Johann Benedict Listing (25 July 1808 – 24 December 1882) was a German mathematician.

Early life and education

J. B. Listing was born in

Frankfurt Frankfurt am Main () is the most populous city in the States of Germany, German state of Hesse. Its 773,068 inhabitants as of 2022 make it the List of cities in Germany by population, fifth-most populous city in Germany. Located in the forela ...

and died in

Göttingen Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...

. He finished his studies at the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 ...

in 1834, and in 1839 he succeeded Wilhelm Weber as professor of

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

Career

Listing first introduced the term "

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

" 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

Möbius strip In mathematics, a Möbius strip, Möbius band, or Möbius loop is a Surface (topology), surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Bened ...

, or half-twisted strip, at the same time (1858) as

August Ferdinand Möbius August Ferdinand Möbius (, ; ; 17 November 1790 – 26 September 1868) was a German mathematician and theoretical astronomer. Life and education Möbius was born in Schulpforta, Electorate of Saxony, and was descended on his mothe ...

, 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 number In mathematics, a Listing number of a topological space is one of several topological invariants introduced by the 19th-century mathematician Johann Benedict Listing and later given this name by Charles Sanders Peirce. Unlike the later invariants ...

s. In

ophthalmology Ophthalmology (, ) is the branch of medicine that deals with the diagnosis, treatment, and surgery of eye diseases and disorders. An ophthalmologist is a physician who undergoes subspecialty training in medical and surgical eye care. Following a ...

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 and ...

describes an essential element of extraocular eye muscle coordination. In

geodesy Geodesy or geodetics is the science of measuring and representing the Figure of the Earth, geometry, Gravity of Earth, gravity, and Earth's rotation, spatial orientation of the Earth in Relative change, temporally varying Three-dimensional spac ...

, he coined in 1872 the term "

geoid The geoid ( ) is the shape that the ocean surface would take under the influence of the gravity of Earth, including gravitational attraction and Earth's rotation, if other influences such as winds and tides were absent. This surface is exte ...

" for the idealized geometric surface of the

figure of the Earth In geodesy, the figure of the Earth is the size and shape used to model planet Earth. The kind of figure depends on application, including the precision needed for the model. A spherical Earth is a well-known historical approximation that is ...

, as previously conceptualized by his doctoral adviser,

Gauss Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, Geodesy, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observat ...

Personal life

Listing's granddaughter was British War Artist

Anna Airy Anna Airy (6 June 1882 – 23 October 1964) was an English oil painter, pastel artist and etcher. She was one of the first women officially commissioned as a war artist and was recognised as one of the leading women artists of her generation. E ...

, by his younger daughter Anna.

References

External links

* *
reprint
of (part of) his famous 1847 article introducing

Topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

, published in ''Vorstudien zur Topologie, Vandenhoeck und Ruprecht'', Göttingen, pp. 67, 1848. 1808 births 1882 deaths 19th-century German mathematicians Scientists from Frankfurt German topologists Fellows of the Royal Society of Edinburgh Vision scientists {{Germany-mathematician-stub