Caspar Wessel

From Wikipedia, the free encyclopedia
Jump to: navigation, search
Caspar Wessel
Born (1745-06-08)June 8, 1745
Died March 25, 1818(1818-03-25) (aged 72)
Nationality  Danish
Fields Mathematics
Alma mater University of Copenhagen
Known for Complex numbers
Complex plane

Caspar Wessel (June 8, 1745, Vestby – March 25, 1818, Copenhagen) was a Norwegian-Danish mathematician and cartographer. In 1799, Wessel was the first person to describe the geometrical interpretation of complex numbers as points in the complex plane. He was the younger brother of poet and playwright Johan Herman Wessel.


Wessel was born in Jonsrud, Vestby, Akershus, Norway. In 1763, having completed secondary school at Oslo Cathedral School, he went to Denmark for further studies. He attended the University of Copenhagen and acquired the degree of candidatus juris in 1778. From 1794, however, he was employed as a surveyor (from 1798 as Royal inspector of Surveying).

It was the mathematical aspect of surveying that led him to exploring the geometrical significance of complex numbers. His fundamental paper, Om directionens analytiske betegning, was published in 1797 by the Royal Danish Academy of Sciences and Letters. Since it was in Danish, it passed almost unnoticed, and the same results were later independently rediscovered by Argand in 1806 and Gauss in 1831.

One of the more prominent ideas presented in "On the Analytical Representation of Direction" was that of vectors. Even though this was not Wessel's main intention with the publication, he felt that a geometrical concept of numbers, with length and direction, was needed. Wessel's approach on addition was: "Two straight lines are added if we unite them in such a way that the second line begins where the first one ends and then pass a straight line from the first to the last point of the united lines. This line is the sum of the united lines". This is the same idea as used today when summing vectors.

Wessel's priority to the idea of a complex number as a point in the complex plane is today universally recognised. His paper was re-issued in French translation in 1899, and in English in 1999 as On the analytic representation of direction (ed. J. Lützen et al.).

Wessel's elder brother Johan Herman Wessel was a major name in Danish-Norwegian literature.

Further reading[edit]

  • Brun, Viggo (1962). Regnekunsten i det gamle Norge. Oslo: Universitetsforlaget. pp. 97–111. 

External links[edit]