Bartel Leendert van der Waerden

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Bartel Leendert van der Waerden

Bartel Leendert van der Waerden (/ ʋardə (n) /) (born February 2, 1903 in Amsterdam , † January 12, 1996 in Zurich ) was a Dutch mathematician .


Van der Waerden was born as the son of the civil engineering and mathematics teacher Theodorus van der Waerden and Dorothea Adriana Endt. He showed a mathematical talent relatively early on. In 1919 he began studying mathematics in Amsterdam. He heard from Gerrit Mannoury , Roland Weitzenböck , Luitzen Egbertus Jan Brouwer and Hendrik de Vries , passed his doctoral examination in 1924 and received his doctorate in 1926 from de Vries in Amsterdam on the fundamentals of counting geometry (Schubert calculus) (De algebraise grondslagen der meetkunde van het aantal). In between, van der Waerden was in Göttingen from 1924 , where he heard from Emmy Noether (algebra), from Hellmuth Kneser (topology) and mathematical methods of physics from Richard Courant (based on the textbook by Courant-Hilbert).

After completing his doctorate in 1926, he spent a year in Hamburg (where he heard from Emil Artin , Otto Schreier and Erich Hecke ) and completed his habilitation in Göttingen in 1927, where he was Richard Courant's assistant . In the winter semester of 1927/28 he gave his first lecture on ideal theory in Göttingen. At that time he was interested in an exact justification of algebraic geometry with methods of modern algebra, which became his main field of work. In algebraic geometry there was an abundance of beautiful geometric results, but they were not strictly proven (for example in Schubert's counting calculus or in the work of the Italian school around Francesco Severi , Guido Castelnuovo , Federigo Enriques ). Other mathematicians also worked on it in competition with van der Waerden, for example André Weil in the 1940s and Oscar Zariski in the USA , whose work later eclipsed that of van der Waerden, much to his chagrin.

In 1928 he became a professor in Groningen . In 1929 he married Camilla Rellich, the sister of Franz Rellich , whom he knew from Göttingen and with whom he had three children. In Groningen he worked on his well-known algebra textbook, which arose from lectures by Artin and Emmy Noether and the first volume of which was first published in 1930. From 1931 to 1945 he was professor at the Mathematical Institute of the University of Leipzig and its director. The simultaneous presence of Werner Heisenberg and an interest in quantum mechanics had drawn him there. The book The Group Theoretical Method in Quantum Mechanics emerged from joint seminars. In the 1940s he ran into difficulties in Germany because he did not want to give up his Dutch citizenship . During the German occupation in 1942, his mother committed suicide in the Netherlands (his father died of cancer in 1940). During the heavy bombing raids on Leipzig, he and his family temporarily moved to Dresden and the surrounding area and shortly before the end of the war to Austria. In 1945 he went back to Amsterdam. On the mediation of Hans Freudenthal, he worked for Shell in The Hague and, from its establishment in 1946, also at the Mathematisch Centrum in Amsterdam, where he represented applied mathematics. In 1947/8 he went to the American Johns Hopkins University , where he turned down a professorship (and instead mediated his student Wei-Liang Chow ), and from 1948 was an associate professor and from 1950 a full professor at the University of Amsterdam, although Brouwer tried to prevent this. He turned down an appointment to Göttingen in 1949, as well as other appointments, but used them to improve his position in Amsterdam. In 1951 he went to the University of Zurich , where Rudolf Fueter's chair had become vacant, and taught there until his retirement in 1972. However, he remained scientifically active as a mathematics historian.


He became famous for his two-volume textbook on algebra , the first edition of which appeared in 1930 under the title Modern Algebra and is based on the lectures of Emil Artin and Emmy Noether . As the first textbook, it consistently carried out the change in algebra that took place in the early 20th century away from concrete computing techniques towards the investigation of abstract structures. This made it an influential reference work for many decades.

In a long series of articles in the Mathematische Annalen he tried to put the Algebraic Geometry of the Italian School around Francesco Severi , Federigo Enriques and others and the “Counting Calculus” by Hermann Schubert on a strict, purely algebraic basis, but was here by André Weil et al. obsolete ".

He also dealt with the application of elementary geometry, the axioms of geometry, statistics, topology, number theory and others, so that one can call him one of the last generalists of mathematics. At the same time as Ernst Witt et al. He gave a geometric description of the classification of Lie algebras . The rate of Van der Waerden is an important set of Ramsey theory , an area of combinatorics .

In 1953, together with Kurt Schütte , he proved the kiss number problem in three dimensions, that a central sphere can touch a maximum of twelve other spheres of the same size. Isaac Newton had already suspected this , while David Gregory said it was 13.

He was also a leading historian of science, particularly concerned with ancient Greek mathematics (and beyond to India) and astronomy and the history of algebra.

Since 1951 he was a corresponding member of the Bavarian Academy of Sciences . In 1960 he was elected a member of the German Academy of Sciences Leopoldina and in 1966 a corresponding member of the Göttingen Academy of Sciences . Van der Waerden was elected honorary member of the Saxon Academy of Sciences on January 12, 1996 , and he was a member of the Royal Netherlands Academy of Sciences. In 1961 he received an honorary doctorate from the University of Athens and in 1985 from the University of Leipzig. In 1969 he received the Cothenius Medal of the Leopoldina. In 1973 he received the Order Pour le Mérite for Science and the Arts. For a long time (from 1934) he was editor of the Mathematische Annalen, was co-editor of the Basic Teachings of Mathematical Sciences and of the Archive for the history of exact sciences . In 1970 he was invited speaker at the International Congress of Mathematicians in Nice (The foundation of algebraic geometry from Severi to André Weil).

His doctoral students include Hans Richter , Wei-Liang Chow , David van Dantzig , Erwin Neuenschwander , Günther Frei , Guerino Mazzola , and Herbert Seifert .

See also


  • Algebra. 2 volumes. 9th edition. Springer, 1993 ( called Modern Algebra in older editions , first 1930/1931)
  • Introduction to Algebraic Geometry. Springer, 1973 (reprint of a series of magazine articles, first in 1939).
  • Groups of linear transformations. Springer, 1935.
  • Mathematical Statistics. Springer, 1971.
  • Awakening Science. Volume 1: Egyptian, Babylonian and Greek Mathematics. Birkhäuser 1956, 2nd edition 1966 (first Dutch 1950, English edition Science Awakening. 1954). The beginnings of astronomy are dealt with in a second volume (2nd edition 1980).
  • The Pythagorean Religious Brotherhood and School of Science, Artemis, 1979.
  • The astronomy of the Greeks. An introduction. Scientific Book Society, 1988.
  • Geometry and algebra in ancient civilizations, Springer 1983,
  • A history of algebra. Springer, 1985
  • Group theory and quantum mechanics. 2nd Edition. Springer 1986 (German: The group theoretical method in quantum mechanics. Springer 1932).
  • (Ed.): Sources of quantum mechanics. 1967. Reprint dover 2007 (reprint of important works in quantum mechanics with a historical introduction by van der Waerden).
  • Mathematics for natural scientists. BI university paperback, 1975.
  • “My years of apprenticeship in Göttingen”. In: Messages from the DMV. Volume 5 (1997), Issue 2 (lecture from 1979), doi : 10.1515 / dmvm-1997-0208 .
  • The arithmetic of the Pythagoreans. Part 1. Part 1. Mathematical annals. 1947/1949. Part 2.
  • Zeno and the basic crisis of Greek mathematics. Mathematical annals. 1940/1941.
  • with Schütte: The problem of the 13 balls. Mathematical annals. 1953.
  • Spinor analysis. Nachr. Akad. Göttingen. 1928.
  • The classification of the simple Lieschen groups. Mathematical journal. 1933.
  • About the interaction between mathematics and physics. Elements of math. 1973.
  • Incursion and reflection in mathematics. Part 1. Elements of Mathematics. 1954. Part 2 and Part 3
  • Algebra since Galois. Annual report DMV. 1966.
  • The astronomy of the Pythagoreans . Amsterdam 1951.


