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: , " Frank ford on the Main"), is the most populous city in the German state of Hesse. Its 791,000 inhabitants as of 2022 make it the fifth-most populous city in Germany. Located on it ...
and died in
Göttingen
Göttingen (, , ; nds, Chöttingen) is a university city in Lower Saxony, central Germany, the capital of the eponymous district. The River Leine runs through it. At the end of 2019, the population was 118,911.
General information
The ori ...
. He first introduced the term "
topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
" 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 at the same time (1858) as
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.
[ 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
Hilary Whitehall Putnam (; July 31, 1926 – March 13, 2016) was an American philosopher, mathematician, and computer scientist, and a major figure in analytic philosophy in the second half of the 20th century. He made significant contributions ...
, 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 surgical subspecialty within medicine that deals with the diagnosis and treatment of eye disorders.
An ophthalmologist is a physician who undergoes subspecialty training in medical and surgical eye care. Following a me ...
,
Listing's law Listing's law, named after German mathematician Johann Benedict Listing (1808–1882), describes the three-dimensional orientation of the eye and its axes of rotation. Listing's law has been shown to hold when the head is stationary and upright a ...
describes an essential element of extraocular eye muscle coordination.
In
geodesy
Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equival ...
, he coined in 1872 the term ''
geoid'' for the idealized geometric surface of the
figure of Earth.
References
External links
*
*
reprintof (part of) his famous 1847 article introducing
Topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
, published in ''Vorstudien zur Topologie, Vandenhoeck und Ruprecht'', Göttingen, pp. 67, 1848.
1808 births
1882 deaths
19th-century German mathematicians
Scientists from Frankfurt
Topologists
Fellows of the Royal Society of Edinburgh
{{Germany-mathematician-stub