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, structure, space, models, and change. History On ...

and

historian of mathematics The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments ...

Biography

Education and early career

Van der Waerden learned advanced mathematics at the

University of Amsterdam The University of Amsterdam (abbreviated as UvA, nl, Universiteit van Amsterdam) is a public research university located in Amsterdam, Netherlands. The UvA is one of two large, publicly funded research universities in the city, the other being ...

and the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...

, from 1919 until 1926. He was much influenced by

Emmy Noether Amalie Emmy NoetherEmmy is the ''Rufname'', the second of two official given names, intended for daily use. Cf. for example the résumé submitted by Noether to Erlangen University in 1907 (Erlangen University archive, ''Promotionsakt Emmy Noethe ...

Göttingen Göttingen (, , ; nds, Chöttingen) 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. At the end of 2019, t ...

Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...

. Amsterdam awarded him a Ph.D. for a thesis on

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

, 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 many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ...

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; nl, Rijksuniversiteit Groningen, 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 in ...

. In his 27th year, 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'', th ...

'', an influential two-volume treatise on

abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''a ...

, still cited, and perhaps the first treatise to treat the subject as a comprehensive whole. This work systematized an ample body of research by

David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...

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. His ...

, and

Emil Artin Emil Artin (; March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent. Artin was one of the leading mathematicians of the twentieth century. He is best known for his work on algebraic number theory, contributing lar ...

. In the following year, 1931, he was appointed professor at the

University of Leipzig Leipzig University (german: Universität Leipzig), 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 Decemb ...

. 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 different ...

, Camilla Juliana Anna, and they had three children.

Nazi Germany

After the

Nazis Nazism ( ; german: Nazismus), the common name in English for National Socialism (german: Nationalsozialismus, ), is the far-right totalitarian political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Na ...

seized power, and through

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

, Van der Waerden remained at Leipzig, and passed up opportunities to leave Nazi Germany for

Princeton Princeton University is a private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the ni ...

and

Utrecht Utrecht ( , , ) is the List of cities in the Netherlands by province, fourth-largest city and a List of municipalities of the Netherlands, municipality of the Netherlands, capital and most populous city of the Provinces of the Netherlands, pro ...

. 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 German state of Saxony. Leipzig's population of 605,407 inhabitants (1.1 million in the larger urban zone) as of 2021 places the city as Germany's eighth most populous, as wel ...

(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 'beer brewer'. Brouwer * Adriaen Brouwer (1605–1638), Flemish painter * Alexander Brouwer (b. 1989), Dutch beach volleyball player * Andries Bro ...

's opposition to Hilbert's school of mathematics. After a year visiting

Johns Hopkins University Johns Hopkins University (Johns Hopkins, Hopkins, or JHU) is a private university, private research university in Baltimore, Maryland. Founded in 1876, Johns Hopkins is the oldest research university in the United States and in the western hem ...

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 Zürich (UZH, german: Universität Zürich) is a public research university located in the city of Zürich, Switzerland. It is the largest university in Switzerland, with its 28,000 enrolled students. It was founded in 1833 f ...

, 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 ( nl, Koninklijke Nederlandse Akademie van Wetenschappen, abbreviated: KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed ...

, in 1951 this was changed to a foreign membership. In 1973 he received the ''

Pour le Mérite The ' (; , ) is an order of merit (german: Verdienstorden) established in 1740 by Frederick the Great, King Frederick II of Prussia. The was awarded as both a military and civil honour and ranked, along with the Order of the Black Eagle, the Or ...

''.

Contributions

Van der Waerden is mainly remembered for his work on

. He also wrote on

topology In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...

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 the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

and

statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, and

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

(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 mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments ...

and

science Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence for ...

. 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 dyadic solenoid. He was a member of the Significs Group. Biography Born to a Jewish family in Amsterdam in ...

(Ph.D. Groningen 1931),

Herbert Seifert Herbert Karl Johannes Seifert (; 27 May 1897, 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 attend ...

(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 ...

Notes

References

* Alexander Soifer (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. His works include over 400 articles and 13 books. Soifer obtained his Ph.D. in 1973 and has been a professor of mathematics at the University of Colorado since 197 ...

''. * Alexander Soifer (2015) ''The Scholar and the State: In Search of Van der Waerden'', Springer books

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 Leipzig University faculty 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 University of Amsterdam faculty University of Göttingen alumni University of Zurich faculty