Bartel Leendert van der Waerden

Bartel Leendert van der Waerden (Dutch: [vɑn dər ˈʋaːrdə(n)]; February 2, 1903 – January 12, 1996) was a Dutch mathematician and historian of mathematics.

Bartel Leendert van der Waerden
ETH-BIB-Waerden, Bartel Leendert van der (1903-1996)-Portrait-Portr 12193
BornFebruary 2, 1903
DiedJanuary 12, 1996 (aged 92)
Alma materUniversity of Amsterdam
University of Göttingen
Known forVan der Waerden notation
Van der Waerden number
Van der Waerden's theorem
Van der Waerden test
Van der Waerden's conjecture
Scientific career
InstitutionsUniversity of Leipzig
University of Zurich
University of Groningen
Doctoral advisorHendrik de Vries
Doctoral studentsDavid van Dantzig
Herbert Seifert


Education and early career

Van der Waerden learned advanced mathematics at the University of Amsterdam and the University of Göttingen, from 1919 until 1926. He was much influenced by Emmy Noether at Göttingen, Germany. Amsterdam awarded him a Ph.D. for a thesis on algebraic geometry, supervised by Hendrick de Vries.[1] Göttingen awarded him the habilitation in 1928. In that year, at the age of 25, he accepted a professorship at the University of Groningen.

In his 27th year, van der Waerden published his Moderne Algebra, an influential two-volume treatise on abstract algebra, still cited, and perhaps the first treatise to treat the subject as a comprehensive whole. This work systematized an ample body of research by Emmy Noether, David Hilbert, Richard Dedekind, and Emil Artin. In the following year, 1931, he was appointed professor at the University of Leipzig.

Nazi Germany

During the rise of the Third Reich and through World War II, van der Waerden remained at Leipzig, and passed up opportunities to leave Nazi Germany for Princeton and Utrecht. However, he was critical of the Nazis and refused to give up his Dutch nationality, both of which led to difficulties for him.[2]

Postwar career

Following the war, van der Waerden was repatriated to the Netherlands rather than returning to Leipzig (then under Soviet control), but struggled to find a position in the Dutch academic system, in part because his time in Germany made his politics suspect and in part due to Brouwer's opposition to Hilbert's school of mathematics. After a year visiting Johns Hopkins University and two years as a part-time professor, in 1950 van der Waerden filled the chair in mathematics at the University of Amsterdam.[3] In 1951, he moved to the University of Zurich, where he spent the rest of his career, supervising more than 40 Ph.D. students.


Van der Waerden is mainly remembered for his work on abstract algebra. He also wrote on algebraic geometry, topology, number theory, geometry, combinatorics, analysis, probability and statistics, and quantum mechanics (he and Heisenberg had been colleagues at Leipzig). In his later years, he turned to the history of mathematics and science. His historical writings include Ontwakende wetenschap (1950), which was translated into English as Science Awakening (1954), Sources of Quantum Mechanics (1967), Geometry and Algebra in Ancient Civilizations (1983), and A History of Algebra (1985).

Van der Waerden has over 1000 academic descendants, most of them through three of his students, David van Dantzig (Ph.D. Groningen 1931), Herbert Seifert (Ph.D. Leipzig 1932), and Hans Richter (Ph.D. Leipzig 1936, co-advised by Paul Koebe).[4]

See also


  1. ^ Bartel Leendert van der Waerden at the Mathematics Genealogy Project
  2. ^ Soifer, pp. 393–417.
  3. ^ Soifer, pp. 418–474.
  4. ^ Bartel Leendert van der Waerden at the Mathematics Genealogy Project


  • Alexander Soifer (2009), The Mathematical Coloring Book, Springer-Verlag ISBN 978-0-387-74640-1. Soifer devotes four chapters and over 100 pages to biographical material about van der Waerden, some of which he had also published earlier in the journal Geombinatorics.
  • Alexander Soifer (2015) The Scholar and the State: In Search of Van der Waerden, Springer books ISBN 978-3-0348-0711-1

Further reading

External links

1903 in science

The year 1903 in science and technology involved some significant events, listed below.

1996 in science

The year 1996 in science and technology involved many significant events, listed below.

Alexander Soifer

Alexander Soifer is a Russian-born American mathematician and mathematics author. His works include over 400 articles, and 13 books.

Soifer received his Ph.D. in 1973. Soifer has been a professor of mathematics at the University of Colorado since 1979. He was visiting fellow at Princeton University 2002–2004, and again 2006–2007. Soifer also teaches courses on art history and European cinema. His publications include 13 books and over 400 articles.

Every spring, Soifer, along with other mathematician colleagues, sponsors the Colorado Mathematical Olympiad (CMO) at the University of Colorado at Colorado Springs. Soifer compiles and writes most of the problems for the contest. The CMO was founded by Soifer on April 18, 1983 (

In 1991 Soifer founded the research quarterly Geombinatorics, and publishes it with the Editorial Board, which includes Ronald L. Graham, Jaroslav Nešetřil, Branko Grünbaum, Heiko Harborth, Peter D. Johnson Jr., Geoffrey Exoo, and János Pach. Paul Erdős was also an editor. (

In July 2006 at the University of Cambridge, Alexander Soifer was presented with the Paul Erdős Award by the World Federation of National Mathematics Competitions.

Soifer is currently the President of the World Federation of National Mathematics Competitions ( Soifer's Erdős number is 1.

Soifer's current projects include new publications and new expanded editions through scientific publisher, Springer of previously published books, "Mathematics as Problem Solving," "How does one cut a triangle?," "Geometric Etudes in Combinatorial Mathematics," and "Colorado Mathematical Olympiad: The First Ten Years and Further Explorations." The latter aforementioned title is expected to be expanded to cover twenty years of the Colorado Mathematical Olympiad, which is currently in its 35th year running.

