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Bartel Leendert van der Waerden

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2 Feb 1903

Amsterdam, Netherlands

12 Jan 1996

Zurich, Switzerland

As a school pupil B L van der Waerden showed remarkable promise and he developed for himself the laws of trigonometry. He studied mathematics at the universities of Amsterdam and Göttingen from 1919 until 1925.

The year 1924 he spent in Göttingen studying with Emmy Noether . His doctorate, supervised by Hendrik de Vries, was awarded by Amsterdam for a thesis on the foundations of algebraic geometry . In 1928 he received his habilitation from Göttingen.

The year 1928 was a busy one for van der Waerden. He received a position at the University of Rostock but was appointed to a lectureship at Groningen in the same year. In 1931 he was appointed professor of mathematics at the University of Leipzig where he became a colleague of Heisenberg .

Before and after World War II van der Waerden had problems as a foreigner from the Nazis. Although working in Germany he refused to give up his Dutch citizenship and his life was made difficult.

After the War van der Waerden worked for Shell in Amsterdam in applied mathematics. In 1947 he visited the USA going to Johns Hopkins University. He returned in 1948 to a chair of mathematics at Amsterdam where he remained until 1951. In 1950 Karl Fueter died and van der Waerden was appointed to fill the vacant chair in Zurich in 1951.

His impact on the department in Zurich was very great. As well as an almost unbelievable range of mathematical research interests, van der Waerden stimulated research in Zurich by supervising over 40 doctoral students during his years there. In fact van der Waerden was to remain in Zurich for the rest of his life.

Van der Waerden worked on algebraic geometry, abstract algebra, groups , topology , number theory , geometry, combinatorics, analysis, probability theory , mathematical statistics, quantum mechanics , the history of mathematics, the history of modern physics, the history of astronomy and the history of ancient science.

In algebraic geometry van der Waerden defined precisely the notions of dimension of an algebraic variety, a concept intuitively defined before. His work in algebraic geometry uses the ideal theory in polynomial rings created by Artin , Hilbert and Emmy Noether . His work also makes considerable use of the algebraic theory of fields.

Van der Waerden's most famous work is Algebra published in 1930. This two volume work reports on the algebra developed by Emmy Noether , Hilbert , Dedekind and Artin .

In Galois theory he showed the asymptotic result that almost all integral algebraic equations have the full symmetric group as Galois group. He produced results in invariant theory , linear groups , Lie groups and generalised some of Emmy Noether 's results on rings.

In group theory he studied the Burnside groups B(3, r) with r generators and exponent 3. These are solutions of the Burnside problem . These groups were shown to be finite by Burnside . In 1933 van der Waerden found the exact order and structure of the groups B(3, r). He showed that the order of B(3, r) is 3N(r) where the exponent

N(r) = r + r(r-1)/2 + r(r-1)(r-2)/6.

Among his many historical books are Ontwakende wetenschap (1950) translated into English as Science Awakening (1954), Geometry and Algebra in Ancient Civilizations (1983) and A History of Algebra (1985). The history of mathematics was not a topic he just turned to late in life: his important paper Die Arithmetik der Pythagoreer appeared in 1947.

Source:School of Mathematics and Statistics University of St Andrews, Scotland