Johann Benedict Listing
Johann Benedict Listing | |
|---|---|
Listing, c. 1860 | |
| Born | 25 July 1808 |
| Died | 24 December 1882 (aged 74) |
| Alma mater | University of Göttingen |
| Known for | Back-and-forth method Listing number Listing's knot Listing's law |
| Scientific career | |
| Fields | Mathematics |
| Doctoral advisor | Carl Friedrich Gauss |
| Doctoral students | Edward Leamington Nichols |
Johann Benedict Listing (25 July 1808 – 24 December 1882) was a German mathematician and physicist. He is remembered as a pioneer of topology, which also takes its name from his work.
Early life and education
J. B. Listing was born in Frankfurt and died in Göttingen. He studied mathematics and architecture at the University of Göttingen, but his interests extended more broadly to topics such as terrestrial magnetism and physiological optics. In 1834 he received his doctorate under Carl Friedrich Gauss.[1] He then spent three years traveling with Wolfgang Sartorius von Waltershausen to study the volcanic activity of Mount Etna in Sicily.
Career
In 1837 Listing became a teacher of machine drawing, machine theory, and applied mathematics at the Höhere Gewerbeschule in Hanover. Two years later, in 1839, he was appointed professor of physics as the successor to Wilhelm Eduard Weber, and in 1849 he became professor of mathematics in Göttingen. Together with his friend, the ophthalmologist Christian Georg Theodor Ruete,[2] he researched the laws of eye movement.
Encouraged by his mentor, Gauss, Listing began to specialize in topology, then known as analysis situs. In 1847 he published Vorstudien zur Topologie (Preliminary Studies in Topology), although he had already used the term “topology” in letters a decade earlier.[3] This book helped introduce the term into general use. Independently of August Ferdinand Möbius, Listing also discovered the special properties of the Möbius strip in 1858 and went further in exploring the properties of strips with higher-order twists (paradromic rings). He discovered topological invariants which came to be called Listing numbers.[4]
In ophthalmology, Listing's law describes an essential element of extraocular eye muscle coordination.
In geodesy, he coined in 1872 the term "geoid" for the idealized geometric surface of the figure of the Earth, as previously conceptualized by his doctoral adviser, Gauss.[5]
Listing was elected a member of the Göttingen Academy of Sciences in 1861 and became an Honorary Fellow of the Royal Society of Edinburgh in 1879.[6]
Personal life
Listing's granddaughter was British War Artist Anna Airy, by his younger daughter Anna.[7]
References
- ^ Johann Benedict Listing at the Mathematics Genealogy Project
- ^ Jaeger, Wolfgang (1978). Die Erfindung der Ophthalmoskopie, dargestellt in den Originalbeschreibungen der Augenspiegel von Helmholtz, Ruete und Giraud-Teulon (in German). Springer. ISBN 978-3-540-08699-4. Retrieved 17 September 2025.
- ^ "Johann Benedict Listing – Biography". Maths History. Retrieved 24 December 2021.
- ^ Peirce, C. S., 1992, Reasoning and the Logic of Things: The Cambridge Conference Lectures of 1898, edited with introduction by Kenneth Laine Ketner and with commentary by Hilary Putnam, who discusses Listing numbers starting on page 99. It is currently difficult to find anything online about Listing numbers except in connection with Peirce.
- ^ Listing, Johann Benedict (1872). Über unsere jetzige Kenntniss der Gestalt und Grösse der Erde: Aus den Nachrichten der K. Ges. der Wiss (in German). Göttingen: Dieterich. Retrieved 6 July 2021.
- ^ "Fellows Directory. Biographical Index: Former RSE Fellows 1783–2002" (PDF). Royal Society of Edinburgh. Archived from the original (PDF) on 18 September 2020. Retrieved 17 September 2025.
- ^ "Suffolk Artists - AIRY, Anna". suffolkartists.co.uk. Retrieved 4 March 2025.
External links
- O'Connor, John J.; Robertson, Edmund F., "Johann Benedict Listing", MacTutor History of Mathematics Archive, University of St Andrews
- A reprint of (part of) his famous 1847 article introducing Topology, published in Vorstudien zur Topologie, Vandenhoeck und Ruprecht, Göttingen, pp. 67, 1848.