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

lawyer A lawyer is a person who is qualified to offer advice about the law, draft legal documents, or represent individuals in legal matters. The exact nature of a lawyer's work varies depending on the legal jurisdiction and the legal system, as w ...

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, mathematical structure, structure, space, Mathematica ...

. In mathematics, he is noted for discovering and classifying the semiregular polytopes in dimensions four and higher, and for his generalization of Descartes' theorem on tangent circles to four and higher dimensions.

Biography

Thorold Gosset was born in Thames Ditton, the son of John Jackson Gosset, a civil servant and statistical officer for HM Customs,UK Census 1871, RG10-863-89-23 and his wife Eleanor Gosset (formerly Thorold). He was admitted to

Pembroke College, Cambridge Pembroke College is a constituent college of the University of Cambridge, England. The college is the third-oldest college of the university and has over 700 students and fellows. It is one of the university's larger colleges, with buildings from ...

as a pensioner on 1 October 1888, graduated BA in 1891, was

called to the bar The call to the bar is a legal term of art in most common law jurisdictions where persons must be qualified to be allowed to argue in court on behalf of another party and are then said to have been "called to the bar" or to have received "call to ...

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 association for barristers and judges. To be called to the Bar and practice as a barrister in England and Wa ...

in June 1895, and graduated

LLM A large language model (LLM) is a language model trained with Self-supervised learning, self-supervised machine learning on a vast amount of text, designed for natural language processing tasks, especially Natural language generation, language g ...

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 transitive group action, transitively on its flag (geometry), flags, thus giving it the highest degree of symmetry. In particular, all its elements or -faces (for all , w ...

s in higher-dimensional (greater than three)

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

. 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 and which are vertex-uniform, as well as the analogous

honeycomb A honeycomb is a mass of Triangular prismatic honeycomb#Hexagonal prismatic honeycomb, hexagonal prismatic cells built from beeswax by honey bees in their beehive, nests to contain their brood (eggs, larvae, and pupae) and stores of honey and pol ...

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

of the exceptional Lie algebras E₆, E₇ and E₈. A new and more precise definition of the Gosset Series of polytopes has been given by

Conway Conway may refer to: Places United States * Conway, Arkansas * Conway County, Arkansas * Lake Conway, Arkansas * Conway, Florida * Conway, Iowa * Conway, Kansas * Conway, Louisiana * Conway, Massachusetts * Conway, Michigan * Conway Townshi ...

in 2008.

References

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

Biography

Mathematics

See also

References