Johann Benedict Listing


Born: 25 July 1808 in Frankfurt am Main, Germany
Died: 24 December 1882 in Göttingen, Germany


Johann Benedict Listing's family were of Czech descent. His father, also named Johann Benedict Listing, was a maker of brushes while his mother, Caroline Friederike Listing, came from a poor peasant background. Listing was an only child and brought up in a family which struggled with financial difficulty.

He was a bright boy and his talents were such that he received help with his education from several benefactors including the Städel foundation, supporters of art and museums. He received a good foundation for his education at the Musterschule which he attended from the age of eight. In this school he first became interested in science and mathematics, mainly because of his talented teacher Müller, but he had a real talent for art. Listing pleased his parents by helping out with the family's finances by earning a little money from drawing and calligraphy from the age of thirteen.

In 1825 Listing entered a Gymnasium where he studied for five years. He mastered English, French, Italian and Latin and well as increasing his knowledge of mathematics and science at this school. He had already decided to pursue an academic career and his talents were recognised by the award of a generous scholarship by the Städel foundation. 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. In addition to these two topics he also took courses on astronomy, anatomy, physiology, botany, mineralogy, geology and chemistry. 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. Gauss invited him to join his circle of friends who included Weber.

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. He also was a talented experimenter and collaborated with Gauss in physics experiments, particularly those relating to terrestrial magnetism. Gauss became the supervisor of Listing's dissertation De superficiebus secundi ordinis which was on surfaces of the second degree and ternary forms. He received his doctorate in June 1834.

Walterhausen was setting out on a trip to Sicily to study volcanoes. He had also agreed to collect data on terrestrial magnetism for Gauss on this trip. 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. He worked in his spare time on mathematics, in particular working on the topological ideas which had first been suggested by Gauss. He decided to summarise his thoughts on the topic and did so in a long letter to his old school teacher Müller. It is in this letter that the word "topology" appears for the first time. He disliked the term "geometria situs", then used for topological ideas, and [4]:-

The entire doctrine being rather new, he felt justified to give it a new name and therefore called it "topology", which he though more appropriate.

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. Without saying yes or no he politely thanked them for the offer. Because of a cholera epidemic Sartorius and Listing delayed their return to Göttingen. In fact they took a ship to England where they spent a short while before returning to Germany. Listing went to Hannover to be interviewed for the post in the Gewerbeschule and was appointed, starting his teaching career in November 1837.

When Victoria became Queen of Britain in 1837 her uncle became ruler of Hanover and revoked the liberal constitution. Weber, the professor of physics at Göttingen and a close collaborator of Gauss, was one of seven professors at the university to sign a protest and all seven were dismissed. Weber remained at Göttingen without a position until 1843. However his professorship of physics had to be filled and after a while Gauss was asked to suggest possible candidates. 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. A versatile scientist, he chose yet another area to the ones which he had already worked in, and began to study the optics of the human eye. He published Beiträge zur physiologischen Optik in 1845 which became a classic. As well as containing data from careful experimental work, the book was beautifully illustrated by Listing using all his skills in drawing and calligraphy.

In September 1846 Listing married Pauline Elvers. Almost immediately the couple were in financial problems as Pauline seemed unable to keep her spending within the family's income.

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. The subject was known as analysis situs for many years and only in the late 1920s was the English word topology used by Lefschetz. In this book, really an extended essay meant only, as the title states, as a preliminary work, Listing writes:-

By topology we mean the doctrine of the modal features of objects, or of the laws of connection, of relative position and of succession of points, lines, surfaces, bodies and their parts, or aggregates in space, always without regard to matters of measure or quantity.

In 1848 the revolution which swept Europe had its consequences. The most marked effect was that Weber was reappointed to the chair at Göttingen which he had lost ten years before. 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.

However, Listing's family life did not go well. The couple had two daughters - one in 1848 and the second in the following year. However Pauline Listing's [4]:-

... treatment of servants brought her before the magistrates any number of times, while her relations with landlords led to many moves for the family.

Neither Listing nor his wife seemed capable of managing the family finances [4]:-

Listing borrowed frequently and heavily, sometimes from usurers; Pauline habitually abused credit, and again ended up in court with some regularity. They tended to live beyond their means, and on one occasion barely avoided bankruptcy.

The near bankruptcy came around the time that Listing was publishing another remarkable contribution to topology. In 1858 he had discovered the properties of the Möbius band at almost the same time, and independently of, Möbius. In 1862 he published Der Census raumlicher Complexe oder Verallgemeinerung des Euler'schen Satzes von den Polyedern which discusses extensions of Euler's formula for the Euler characteristic of oriented three-dimensional polyhedra to the case of certain four-dimensional simplicial complexes. This second work on topology by Listing is discussed by detail in [8] where Tripodi compares it with some work by Cayley.

In fact bankruptcy was avoided due to the ministry in Hannover saving him. 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. However, Listing did not find favour with his colleagues because of the behaviour of himself and his wife and it is certain that he received less recognition for his scientific achievements because of it. Yet he was [4]:-

... industrious and inquisitive, kind and helpful, gregarious and witty, good-natured to a degree, a true friend to many, and an enemy to none.

The range of contributions made by Listing is quite remarkable. Breitenberger in [4] writes:-

... he studied the figure of the earth in minute detail; he made observations in meteorology, terrestrial magnetism, and spectroscopy; he wrote on the quantitative determination of sugar in the urine of diabetics; he promoted the nascent optical industry in Germany and better street lighting in Göttingen; he travelled to the world exhibitions in London 1851, Vienna 1873 and London 1876 as an observer for his government; he assisted in geodetic surveys; ... he invented a good many terms [other than topology], some of which have became current: "entropic phenomenona", "nodal points", "homocentric light", "telescopic system", " geoid" ...he coined "one micron" for the millionth of a metre ...

Among the honours which Listing did receive were election to the Göttingen Academy and the Royal Society of Edinburgh. He was awarded an honorary doctorate by Tübingen.

He died of a stroke.

Article by: J J O'Connor and E F Robertson

September 2000


MacTutor History of Mathematics
[http://www-history.mcs.st-andrews.ac.uk/Biographies/Listing.html]