimamoto. During the crucial phase of his project, the German Research Foundation cut his financial support. After the success of Kenneth Appel and Wolfgang Haken in 1977, Heesch worked on refining and shortening their proof, even after his retirement (1975). In 1981 a celebratory colloquium was held at the University of Hanover on the occasion of his 75th birthday, in which HSM Coxeter took part.

He is buried in the Eichhof park cemetery near Kiel. He played the violin well and even as a schoolboy played chamber music evenings with the mathematics professors in Kiel Otto Toeplitz and Ernst Steinitz . His sister Elli (1904-1993) was a doctor of philosophy and mathematician and later a Catholic nun. Heesch also later converted to the Catholic faith.

Heesch's group in the theory of hexagonal space groups is named after him (by JJ Burckhardt 1933).

Works

  • Heinrich Heesch: Investigations into the four-color problem . Mannheim: Bibliographical Institute 1969.
  • Heinrich Heesch: Collected treatises . Edited by Hans-Günther Bigalke. Bad Salzdetfurth: Franzbecker 1986, ISBN 3-88120-157-2 .

literature

  • Hans-Günther Bigalke: Heinrich Heesch: Crystal geometry, tiling, four-color research . Basel: Birkhäuser 1988, ISBN 3-7643-1954-2 .

Web links

References

  1. ^ Mathematics Genealogy Project
  2. ↑ Published in About the four-dimensional groups of three-dimensional space , Z. f. Kristallographie, Volume 73, 1930, pp. 325-345, On the symmetries of the second kind in continuums and semidiscontinues , Z. f. Kristallographie, Vol. 73, 1930, pp. 346-356
  3. ↑ Heesch On the structure theory of the plane symmetry groups , Z. f. Kristallographie, Vol. 71, 1929, pp. 95-102
  4. ^ Johann Jakob Burckhardt Symmetry of Crystals , Birkhäuser 1988, p. 146ff
  5. ↑ Heesch on systematic structure theory II , Zeitschrift für Kristallographie, Volume 72, 1929, pp. 177–201
  6. ↑ The parquets are illustrated e.g. E.g. in Ehrhard Behrends Escher seen over his shoulder - an invitation , in Behrends, Gritzmann, Ziegler (editor) Pi and Co , Springer Verlag, 2008, p. 329
  7. ↑ Donald MacKenzie Mechanizing proof , MIT Press 2001, p. 120. In Appel and Haken's proof, it was only around 2000 and at the end around 1400.
personal data
SURNAME Heesch, Heinrich
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH June 25, 1906
PLACE OF BIRTH Kiel
DATE OF DEATH July 26, 1995
Place of death Hanover