Person: Listing, Johann Benedict
Johann Listing wrote one of the earliest texts on Topology.
Mathematical Profile (Excerpt):
- In 1825 Listing entered a Gymnasium where he studied for five years.
- Being an art foundation they could not support Listing to undertake a degree in mathematics, which would have been his preferred option, but instead awarded him the scholarship for the study of mathematics and architecture.
- Although there was a time when architecture was considered as a branch of mathematics, it certainly was not considered such in Listing's day so the combination was a rather peculiar one dictated by a compromise between Listing's wishes and the remit of the Städel foundation.
- Listing entered Göttingen University in 1830 and attended a remarkably broad range of courses, much broader than the mathematics and architecture specified by his scholarship.
- Soon Listing was attending mathematics courses given by Gauss and he was quickly spotted by Gauss as being both a very able and a very hard working student.
- Listing was not the only student invited into close friendship with Gauss.
- Another student was Sartorius von Walterhausen who was one year younger than Listing.
- Walterhausen, who was interested in geology, became a lifelong friend of Listing.
- The influence of Gauss on Listing was, however, very marked.
- It was from Gauss that Listing began to learn topological concepts.
- Gauss became the supervisor of Listing's dissertation De superficiebus secundi ordinis Ⓣ(Surfaces of the second order) which was on surfaces of the second degree and ternary forms.
- Listing was an obvious choice for an assistant to accompany him and the pair set off less than a month after Listing had obtained his doctorate.
- It was a journey on which Listing maintained his interests in many different topics and as well as the geology and physics which were the purpose of the trip.
- While on his travels Listing was approached by the Höhere Gewerbeschule Hannover asking if he would be interested in a post as a teacher of applied mathematics.
- Because of a cholera epidemic Sartorius and Listing delayed their return to Göttingen.
- Listing went to Hannover to be interviewed for the post in the Gewerbeschule and was appointed, starting his teaching career in November 1837.
- He produced a list of three names with Listing in third place.
- When the first two turned down the offer, Listing was appointed in 1839 despite never having published a paper.
- As professor of physics Listing could choose his area for research.
- As well as containing data from careful experimental work, the book was beautifully illustrated by Listing using all his skills in drawing and calligraphy.
- Listing continued to think about topological ideas, however, and he wrote the book Vorstudien zur Topologie in 1847.
- It was the first published use of the word topology although, as we mentioned above, it was first used in Listing's letter of 1836.
- Of course Listing had been appointed to fill Weber's chair so a compromise had to be reached.
- This was that Listing was promoted to ordinary professor of mathematical physics while Weber became professor of experimental physics.
- Although little changed in the research that Listing undertook, since he had always gone in the direction which interested him, he did have to give up a large part of his laboratory to Weber.
- The near bankruptcy came around the time that Listing was publishing another remarkable contribution to topology.
- It was Sartorius who had arranged for the rescue act by the ministry and here he was repaying a debt to Listing who had saved his life by nursing him through a serious illness during their journey of nearly thirty years earlier.
- The range of contributions made by Listing is quite remarkable.
- Among the honours which Listing did receive were election to the Göttingen Academy and the Royal Society of Edinburgh.
Born 25 July 1808, Frankfurt am Main, Germany. Died 24 December 1882, Göttingen, Germany.
View full biography at MacTutor
Tags relevant for this person:
Knot Theory, Origin Germany, Physics, Topology
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive