Bartel Leendert van der Waerden
Encyclopedia
Bartel Leendert van der Waerden (February 2, 1903, Amsterdam
, Netherlands
– January 12, 1996, Zürich
, Switzerland
) was a Dutch
mathematician
and historian of mathematics
.
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. Amsterdam awarded him a Ph.D. for a thesis on algebraic geometry
, supervised by Hendrick de Vries. Göttingen awarded him the habilitation
in 1928.
In his 27th year, van der Waerden published his 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
.
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. Following the war, he was repatriated to the Netherlands rather than returning to Leipzig (then under Russian 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. 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), Geometry and Algebra in Ancient Civilizations (1983), and A History of Algebra (1985).
Amsterdam
Amsterdam is the largest city and the capital of the Netherlands. The current position of Amsterdam as capital city of the Kingdom of the Netherlands is governed by the constitution of August 24, 1815 and its successors. Amsterdam has a population of 783,364 within city limits, an urban population...
, Netherlands
Netherlands
The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...
– January 12, 1996, Zürich
Zürich
Zurich is the largest city in Switzerland and the capital of the canton of Zurich. It is located in central Switzerland at the northwestern tip of Lake Zurich...
, Switzerland
Switzerland
Switzerland name of one of the Swiss cantons. ; ; ; or ), in its full name the Swiss Confederation , is a federal republic consisting of 26 cantons, with Bern as the seat of the federal authorities. The country is situated in Western Europe,Or Central Europe depending on the definition....
) was a Dutch
Netherlands
The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...
mathematician
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and historian of mathematics
History of mathematics
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past....
.
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
Emmy Noether
Amalie Emmy Noether was an influential German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Described by David Hilbert, Albert Einstein and others as the most important woman in the history of mathematics, she revolutionized the theories of...
at Göttingen. Amsterdam awarded him a Ph.D. for a thesis on algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, supervised by Hendrick de Vries. Göttingen awarded him the habilitation
Habilitation
Habilitation is the highest academic qualification a scholar can achieve by his or her own pursuit in several European and Asian countries. Earned after obtaining a research doctorate, such as a PhD, habilitation requires the candidate to write a professorial thesis based on independent...
in 1928.
In his 27th year, van der Waerden published his Algebra, an influential two-volume treatise on abstract algebra
Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...
, 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
Emmy Noether
Amalie Emmy Noether was an influential German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Described by David Hilbert, Albert Einstein and others as the most important woman in the history of mathematics, she revolutionized the theories of...
, David Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
, Richard Dedekind
Richard Dedekind
Julius Wilhelm Richard Dedekind was a German mathematician who did important work in abstract algebra , algebraic number theory and the foundations of the real numbers.-Life:...
, and Emil Artin
Emil Artin
Emil Artin was an Austrian-American mathematician of Armenian descent.-Parents:Emil Artin was born in Vienna to parents Emma Maria, née Laura , a soubrette on the operetta stages of Austria and Germany, and Emil Hadochadus Maria Artin, Austrian-born of Armenian descent...
. In the following year, 1931, he was appointed professor at the University of Leipzig
University of Leipzig
The University of Leipzig , located in Leipzig in the Free State of Saxony, Germany, is one of the oldest universities in the world and the second-oldest university in Germany...
.
During the rise of the Third Reich and through World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, van der Waerden remained at Leipzig, and passed up opportunities to leave Nazi Germany for Princeton
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
and Utrecht
Utrecht University
Utrecht University is a university in Utrecht, Netherlands. It is one of the oldest universities in the Netherlands and one of the largest in Europe. Established March 26, 1636, it had an enrollment of 29,082 students in 2008, and employed 8,614 faculty and staff, 570 of which are full professors....
. However, he was critical of the Nazis and refused to give up his Dutch nationality, both of which led to difficulties for him. Following the war, he was repatriated to the Netherlands rather than returning to Leipzig (then under Russian 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
Luitzen Egbertus Jan Brouwer
Luitzen Egbertus Jan Brouwer FRS , usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, a graduate of the University of Amsterdam, who worked in topology, set theory, measure theory and complex analysis.-Biography:Early in his career,...
's opposition to Hilbert's school of mathematics. After a year visiting Johns Hopkins University
Johns Hopkins University
The Johns Hopkins University, commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States...
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
University of Zurich
The University of Zurich , located in the city of Zurich, is the largest university in Switzerland, with over 25,000 students. It was founded in 1833 from the existing colleges of theology, law, medicine and a new faculty of philosophy....
, 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
Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...
. He also wrote on algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
, number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
, analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
, probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
and statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, and quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
(he and Heisenberg had been colleagues at Leipzig). In his later years, he turned to the history of mathematics
History of mathematics
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past....
and science
History of science
The history of science is the study of the historical development of human understandings of the natural world and the domains of the social sciences....
. His historical writings include Ontwakende wetenschap (1950), which was translated into English as Science Awakening (1954), Geometry and Algebra in Ancient Civilizations (1983), and A History of Algebra (1985).
See also
- Van der Waerden's theorem
- Van der Waerden number
- Van der Waerden testVan der Waerden testNamed for 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...
- Van der Waerden notationVan der Waerden notationIn theoretical physics, van der Waerden notation refers to the usage of two-component spinors in four spacetime dimensions. This is standard in twistor theory and supersymmetry....
- Van der Waerden's conjecture
Additional reading
- Schlote, K.-H., 2005, "Moderne Algebra" in Grattan-Guinness, I.Ivor Grattan-GuinnessIvor Grattan-Guinness, born 23 June 1941, in Bakewell, in England, is a historian of mathematics and logic.He gained his Bachelor degree as a Mathematics Scholar at Wadham College, Oxford, got an M.Sc in Mathematical Logic and the Philosophy of Science at the London School of Economics in 1966...
, ed., Landmark Writings in Western Mathematics. Elsevier: 901–16. - An interview with van der Waerden, published after his death.
- A Review of: B. L. van der Waerden, Science awakening, by Hans FreudenthalHans FreudenthalHans Freudenthal was a Dutch mathematician. He made substantial contributions to algebraic topology and also took an interest in literature, philosophy, history and mathematics education....
in Bull. Amer. Math. Soc., Vol. 68, Number 6 (1962), 543–545. http://projecteuclid.org/euclid.bams/1183524913