Johann Jakob Burckhardt (mathematician)

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Johann Jakob Burckhardt (born July 13, 1903 in Basel ; † November 5, 2006 ) was a Swiss mathematician and crystallographer .

Life

Johann Jakob Burckhardt came from an old Basel family. One of his ancestors was a brother (Hieronimus) of Jakob I and Johann I Bernoulli . His father was a lawyer and legal advisor at the German consulate in Basel. Burckhardt attended the humanistic grammar school and the upper secondary school in Basel and studied from 1922 at the University of Basel .

In 1923 he studied in the summer semester at the Ludwig Maximilians University in Munich , among others with Arnold Sommerfeld , Oskar Perron , Friedrich Hartogs and Wilhelm Wien , and in 1924 at the University of Hamburg , among others with Hans Rademacher and Erich Hecke .

Inspired by reading the group theory textbook by Andreas Speiser , which also had applications on ornamentation and crystallography, he continued his studies in 1924 at the University of Zurich . There he heard among others Speiser, Rudolf Fueter , the astronomer Alfred Wolfer and Erwin Schrödinger , and at the ETH Zurich Hermann Weyl , George Pólya (whose seminar he attended) and the mineralogist Paul Niggli . He also studied crystallography with Leonhard Weber .

In 1927 he passed the examination for the higher teaching post and received his doctorate in mathematics with Speiser ( Die Algebras der Diedergruppen ). At the end of 1927 he continued his studies at the University of Paris with Jacques Hadamard and then in 1928 at the University of Göttingen , where he attended the seminars of Emmy Noether and Richard Courant and heard geometry from Gustav Herglotz . Here he also met Bartel Leendert van der Waerden and Otto Neugebauer , both of whom later became well-known mathematicians (van der Waerden was later his colleague in Zurich).

Since he did not like the political climate with the rise of the National Socialists in Germany, he turned down the offer of an assistant position in Göttingen and went back to Basel, where he was an assistant teacher at the lower secondary school. He then moved to the University of Zurich as Fueter's assistant.

Burckhardt completed his habilitation in 1933 at the University of Zurich with a thesis on the theory of movement groups , then taught as a representative at the Technikum Winterthur and the daughter's school on the Hohen Promenade in Zurich. He turned down an offer as a professor at Cairo University . In 1942 he became adjunct professor at the University of Zurich. In 1943/1944 he was Otto Spiess' representative in Basel. From 1945 until his retirement in 1970 he was senior assistant at the Mathematical Institute at the University of Zurich.

Burckhardt was an honorary member of the Swiss Mathematical Society , of which he was president in 1954/1955, and the Natural Research Society of Zurich .

He was an avid hiker and mountaineer.

plant

Burckhardt is known for his derivation of crystallographic space groups , the subject of a standard work written by him. The 230 room groups were set up by Schoenflies and Fjodorow around 1890 . The two-dimensional case was treated mathematically by Pólya and Niggli in 1924. Burckhardt solved the three-dimensional case mathematically in the 1930s, that is, he gave an algebraic method of determination. Here he built on the work of Frobenius and Bieberbach on groups of movements in n-dimensional spaces and introduced the concept of the arithmetic crystal class . His method can also be used in higher dimensions.

On behalf of Speiser and Fueter, he wrote a description of Paul Finsler's set theory . This happened at the suggestion of Fueter and Speiser, in order to explain Finsler's mostly negative ideas to other mathematicians.

Burckhardt also dealt with the history of mathematics . Among other things, he dealt with Ludwig Schläfli , wrote the article about him for the Dictionary of Scientific Biography , a biography of Schläfli for the journal Elements of Mathematics , and edited his collected treatises as a member of the Steiner-Schläfli Committee.

He studied (partly with van der Waerden) medieval Islamic astronomers (such as the planetary tables of al-Chwarizmi ).

He was also involved in the Euler Complete Edition, as a member of the Swiss Euler Commission (1952–1975), of which he was Vice President from 1957 to 1975.

Burckhardt also wrote a book on the history of crystallography and essays on the history of the discovery of the space groups by Fjodorow and Schoenflies. In 1966 he published Ulrich Wagner's arithmetic book from 1483, of which he found a copy in the Zurich Central Library .

He wrote biographies of mathematicians for the Neue Deutsche Biographie and the Dictionary of Scientific Biography on Fueter, Marcel Grossmann , Heinz Hopf , Karl Heinrich Gräffe , Ferdinand Rudio , Carl Friedrich Geiser , Rudolf Wolf , Jakob Steiner and Schläfli.

Burckhardt also worked as a translator. In 1923 he and Emil Schubarth translated Leonard Dickson's book Algebras and their Number Theory (Orell Füssli, Zurich 1927) on behalf of Andreas Speiser - at that time it had a great influence on the development of algebra theory and algebraic number theory in Germany. He also translated the well-known geometry textbook by Coxeter ( Immortal Geometry , Birkhäuser, Basel 1963).

From 1950 to 1982 he was editor of the Commentarii Mathematici Helvetici .

Fonts

  • The movement groups of crystallography. Birkhäuser, Basel 1947; 2nd, revised edition. 1966.
  • Ludwig Schläfli: 1814 - 1895 . In: Elements of Mathematics , Supplement 4, 1948, Online
  • Mathematics reader. Sources from Euclid to the present day. Räber, Lucerne 1968.
  • Mathematics at the University of Zurich 1916–1950 under the professors R. Fueter, A. Speiser, P. Finsler. In: Elements of Mathematics. Supplement 16, 1980, online .
  • Editor with Emil Fellmann , Walter Habicht: Leonhard Euler 1707–1783. Contributions to life and work. Commemorative volume of the canton of Basel-Stadt. Birkhäuser, Basel 1983 (in it by Burckhardt: The Euler Commission of the Swiss Natural Research Society - a contribution to the history of editions , pp. 501-510, and Euleriana - directory of the literature on Leonhard Euler. Pp. 511-552).
  • The symmetry of the crystals. From René-Just Haüy to the crystallographic school in Zurich. With a contribution by Erhard Scholz . Birkhäuser, Basel 1988. (History of crystallography).

literature

  • Günther Frei : Johann Jakob Burckhardt on his hundredth birthday on July 13, 2003. In: Elements of Mathematics. Volume 58, 2003, pp. 134-140, doi : 10.5169 / seals-8491 (the issue is dedicated to Burckhardt).
  • Ralph Strebel: Burckhardt's determination of the space groups I. In: Elements of mathematics. Volume 58, 2003, pp. 141-155, doi : 10.5169 / seals-8492 .
  • Ralph Strebel: Burckhardtsche determination of space groups II. In: Elements of mathematics. Volume 59, 2004, pp. 1-18, doi : 10.5169 / seals-9305 .

Web links

Individual evidence

  1. ↑ JJ Burckhardt: On the theory of movement groups . In: Comm. Math. Helv. Volume 6, 1934, pp. 159-184, digitized
  2. ↑ Cover text on Burckhardt's Symmetry of Crystals , 1988.
  3. ↑ Georg Pólya: About the analogy of the crystal symmetry in the plane. In: Journal of Crystallography and Mineralogy . Volume 60, 1924, pp. 278-283 ( doi : 10.1524 / zkri.1924.60.1.278 ). Paul Niggli: The surface symmetries of homogeneous continuums. ibid, pp. 283-298 ( doi : 10.1524 / zkri.1924.60.1.283 ).
  4. ↑ Comments on the arithmetic calculation of the movement groups. Comm. Math. Helv., Vol. 2, 1930, pp. 91-98 ( doi : 10.1007 / BF01214452 ); On the theory of movement groups. Comm. Math. Helv., Vol. 6, 1934, pp. 159-184 ( doi : 10.1007 / BF01297330 ); Movement groups in multi-dimensional spaces. Comm. Math. Helv., Volume 9, 1936, pp. 284-302 ( doi : 10.1007 / BF01258194 ).
  5. ↑ On the new justification of set theory. In: Annual report of the German Mathematicians Association 1938/1939.
  6. ↑ JJ Burckhardt: Ludwig Schläfli 1814–1895. In: E lemente der Mathematik . Supplement 4, 1948, pp. 3–23 (to the pdf file) .
  7. ^ Editor together with Louis Kollros, Hugo Hadwiger . 3 volumes. Birkhäuser, Basel 1950/1953/1956.
  8. ↑ Burckhardt, van der Waerden: The astronomical system of the Persian tables. Part 1. In: Centaurus , Volume 13, 1969, pp. 1-28 ( doi : 10.1111 / j.1600-0498.1969.tb00102.x ).
  9. ↑ The Astronomical Tables of Al-Khwarizmi. In: L'Enseignement Mathematique . Volume 2, 1956. / The mean movements of the planets in the tables of Kwarizmi. (pdf file) In: Quarterly journal Naturforschende Gesellschaft Zürich . Volume 106, 1961, pp. 213-231.
  10. ↑ Together with Karl Matter and Edmund Hoppe, he was the editor of Volume III / 2 of the Euler Complete Edition Rechenkunst (Geneva 1942). In this context he edited some of Euler's physical treatises and was involved in the compilation of the list of correspondence (Series IV A, Volume 1, 1975.)
  11. ↑ The story of the discovery of the 230 room groups. Archive for the History of Exact Sciences, Volume 4, 1967, pp. 235-246 ( doi : 10.1007 / BF00412962 ). In the same journal (Volume 7, 1971 pp. 91-141) ( doi : 10.1007 / BF00411807 ) he published on the correspondence Fjodorow-Schoenflies and (Volume 9, 1972, pp. 85-93) ( doi : 10.1007 / BF00348577 ) for Fyodorov's correspondence with Felix Klein .
  12. ↑ Only two copies are known. The other one is in Zwickau.
  13. ^ EMS - European Mathematical Society Publishing House. Retrieved March 27, 2018 .
personal data
SURNAME Burckhardt, Johann Jakob
BRIEF DESCRIPTION Swiss mathematician and crystallographer
DATE OF BIRTH July 13, 1903
PLACE OF BIRTH Basel
DATE OF DEATH November 5, 2006