**Caspar Wessel** was a Norwegian mathematician who invented a geometric way of representing complex numbers which pre-dated Argand.

- Caspar could not attend university in Norway for, at that time, there were no Norwegian universities.
- Ole Christopher and Caspar were studying at the University of Copenhagen for a law degree.
- Ole Christopher started to work as a surveyor to help pay his way through university while Caspar was still at school.
- Throughout his life Wessel suffered financial hardship.
- Work which had originally been intended to provide Wessel with the financial support to complete his university course had become such a major undertaking that there was not enough time left for him to study.
- Wessel's sabbatical was granted and he was indeed able to complete his law degree.
- Such tasks required demanding mathematical skills and Wessel was an innovator in finding new methods and techniques.
- When he compiled reports on his work, Wessel appended short articles explaining the theoretical ideas behind the methods he was employing.
- In May 1782 Wessel was released from his work with the Royal Danish Academy so that he could conduct a trigonometrical survey of the duchy of Oldenburg.
- Wessel worked on the survey of Oldenburg until the summer of 1785 when he returned to his work with the Royal Danish Academy.
- This report already contains Wessel's brilliant mathematical innovation, namely the geometric interpretation of complex numbers.
- By 1796 Wessel had completed the triangulation of Denmark and used the data to produce the first really accurate map of the country.
- Only in the year before had the Academy relaxed its rule that all papers must be written by members of the Academy, and Wessel's paper was the first to be accepted which was not authored by a member.
- Wessel's fame as a mathematician rests solely on this paper, which was published in 1799, giving for the first time a geometrical interpretation of complex numbers.
- Today we call this geometric interpretation the Argand diagram but Wessel's work came first.
- It was so named before the world of mathematics learnt of Wessel's prior publication.
- Wessel's paper was not noticed by the mathematical community until 1895 when Juel draw attention to it and, in the same year, Sophus Lie republished Wessel's paper.
- Johannes Nikolaus Tetens was a professor of mathematics and philosophy at the University of Copenhagen near the end of the 18th century, and it was because of his encouragement that Wessel presented his paper to the Academy.
- Wessel, not being a member of the Academy, was not present when his paper was read.
- One can only suppose that, despite Tetens encouraging Wessel, he could not have realised its importance for otherwise he certainly could have translated it from Danish to German and thus ensured for Wessel the world-wide fame as a mathematician which he has not achieved until very recent times.
- Wessel's initial formulation was remarkably clear, direct, concise and modern.
- However more is claimed for Wessel's single mathematical paper than the first geometric interpretation of complex numbers.
- Again this shows the depth of Wessel's thinking but again, as the paper was unnoticed it had no influence on mathematical development despite appearing in the Mémoires of the Royal Danish Academy which by any standard was a major source of publications.
- In many ways Wessel was a remarkable person, and here we are not only referring to his mathematical brilliance.

Born 8 June 1745, Vestby (near Dröbak), Norway. Died 25 March 1818, Copenhagen, Denmark.

View full biography at MacTutor

Origin Norway

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive