Caspar Wessel | Biography

Casper Wesselmade a significant contribution to mathematics, but his legacy is to be a footnote in histories of other great mathematicians. Karl Friedrich Gauss and Jean Robert Argand are most often given credit for expressing complex numbersas geometric shapes, but it was an idea that Wessel, a surveyor and map-maker, was first to develop. Because he was not a professional mathematician and made no great effort to publish his one breakthrough paper, it went largely unknown for a century.

Wessel was born on June 8, 1745, in Jonsrud in Akershus county, Norway (then part of Denmark), to Jonas Wessel, a church vicar, and Maria Schumacher, his wife. He attended the Christiania Cathedral School in Oslo from 1757 to 1763 and then spent a year at the University of Copenhagen. Wessel's career in cartography, or map-making, began in 1764, when he became an assistant to the Danish Survey Commission soon after leaving the University of Copenhagen. He earned a law degree in 1778 and rose to survey superintendent in 1798.

In 1797, Wessel published a little-noticed paper on the geometric representation of complex numbers, which he presented to the Royal Danish Academy of Sciences. Gauss reportedly had been working on the problem as early as 1799, but did not publish the idea until 1831. Argand, a bookkeeper, published the concept in 1806, and that work became very influential, hence many refer to a plane of complex numbers as the Argand planeor an Argand diagram. "And yet [Wessel's] exposition was, in some respects, superior to and more modern in spirit than Argand's," writes Phillip S. Jones in the Dictionary of Scientific Biography. Wessel's work lay forgotten for 98 years and was republished in French on the 100th anniversary of the original publication. "It is regrettable that it was not appreciated for nearly a century and hence did not have the influence it merited," writes Jones. Biographical information about Wessel is also lacking, as he had been deceased 79 years before his achievement was recognized.

Graphical representation of complex numbers is a key mathematical component of contemporary computer graphicsand was a major breakthrough for mathematicians grappling with understanding higher concepts. "The simple idea of considering the real and imaginary parts of a complex number a + bi as the rectangular coordinates of a point in a plane made mathematicians feel much more at ease with imaginary numbers," Howard Eves wrote in An Introduction to the History of Mathematics. "Seeing is believing, and former ideas about the nonexistence or fictitiousness of imaginary numbers were generally abandoned."

Some scholars also credit Wessel with advancing the idea of adding vectors in a three-dimensional space, a basic concept in modern physics. The mapmaker realized that nonparallel vectors could be added together by laying the terminal end of one line at the beginning of a second, and then summing them by drawing a line from the beginning of the first vector to the end of the second.

Although he is now best known for the work on complex numbers, Wessel was actually quite famous in his day as a geographer. His work as a surveyor was so highly regarded that he was awarded a medal by the Royal Danish Academy of Sciences and was knighted in Danebrog in 1815. He had retired in 1805, but continued working until 1812, when his rheumatism became too severe. Wessel died on March 25, 1818, in Copenhagen, Denmark.