In recognition of 35 years of leadership, the judges and winners decided in 2018 to rename the Colorado Mathematical Olympiad to the Soifer Mathematical Olympiad.

Soifer is the father of four children, Mark Soifer, Julia Soifer, Isabelle Soifer and Leon Soifer.

Arthur Byron Coble

Arthur Byron Coble (November 3, 1878 – December 8, 1966) was an American mathematician. He did research on finite geometries and the group theory related to them, Cremona transformations associated with the Galois theory of equations, and the relations between hyperelliptic theta functions, irrational binary invariants, the Weddle surface and the Kummer surface. He was President of the American Mathematical Society from 1933 to 1934.


Bartel could refer to:

Bartel, one of the Companions of Saint Nicholas

Bartel (radio personality) - New York City radio personality on WKTU

Beate Bartel - Musician (Liaisons Dangereuses, Einstürzende Neubauten)

Jimmy Bartel - footballer

Jonny Ray Bartel - Musician ( The Red Devils, The Knitters)

Kazimierz Bartel - Former Polish Prime Minister

Mateusz Bartel - Polish chess player

Michael Bartel (actor) - Arrested Development performer, born 1989

Michael Bartel (New York politician) - 1950 Socialist Workers candidate for NY governor

Paul Bartel - actor

Richard Bartel - American football player

Ryszard Bartel - Polish aeronautical engineer and aircraft designer

Bartel J. Jonkman - Michigan politician

Bartel Leendert van der Waerden - mathematician

Max Bartel - entomologist

David van Dantzig

David van Dantzig (September 23, 1900 – July 22, 1959) was a Dutch mathematician, well known for the construction in topology of the dyadic solenoid. He was a member of the Significs Group.

Eugene Dynkin

Eugene Borisovich Dynkin (Russian: Евге́ний Бори́сович Ды́нкин; 11 May 1924 – 14 November 2014) was a Soviet and American mathematician. He has made contributions to the fields of probability and algebra, especially semisimple Lie groups, Lie algebras, and Markov processes. The Dynkin diagram, the Dynkin system, and Dynkin's lemma are named after him.

Hassler Whitney

Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician. He was one of the founders of singularity theory, and did foundational work in manifolds, embeddings, immersions, characteristic classes, and geometric integration theory.

Jan van Deemter

Jan Jozef van Deemter (31 March 1918–10 October 2004) was a Dutch physicist and engineer known for the Van Deemter equation in chromatography.

L. E. J. Brouwer

Luitzen Egbertus Jan Brouwer (; Dutch: [ˈlœy̯tsə(n) ɛɣˈbɛrtəs jɑn ˈbrʌu̯ər]; 27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, who worked in topology, set theory, measure theory and complex analysis. He was the founder of the mathematical philosophy of intuitionism.

List of Leipzig University people

The following is a list of notable alumni and faculty of the University of Leipzig.

Moderne Algebra

Moderne Algebra is a two-volume German textbook on graduate abstract algebra by Bartel Leendert van der Waerden (1930, 1931), originally based on lectures given by Emil Artin in 1926 and by Emmy Noether (1929) from 1924 to 1928. The English translation of 1949–1950 had the title Modern algebra, though a later, extensively revised edition in 1970 had the title Algebra.

The book was one of the first textbooks to use an abstract axiomatic approach to groups, rings, and fields, and was by far the most successful, becoming the standard reference for graduate algebra for several decades. It "had a tremendous impact, and is widely considered to be the major text on algebra in the twentieth century."In 1975 van der Waerden described the sources he drew upon to write the book.In 1997 Saunders Mac Lane recollected the book's influence:

Upon its publication it was soon clear that this was the way that algebra should be presented.

Its simple but austere style set the pattern for mathematical texts in other subjects, from Banach algebras to topological group theory.

[Van der Waerden's] two volumes on modern algebra ... dramatically changed the way algebra is now taught by providing a decisive example of a clear and perspicacious presentation. It is, in my view, the most influential text of algebra of the twentieth century.

Outline of combinatorics

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.

Ramsey theory

Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear. Problems in Ramsey theory typically ask a question of the form: "how many elements of some structure must there be to guarantee that a particular property will hold?" More specifically, Ron Graham describes Ramsey theory as a "branch of combinatorics".

Seleucus of Seleucia

Seleucus of Seleucia (Greek: Σέλευκος Seleukos; born c. 190 BC; fl. c. 150 BC) was a Hellenistic astronomer and philosopher. Coming from Seleucia on the Tigris, Mesopotamia, the capital of the Seleucid Empire, or, alternatively, Seleukia on the Erythraean Sea, he is best known as a proponent of heliocentrism and for his theory of the origin of tides.

Van der Waerden notation

In theoretical physics, van der Waerden notation refers to the usage of two-component spinors (Weyl spinors) in four spacetime dimensions. This is standard in twistor theory and supersymmetry. It is named after Bartel Leendert van der Waerden.

Van der Waerden test

Named after the Dutch mathematician Bartel Leendert van der Waerden, the Van der Waerden test is a statistical test that k population distribution functions are equal. The Van der Waerden test converts the ranks from a standard Kruskal-Wallis one-way analysis of variance to quantiles of the standard normal distribution (details given below). These are called normal scores and the test is computed from these normal scores.

The k population version of the test is an extension of the test for two populations published by Van der Waerden (1952,1953).

Wilbur Knorr

Wilbur Richard Knorr (August 29, 1945 – March 18, 1997) was an American historian of mathematics and a professor in the departments of philosophy and classics at Stanford University. He has been called "one of the most profound and certainly the most provocative historian of Greek mathematics" of the 20th century.

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