Egbert Rudolf van Kampen (28 May 1908, Berchem

Berchem

The 'Ring', Antwerp's circular motorway which follows the track of the former city defense walls, cuts Berchem in two parts, separating the urban inner city area of Oud-Berchem from the more residential and suburban areas Groenenhoek en Nieuw Kwartier .-Demography:Berchem's total surface is over ,...

, Belgium

Belgium

Belgium , officially the Kingdom of Belgium, is a federal state in Western Europe. It is a founding member of the European Union and hosts the EU's headquarters, and those of several other major international organisations such as NATO.Belgium is also a member of, or affiliated to, many...

 – 11 February 1942, Baltimore

Baltimore

Baltimore is the largest independent city in the United States and the largest city and cultural center of the US state of Maryland. The city is located in central Maryland along the tidal portion of the Patapsco River, an arm of the Chesapeake Bay. Baltimore is sometimes referred to as Baltimore...

, Maryland

Maryland

Maryland is a U.S. state located in the Mid Atlantic region of the United States, bordering Virginia, West Virginia, and the District of Columbia to its south and west; Pennsylvania to its north; and Delaware to its east...

) was a mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

. He made important contributions to 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...

, especially to the study of fundamental groups

Fundamental group

In mathematics, more specifically algebraic topology, the fundamental group is a group associated to any given pointed topological space that provides a way of determining when two paths, starting and ending at a fixed base point, can be continuously deformed into each other...

.

Van Kampen received his Ph.D. degree from Leiden University

Leiden University

Leiden University , located in the city of Leiden, is the oldest university in the Netherlands. The university was founded in 1575 by William, Prince of Orange, leader of the Dutch Revolt in the Eighty Years' War. The royal Dutch House of Orange-Nassau and Leiden University still have a close...

 in 1929. His dissertation, entitled Die kombinatorische Topologie und die Dualitaetssaetze, was written under the direction of Willem van der Woude.

In 1931 van Kampen left Europe

Europe

Europe is, by convention, one of the world's seven continents. Comprising the westernmost peninsula of Eurasia, Europe is generally 'divided' from Asia to its east by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas, and the waterways connecting...

 and travelled to the United States

United States

The United States of America is a federal constitutional republic comprising fifty states and a federal district...

 to take up the position which he had been offered at 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...

 in Baltimore, Maryland. There he met Oscar Zariski

Oscar Zariski

Oscar Zariski was a Russian mathematician and one of the most influential algebraic geometers of the 20th century.-Education:...

 who had taught at Johns Hopkins University as a Johnston Scholar from 1927 until 1929 when he had joined the Faculty. Zariski had been working on the fundamental group of the complement

Complement (set theory)

In set theory, a complement of a set A refers to things not in , A. The relative complement of A with respect to a set B, is the set of elements in B but not in A...

 of an algebraic curve

Algebraic curve

In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with circles and other conic sections.- Plane algebraic curves...

, and he had found generators and relations for the fundamental group but was unable to show that he had found sufficient relations to give a presentation

Presentation of a group

In mathematics, one method of defining a group is by a presentation. One specifies a set S of generators so that every element of the group can be written as a product of powers of some of these generators, and a set R of relations among those generators...

 for the group. Van Kampen solved the problem, showing that Zariski's relations were sufficient, and the result is now known as the Zariski–van Kampen theorem. This led van Kampen to formulate and prove what is nowadays known as the Seifert–van Kampen theorem

Seifert–van Kampen theorem

In mathematics, the Seifert-van Kampen theorem of algebraic topology, sometimes just called van Kampen's theorem, expresses the structure of the fundamental group of a topological space X, in terms of the fundamental groups of two open, path-connected subspaces U and V that cover X...

.

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