Hanfried Lenz

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Hanfried Lenz

Hanfried Lenz (born April 22, 1916 in Munich ; † June 1, 2013 in Berlin ) was a German mathematician , university professor and author.

Studies and military service

Lenz was born the son of the human geneticist and racial hygienist Fritz Lenz . After graduating from high school and taking part in the Reich Labor Service , he began studying mathematics and physics at the Eberhard Karls University in Tübingen . He became a member of the Association of German Students and interrupted his studies from 1935 to 1937 to do military service. He then continued his studies, first at the Ludwig Maximilians University in Munich , at the Friedrich Wilhelms University in Berlin and finally at the University of Leipzig . In the summer of 1939 he was drafted as a soldier and served on the Western Front after the outbreak of World War II . In the spring of 1941 he passed the state examination for the higher teaching post while on home leave in Leipzig. As a result, Lenz took part in the war in the Soviet Union . Lenz's brother is the human geneticist Widukind Lenz .

Even when he was still at school he had a crush on Hitler and only realized his mistake late, partly disillusioned by the crimes committed by Germans in Eastern Europe and not entirely unknown despite secrecy, in particular the deportations of the Jews, about which he learned from his father. A jaundice illness during a vacation meant that Lenz returned home. There he married Helene Ranke (1920–1994) in 1943, who was close to the Confessing Church . From this marriage came four children, the judge Inge Lenz, the engineer Erich Lenz, the sociologist Ilse Lenz and the lawyer Karl-Friedrich Lenz . From 1943 to 1945 he worked in the high frequency laboratory of the Physikalisch-Technische Reichsanstalt in Berlin and then in Zeulenroda. Here he devoted himself in a subordinate position to the development of the "war important" radar technology.

Political engagement and professorship

At the end of the war, his path led him via Heidelberg to Hanover and then to Munich. In his denazification process he was classified as a “fellow traveler”. He first completed his training in Munich and then worked for a good year as a math and physics teacher at the Klenze secondary school. From 1949, Professor Frank Löbell brought him to the chair of geometry at the TH Munich as a scientific assistant . 1951 followed the doctorate with Josef Lense and 1953 the habilitation.

Lenz also began to become politically active and resigned in protest against the rearmament plans in 1953 in the All-German People's Party of Gustav Heinemann , but declined to run for the parliament. In 1954 he switched to the SPD . In 1956 he was one of the founding editors of the papers for German and international politics . In the meantime he continued to work as a private lecturer and in 1959 became an adjunct professor at the TH Munich. In the academic year 1967/68 he was visiting professor at Ohio State University in Columbus, Ohio, USA.

As a result, he got a call to West Berlin, where he became a full professor at the Free University in 1969 . In his first years there he was very busy with academic self-administration and university politics, especially in the faculty council as chairman and in the academic senate, so that he had little time for research (see the list of his work at the end of his autobiography, see p . below). There he experienced the sometimes radical demands of the 1968 students, who often disrupted his lectures, and as a reaction he took on increasingly conservative views.

In 1972 he moved from the SPD to the CDU. The retirement was done against his will in 1981, but was reversed on appeal and its happened for the second time in 1984. Small lectures he held until 2004. From his 60th birthday, organized by the Department of Mathematics at the Free University every five years a colloquium.

Achievements as a mathematician

Lenz is best known for his classification of projective planes , which was later significantly expanded by Adriano Barlotti . In addition, in 1954 he showed how one can define affine spaces axiomatically without resorting to projective spaces or vector spaces . This result is now also known as Lenz's theorem. In the later years he devoted himself mainly to combinatorics in addition to geometry . In addition to his former doctoral student Dieter Jungnickel and his younger colleague Thomas Beth (* 1949; † 2005), he was co-author of the book "Design Theory", which appeared in 1987 (2nd extended edition 1999).

Previously, he wrote a number of other mathematical works: In 1954 he was with the writing "In support of analytical geometry" habilitation . This was followed by the books “Fundamentals of Elementary Mathematics” (1961), “Lectures on Projective Geometry” (1965) and “Non-Euclidean Geometry” (1967). In 1995, Hanfried Lenz was awarded the Euler Medal by the Institute of Combinatorics and its Applications for his achievements .

His autobiography "More Happiness Than Mind" contains a list of his publications.


  • Fundamentals of elementary mathematics (= university books for mathematics . Vol. 52). Deutscher Verlag der Wissenschaften, Berlin 1961. 3rd edition: Hanser 1976.
  • Lectures on projective geometry. Geest and Portig, Leipzig 1965.
  • Non-Euclidean Geometry. BI university paperback 1967.
  • with Thomas Beth, Dieter Jungnickel: Design Theory. Bibliographical Institute, Mannheim 1985.
  • Little Desargue's sentence and duality in projective planes. Annual report DMV 1954. Lenz-Barlotti classification ( online ).
  • About the introduction of an absolute polarity into the projective and affine geometry of space. In: Mathematical Annals. Volume 128, 1954, p. 363 ( online ).
  • To define the areas of the second order. In: Mathematical Annals. Volume 131, 1956, p. 385. ( online ).
  • Half turns in space. In: Mathematical Journal. Volume 78, 1962, p. 410 ( online ).
  • On the axiomatics of plane Euclidean geometry. Elements of math. Volume 22. 1966 ( online ).
  • More luck than mind. Self-published (Books on Demand), Munich 2002, ISBN 3-8311-3618-1 .


  • Martin Aigner, Dieter Jungnickel (Eds.): Geometries and Groups . In: Proceedings of a Colloquium at the FU Berlin May 1981, dedicated to Prof. Dr. Hanfried Lenz on his 65th birthday . Springer 1981.
  • Walter Benz: On the mathematical work of Hanfried Lenz . In: Journal of Geometry . No. 43, 1992.
  • Dieter Jungnickel, Günter Pickert: A life's work in geometry: homage to Hanfried Lenz . Designs, Codes and Cryptography. Volume 8. 1996, p. 9.

Web links

Individual evidence

  1. Desargue's Small Theorem and Duality in Projective Planes , Annual Report of the German Mathematicians Association, Vol. 57, 1954, p. 20
  2. Barlotti: Le possibili configurazioni del sistema delle coppie punto-retta per cui un piano grafico risulta -transitivo . Bolletino Unione Matematica Italiana. Volume 12. 1957, pp. 212-226.
  3. Lenz: On the justification of analytical geometry . Session reports of the Bavarian Academy of Sciences, Mathematical and Natural Science Class, 1954, pp. 17–72.
  4. ^ Albrecht Beutelspacher : Introduction to Finite Geometry II. Projective Spaces . Bibliographisches Institut, Mannheim 1983, ISBN 3-41101648-5 , p. 49ff.
  5. ^ The ICA Medals. Institute of Combinatorics and its Applications, accessed June 17, 2018 .