van der Waerden
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Bartel Leendert van der Waerden (; 2 February 1903 – 12 January 1996) was a Dutch
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
and
historian of mathematics The history of mathematics deals with the origin of discoveries in mathematics and the History of mathematical notation, mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples ...
.


Biography


Education and early career

Van der Waerden learned advanced mathematics at the
University of Amsterdam The University of Amsterdam (abbreviated as UvA, ) is a public university, public research university located in Amsterdam, Netherlands. Established in 1632 by municipal authorities, it is the fourth-oldest academic institution in the Netherlan ...
and the
University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 ...
, from 1919 until 1926. He was much influenced by
Emmy Noether Amalie Emmy Noether (23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra. She also proved Noether's theorem, Noether's first and Noether's second theorem, second theorems, which ...
at
Göttingen Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...
,
Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...
. Amsterdam awarded him a Ph.D. for a thesis on
algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
, supervised by Hendrick de Vries. Göttingen awarded him the
habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excelle ...
in 1928. In that year, at the age of 25, he accepted a professorship at the
University of Groningen The University of Groningen (abbreviated as UG; , abbreviated as RUG) is a Public university#Continental Europe, public research university of more than 30,000 students in the city of Groningen (city), Groningen, Netherlands. Founded in 1614, th ...
. At 27, Van der Waerden published his ''
Moderne Algebra ''Moderne Algebra'' is a two-volume German textbook on graduate abstract algebra by , originally based on lectures given by Emil Artin in 1926 and by from 1924 to 1928. The English translation of 1949–1950 had the title ''Modern algebra'', tho ...
'', an influential two-volume treatise on
abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...
, 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 Amalie Emmy Noether (23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra. She also proved Noether's theorem, Noether's first and Noether's second theorem, second theorems, which ...
,
David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental idea ...
,
Richard Dedekind Julius Wilhelm Richard Dedekind (; ; 6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to number theory, abstract algebra (particularly ring theory), and the axiomatic foundations of arithmetic. H ...
, and
Emil Artin Emil Artin (; March 3, 1898 – December 20, 1962) was an Austrians, Austrian mathematician of Armenians, Armenian descent. Artin was one of the leading mathematicians of the twentieth century. He is best known for his work on algebraic number t ...
. In the following year, 1931, he was appointed professor at the
University of Leipzig Leipzig University (), in Leipzig in Saxony, Germany, is one of the world's oldest universities and the second-oldest university (by consecutive years of existence) in Germany. The university was founded on 2 December 1409 by Frederick I, Electo ...
. In July 1929 he married the sister of mathematician
Franz Rellich Franz Rellich (September 14, 1906 – September 25, 1955) was an Austrian-German mathematician. He made important contributions in mathematical physics, in particular for the foundations of quantum mechanics and for the theory of partial differen ...
, Camilla Juliana Anna, and they had three children.


Nazi Germany

After the
Nazis Nazism (), formally named National Socialism (NS; , ), is the far-right politics, far-right Totalitarianism, totalitarian socio-political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Germany. During H ...
seized power, and through
World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
, Van der Waerden remained at Leipzig, and passed up opportunities to leave Nazi Germany for
Princeton Princeton University is a private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the Unit ...
and
Utrecht Utrecht ( ; ; ) is the List of cities in the Netherlands by province, fourth-largest city of the Netherlands, as well as the capital and the most populous city of the Provinces of the Netherlands, province of Utrecht (province), Utrecht. The ...
. However, he was critical of the Nazis and refused to give up his Dutch nationality, both of which led to difficulties for him.


Postwar career

Following the war, Van der Waerden was repatriated to the Netherlands rather than returning to
Leipzig Leipzig (, ; ; Upper Saxon: ; ) is the most populous city in the States of Germany, German state of Saxony. The city has a population of 628,718 inhabitants as of 2023. It is the List of cities in Germany by population, eighth-largest city in Ge ...
(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 Brouwer (also Brouwers and de Brouwer) is a Dutch and Flemish surname. The word ''brouwer'' means 'brewer'. Brouwer * Adriaen Brouwer (1605–1638), Flemish painter * Alexander Brouwer (b. 1989), Dutch beach volleyball player * Andries Brouwer ( ...
's opposition to Hilbert's school of mathematics. After a year visiting
Johns Hopkins University The Johns Hopkins University (often abbreviated as Johns Hopkins, Hopkins, or JHU) is a private university, private research university in Baltimore, Maryland, United States. Founded in 1876 based on the European research institution model, J ...
and two years as a part-time professor, in 1950, Van der Waerden filled the chair in mathematics at the University of Amsterdam. In 1951, he moved to the
University of Zurich The University of Zurich (UZH, ) is a public university, public research university in Zurich, Switzerland. It is the largest university in Switzerland, with its 28,000 enrolled students. It was founded in 1833 from the existing colleges of the ...
, where he spent the rest of his career, supervising more than 40 Ph.D. students. In 1949, Van der Waerden became member of the
Royal Netherlands Academy of Arts and Sciences The Royal Netherlands Academy of Arts and Sciences (, KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed in the Trippenhuis in Amsterdam. In addition to various advisory a ...
, in 1951 this was changed to a foreign membership. In 1973 he received the ''
Pour le Mérite The (; , ), also informally known as the ''Blue Max'' () after German WWI flying ace Max Immelmann, is an order of merit established in 1740 by King Frederick II of Prussia. Separated into two classes, each with their own designs, the was ...
''.


Contributions

Van der Waerden is mainly remembered for his work on
abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...
. He also wrote on
algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
,
topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...
,
number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
,
geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
,
combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...
,
analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...
,
probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...
and
statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...
, and
quantum mechanics Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
(he and Heisenberg had been colleagues at Leipzig). In later years, he turned to the
history of mathematics The history of mathematics deals with the origin of discoveries in mathematics and the History of mathematical notation, mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples ...
and
science Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which stu ...
. 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 David van Dantzig (September 23, 1900 – July 22, 1959) was a Dutch mathematician, well known for the construction in topology of the solenoid. He was a member of the Significs Group. Biography Born to a Jewish family in Amsterdam in 1900, D ...
(Ph.D. Groningen 1931),
Herbert Seifert Herbert Karl Johannes Seifert (; 27 May 1907, Bernstadt – 1 October 1996, Heidelberg) was a German mathematician known for his work in topology. Biography Seifert was born in Bernstadt auf dem Eigen, but soon moved to Bautzen, where he atte ...
(Ph.D. Leipzig 1932), and Hans Richter (Ph.D. Leipzig 1936, co-advised by
Paul Koebe Paul Koebe (15 February 1882 – 6 August 1945) was a 20th-century German mathematician. His work dealt exclusively with the complex numbers, his most important results being on the uniformization of Riemann surfaces in a series of four papers in ...
).


See also

* Van der Waerden notation * Van der Waerden number *
Van der Waerden's conjecture In linear algebra, the permanent of a square matrix is a function of the matrix similar to the determinant. The permanent, as well as the determinant, is a polynomial in the entries of the matrix. Both are special cases of a more general function o ...
*
Van der Waerden's theorem Van der Waerden's theorem is a theorem in the branch of mathematics called Ramsey theory. Van der Waerden's theorem states that for any given positive integers ''r'' and ''k'', there is some number ''N'' such that if the integers are colored, eac ...
*
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 ...


Notes


References

*
Alexander Soifer Alexander Soifer is a Russian-born American mathematician and mathematics author. Soifer obtained his Ph.D. in 1973 and has been a professor of mathematics at the University of Colorado since 1979. He was visiting fellow at Princeton University ...
(2009), '' The Mathematical Coloring Book'', Springer-Verlag . 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 is a Russian-born American mathematician and mathematics author. Soifer obtained his Ph.D. in 1973 and has been a professor of mathematics at the University of Colorado since 1979. He was visiting fellow at Princeton University ...
''. * Alexander Soifer (2015) ''The Scholar and the State: In Search of Van der Waerden'',
Springer books Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...


Further reading

*Schlote, K.-H., 2005, "Moderne Algebra" in Grattan-Guinness, I., ed., ''Landmark Writings in Western Mathematics''. Elsevier: 901–16. * * * Freudenthal, H., 1962
"Review: B. L. van der Waerden, ''Science Awakening''"
in ''Bull. Amer. Math. Soc.'', 68 (6):543–45.


External links

* {{DEFAULTSORT:Waerden, Bartel Leendert Van Der 20th-century Dutch mathematicians 20th-century Dutch historians 1903 births 1996 deaths Algebraists Combinatorialists Historians of mathematics Academic staff of Leipzig University Members of the Royal Netherlands Academy of Arts and Sciences Recipients of the Pour le Mérite (civil class) Scientists from Amsterdam University of Amsterdam alumni Academic staff of the University of Amsterdam University of Göttingen alumni Academic staff of the University of Zurich Recipients of the Cothenius Medal