He was born in Jonsrud, Vestby, Akershus, Norway. In 1763, having completed secondary school, he went to Denmark for further studies (since Norway didn't have any university in 1763). In 1778 he acquired got degree of candidatus juris. In 1794 he was hired as a surveyor; in 1798, a Royal inspector of Surveying.
As surveying is related to mathematics, he later studied the geometrical importance of complex numbers. His most important paper, Om directionens analytiske betegning, (On the Analytical Representation of Direction) was published in 1799 by the Royal Danish Academy of Sciences and Letters. Since it was in Danish, it was not noticed by many people. Later, Jean-Robert Argand and Carl Friedrich Gauss's paper showed the same results.
One of the more important, but missed ideas shown in Wessel's Om directionens analytiske betegning was vectors. Wessel's main thing he wanted to show in the paper was not this, but he felt that the concept of numbers, with length and direction would be needed. Wessel's thoughts 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". Today, the same idea is used when adding vectors.
Johan Herman Wessel, Wessel's brother was a famous person in Danish-Norwegian books.
- "Wolfram|Alpha: Caspar Wessel : birth date, death date, birth place, ...". 14 July 2010. http://www.wolframalpha.com/entities/people/caspar_wessel/uf/n1/x7/. Retrieved 25 April 2011.
- "Wessel biography". February 2000. http://www-history.mcs.st-and.ac.uk/Biographies/Wessel.html. Retrieved 25 April 2011.