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Johann Benedict Listing (25 July 1808 – 24 December 1882) was a German mathematician. J. B. Listing was born in
Frankfurt Frankfurt, officially Frankfurt am Main (; Hessian dialects, Hessian: , "Franks, Frank ford (crossing), ford on the Main (river), Main"; french: Francfort-sur-le-Main), is the most populous city in the States of Germany, German state of Hess ...

Frankfurt
and died in
Göttingen Göttingen (, , ; nds, Chöttingen) is a university city in Lower Saxony Lower Saxony (german: Niedersachsen ; nds, Neddersassen; stq, Läichsaksen) is a German state The Federal Republic of Germany, as a federal state, consist ...
. He first introduced the term "
topology In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities ...

topology
" to replace the older term "geometria situs" (also called sometimes "Analysis situs"), in a famous article published in 1847, although he had used the term in correspondence some years earlier. He (independently) discovered the properties of the
half-twisted strip
half-twisted strip
at the same time (1858) as
August Ferdinand Möbius August Ferdinand Möbius (, ; ; 17 November 1790 – 26 September 1868) was a Germany, German mathematician and theoretical astronomer. Early life and education Möbius was born in Schulpforta, Saxony-Anhalt, and was descended on his ...

August Ferdinand Möbius
, 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., 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 Hilary Whitehall Putnam (; July 31, 1926 – March 13, 2016) was an American philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about Met ...

Hilary Putnam
, who discusses Listing numbers starting on page 99. It is currently difficult to find anything online about Listing number
except in connection with Peirce
In
ophthalmology Ophthalmology () is a branch of medicine and surgery that deals with the diagnosis and treatment of disorders of the eye. An ophthalmologist is a physician who Specialty (medicine), specializes in ophthalmology. The credentials include a degree i ...
,
Listing's lawListing's law, named after German mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical s ...
describes an essential element of extraocular eye muscle coordination. In
geodesy Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's geometric shape, orientation in space, and gravitational field. The field also incorporates studies of how these properties change over time and equivalent measu ...
, he coined in 1872 the term ''
geoid The geoid () is the shape that the ocean The ocean (also the or the world ocean) is the body of that covers approximately 70.8% of the surface of and contains 97% of . Another definition is "any of the large bodies of water into wh ...

geoid
'' for the idealized geometric surface of the figure of Earth.


External links

* *
reprint
of (part of) his famous 1847 article introducing
Topology In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities ...

Topology
, published in ''Vorstudien zur Topologie, Vandenhoeck und Ruprecht'', Göttingen, pp. 67, 1848.


Notes

1808 births 1882 deaths 19th-century German mathematicians Scientists from Frankfurt Topologists Fellows of the Royal Society of Edinburgh {{Germany-mathematician-stub