  • Günther Eisenreich : Van der Waerden's work from 1931 to 1945 in Leipzig. In: Herbert Beckert , Horst Schumann (Ed.) 100 Years of Mathematical Seminar at the Karl Marx University in Leipzig. German Science Publishers, Berlin 1981.
  • Rüdiger Thiele : Van der Waerden's years in Leipzig, 1931–1945. In: Messages from the DMV. Volume 12, No. 1, 2004, pp. 8-20.
  • Rüdiger Thiele: Van der Waerden in Leipzig. Edition at Gutenbergplatz Leipzig 2009, ISBN 978-3-937219-36-3 (EAGLE 036).
  • Günther Frei : In memory of Bartel Leendert van der Waerden. In: Elements of Mathematics. Volume 53, 1998, p. 133.
  • Interview with Yvonne Dold-Samplonius . In: NTM Journal for the History of Science, Technology, Medicine. Volume 2, 1993, p. 129.
  • Obituary by Dold-Samplonius. In: Historia Mathematica. Volume 24, 1997, pp. 125-130.
  • Jan Hogendijk : BL van der Waerden's detective work in ancient and medieval mathematical astronomy. In: Nieuw Archief voor Wiskunde. Volume 12, 1994, pp. 145-158.
  • Erwin Neuenschwander : Waerden, Bartel Leendert van der. In: JW Dauben, C. Scriba (Ed.): Writing the History of Mathematics. Springer, 2002, pp. 547-551.
  • Martina Schneider: Between two disciplines: BL van der Waerden and the development of quantum mechanics. Springer 2011.
  • Reinhard Siegmund-Schultze : Bartel Leendert van der Waerden (1903–1996) in the Third Reich: Modern Algebra in the Service of Anti-Modernism? In: Dieter Hoffmann , Mark Walker (ed.): Foreign scientists in the Third Reich: the Debye affair in context. Wallstein, Göttingen 2011, pp. 200–229.
  • Reinhard Siegmund-Schulze: Mathematicians fleeing from Nazi Germany. Princeton University Press, 2009 (first in German, Vieweg 1998).
  • Norbert Schappacher : A historical sketch of BL van der Waerden's work on algebraic geometry 1926-1946. In: Jeremy Gray, Karen Parshall (eds.): Episodes in the History of Modern Algebra 1800–1950. AMS 2007, pp. 245-283.
  • Alexander Soifer : The Scholar and the State: In Search of Van der Waerden. Birkhäuser 2015, ISBN 978-3-0348-0711-1 , doi : 10.1007 / 978-3-0348-0712-8
  • Alexander Soifer: The mathematical coloring book. Springer 2009.

Web links


  1. Brouwer had given van der Waerden a letter of recommendation to the Göttingen private lecturer Kneser, who then invited him regularly for lunch walks in Göttingen, where he taught him topology. At that time Brouwer was no longer teaching topology in Amsterdam, only intuitionistic mathematics. He also recommended van der Waerden to study with Emmy Noether.
  2. A professorship in Utrecht, which Freudenthal initially wanted to arrange, was not possible because of his German past
  3. Martina Schneider: Between two disciplines: BL van der Waerden and the development of quantum mechanics, Springer 2011, p. 76. Their relationship was initially unencumbered, but cooled off when Brouwer David van Dantzig , who was friends with van der Waerden, refused the doctorate and accused him of plagiarism (he then did his doctorate with van der Waerden), and after Brouwer came into open conflict with the Hilbert school.
  4. Casselman on the Kissing Number problem and its history, Notices of the AMS, 2004, Issue 8, PDF file
  5. Bartel Leendert van der Waerden Obituary by Wulf-Dieter Geyer and memories of Carl Friedrich von Weizsäcker in the 1997 yearbook of the Bavarian Academy of Sciences (PDF file).
  6. ↑ List of members Leopoldina, Bartel L. van der Waerden
  7. {Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class . Volume 3, Vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 250.
  8. ^ Mathematics Genealogy Project
  9. ^ Critical review by Reinhard Siegmund-Schultze, Notices AMS, 2015, No. 8, pdf