John Herbert de Paz Thorold Gosset (16 October 1869 – December 1962) was an

English English usually refers to: * English language * English people English may also refer to: Peoples, culture, and language * ''English'', an adjective for something of, from, or related to England ** English national ide ...

lawyer A lawyer is a person who practices law. The role of a lawyer varies greatly across different legal jurisdictions. A lawyer can be classified as an advocate, attorney, barrister, canon lawyer, civil law notary, counsel, counselor, solic ...

and an amateur

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. In mathematics, he is noted for discovering and classifying the

semiregular polytope In geometry, by Thorold Gosset's definition a semiregular polytope is usually taken to be a polytope that is vertex-transitive and has all its facets being regular polytopes. E.L. Elte compiled a longer list in 1912 as ''The Semiregular Polyt ...

s in dimensions four and higher, and for his generalization of

Descartes' theorem In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given, mu ...

on tangent circles to four and higher dimensions.

Biography

Thorold Gosset was born in

Thames Ditton Thames Ditton is a suburban village on the River Thames, in the Elmbridge borough of Surrey, England. Apart from a large inhabited island in the river, it lies on the southern bank, centred 12.2 miles (19.6 km) southwest of Charing Cross ...

, the son of John Jackson Gosset, a civil servant and statistical officer for

HM Customs HM Customs (His or Her Majesty's Customs) was the national Customs service of England (and then of Great Britain from 1707, the United Kingdom from 1801) until a merger with the Department of Excise in 1909. The phrase 'HM Customs', in use si ...

,UK Census 1871, RG10-863-89-23 and his wife Eleanor Gosset (formerly Thorold). He was admitted to Pembroke College, Cambridge as a pensioner on 1 October 1888, graduated BA in 1891, was called to the bar of the

Inner Temple The Honourable Society of the Inner Temple, commonly known as the Inner Temple, is one of the four Inns of Court and is a professional associations for barristers and judges. To be called to the Bar and practise as a barrister in England and ...

in June 1895, and graduated

LLM A Master of Laws (M.L. or LL.M.; Latin: ' or ') is an advanced postgraduate academic degree, pursued by those either holding an undergraduate academic law degree, a professional law degree, or an undergraduate degree in a related subject. In mos ...

in 1896. In 1900 he married Emily Florence Wood, and they subsequently had two children, named Kathleen and John.UK Census 1911, RG14-181-9123-19

Mathematics

According to H. S. M. Coxeter, after obtaining his law degree in 1896 and having no clients, Gosset amused himself by attempting to classify the

regular polytope In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. All its elements or -faces (for all , where is the dimension of the polytope) — cells, ...

s in higher-dimensional (greater than three)

Euclidean space Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean ...

. After rediscovering all of them, he attempted to classify the "semi-regular polytopes", which he defined as

polytope In elementary geometry, a polytope is a geometric object with flat sides ('' faces''). Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions. Polytopes may exist in any general number of dimensions as an ...

s having regular

facets A facet is a flat surface of a geometric shape, e.g., of a cut gemstone. Facet may also refer to: Arts, entertainment, and media * ''Facets'' (album), an album by Jim Croce * ''Facets'', a 1980 album by jazz pianist Monty Alexander and his tri ...

and which are

vertex-uniform In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex is surrounded by the same kinds of face in ...

, as well as the analogous

honeycomb A honeycomb is a mass of hexagonal prismatic wax cells built by honey bees in their nests to contain their larvae and stores of honey and pollen. Beekeepers may remove the entire honeycomb to harvest honey. Honey bees consume about of honey ...

s, which he regarded as degenerate polytopes. In 1897 he submitted his results to James W. Glaisher, then editor of the journal ''

Messenger of Mathematics The ''Messenger of Mathematics'' is a defunct British mathematics journal. The founding editor-in-chief was William Allen Whitworth with Charles Taylor and volumes 1–58 were published between 1872 and 1929. James Whitbread Lee Glaisher was th ...

''. Glaisher was favourably impressed and passed the results on to

William Burnside :''This English mathematician is sometimes confused with the Irish mathematician William S. Burnside (1839–1920).'' __NOTOC__ William Burnside (2 July 1852 – 21 August 1927) was an English mathematician. He is known mostly as an early rese ...

and Alfred Whitehead. Burnside, however, stated in a letter to Glaisher in 1899 that "the author's method, a sort of geometric intuition" did not appeal to him. He admitted that he never found the time to read more than the first half of Gosset's paper. In the end Glaisher published only a brief abstract of Gosset's results. Gosset's results went largely unnoticed for many years. His semiregular polytopes were rediscovered by Elte in 1912 and later by H.S.M. Coxeter who gave both Gosset and Elte due credit. Coxeter introduced the term Gosset polytopes for three semiregular polytopes in 6, 7, and 8 dimensions discovered by Gosset: the 2₂₁, 3₂₁, and 4₂₁ polytopes. The vertices of these polytopes were later seen to arise as the

roots A root is the part of a plant, generally underground, that anchors the plant body, and absorbs and stores water and nutrients. Root or roots may also refer to: Art, entertainment, and media * ''The Root'' (magazine), an online magazine focusing ...

of the

exceptional Lie algebra In mathematics, an exceptional Lie algebra is a complex simple Lie algebra whose Dynkin diagram is of exceptional (nonclassical) type. There are exactly five of them: \mathfrak_2, \mathfrak_4, \mathfrak_6, \mathfrak_7, \mathfrak_8; their respective ...

s E₆, E₇ and E₈. A new and more precise definition of the Gosset Series of polytopes has been given by Conway in 2008.

References

{{DEFAULTSORT:Gosset, Thorold Amateur mathematicians 19th-century British mathematicians 20th-century British mathematicians 1869 births 1962 deaths

Biography

Mathematics

See also

References