Guillaume-Jules Hoüel (7 April 1823 – 14 June 1886) was a

French French (french: français(e), link=no) may refer to: * Something of, from, or related to France ** French language, which originated in France, and its various dialects and accents ** French people, a nation and ethnic group identified with Franc ...

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 ...

. He entered the

École Normale Supérieure École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

in 1843 and received his doctoral degree in 1855 from the

Sorbonne Sorbonne may refer to: * Sorbonne (building), historic building in Paris, which housed the University of Paris and is now shared among multiple universities. *the University of Paris (c. 1150 – 1970) *one of its components or linked institution, ...

. He was sought by

Urbain Le Verrier Urbain Jean Joseph Le Verrier FRS (FOR) HFRSE (; 11 March 1811 – 23 September 1877) was a French astronomer and mathematician who specialized in celestial mechanics and is best known for predicting the existence and position of Neptune using ...

at the

Paris Observatory The Paris Observatory (french: Observatoire de Paris ), a research institution of the Paris Sciences et Lettres University, is the foremost astronomical observatory of France, and one of the largest astronomical centers in the world. Its histor ...

, but chose instead to return to Thaon to study there. In 1859 he began to teach at

Bordeaux Bordeaux ( , ; Gascon oc, Bordèu ; eu, Bordele; it, Bordò; es, Burdeos) is a port city on the river Garonne in the Gironde department, Southwestern France. It is the capital of the Nouvelle-Aquitaine region, as well as the prefectur ...

. In 1863 Hoüel expressed his doubts about the verifiability of the

parallel postulate In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry: ''If a line segment ...

Euclid Euclid (; grc-gre, Wikt:Εὐκλείδης, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the ''Euclid's Elements, Elements'' trea ...

. In 1867 Hoüel produced French translations of two key publications of

non-Euclidean geometry In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geo ...

: Lobachevski's ''Geometrical Studies on the Theory of Parallels'' and Bolyai's ''Science of Absolute Space''. Hoüel published a four volume work titled ''Théorie Élémentaire des Quantités Complexes''. Volume four, published in 1874, began with an discussion of properties of algebraic operations (commutativity, associativity, distribution, and inverses) and used the algebra of

quaternion In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. Hamilton defined a quatern ...

s and

versor In mathematics, a versor is a quaternion of norm one (a ''unit quaternion''). The word is derived from Latin ''versare'' = "to turn" with the suffix ''-or'' forming a noun from the verb (i.e. ''versor'' = "the turner"). It was introduced by Willi ...

s to describe

spherical trigonometry Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are gr ...

. However, in 1890

P. G. Tait Peter Guthrie Tait FRSE (28 April 1831 – 4 July 1901) was a Scottish mathematical physicist and early pioneer in thermodynamics. He is best known for the mathematical physics textbook '' Treatise on Natural Philosophy'', which he co-wrote w ...

revealed his dissatisfaction with Hoüel's changes in notation with text that Tait had given for Hoüel's use. Tait wrote: :The earliest offender in this class was the late M. Hoüel who, while availing himself of my permission to reproduce, in his ''Théorie Élémentaire des Quantités Complexes'', large parts of this volume, made his pages absolutely repulsive by introducing fancied improvements in the notation. In 1876 Hoüel reviewed a

Russian language Russian (russian: русский язык, russkij jazyk, link=no, ) is an East Slavic languages, East Slavic language mainly spoken in Russia. It is the First language, native language of the Russians, and belongs to the Indo-European langua ...

quaternion textbook written by Romer (1868)J. Hoüel (1876) "Principles fundamentaux de la Méthode de Quaternions", ''Bulletin ces Sciences Mathématiques et Astronomique'' 11: 113,4

References

G. B. Halsted George Bruce Halsted (November 25, 1853 – March 16, 1922), usually cited as G. B. Halsted, was an American mathematician who explored foundations of geometry and introduced non-Euclidean geometry into the United States through his own work and ...

(1897
Guillaume-Jules Hoüel

American Mathematical Monthly ''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an e ...

4:99–101, link from

Jstor JSTOR (; short for ''Journal Storage'') is a digital library founded in 1995 in New York City. Originally containing digitized back issues of academic journals, it now encompasses books and other primary sources as well as current issues of j ...

early content. * * {{DEFAULTSORT:Houel, Jules People from Calvados (department) 1823 births 1886 deaths Geometers 19th-century French mathematicians Russian–French translators 19th-century translators