Eugène Charles Catalan (30 May 1814 – 14 February 1894) was a French and
Belgian mathematician who worked on
continued fraction
In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integ ...
s,
descriptive geometry,
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...
and
combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...
. His notable contributions included discovering a periodic minimal surface in the space
; stating the famous
Catalan's conjecture
Catalan's conjecture (or Mihăilescu's theorem) is a theorem in number theory that was conjectured by the mathematician Eugène Charles Catalan in 1844 and proven in 2002 by Preda Mihăilescu at Paderborn University. The integers 23 and 32 are ...
, which was eventually proved in 2002; and, introducing the
Catalan number
In combinatorial mathematics, the Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named after the French-Belgian mathematician Eugène Charles C ...
to solve a combinatorial problem.
Biography
Catalan was born in
Bruges
Bruges ( , nl, Brugge ) is the capital and largest city
A city is a human settlement of notable size.Goodall, B. (1987) ''The Penguin Dictionary of Human Geography''. London: Penguin.Kuper, A. and Kuper, J., eds (1996) ''The Social Scienc ...
(now in
Belgium
Belgium, ; french: Belgique ; german: Belgien officially the Kingdom of Belgium, is a country in Northwestern Europe. The country is bordered by the Netherlands to the north, Germany to the east, Luxembourg to the southeast, France to ...
, then under
Dutch rule even though the
Kingdom of the Netherlands
, national_anthem = )
, image_map = Kingdom of the Netherlands (orthographic projection).svg
, map_width = 250px
, image_map2 = File:KonDerNed-10-10-10.png
, map_caption2 = Map of the four constituent countries shown to scale
, capital = ...
had not yet been formally instituted), the only child of a French jeweller by the name of Joseph Catalan, in 1814. In 1825, he traveled to Paris and learned mathematics at
École Polytechnique
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
The Seine ( , ) is a river in northern Franc ...
, where he met
Joseph Liouville
Joseph Liouville (; ; 24 March 1809 – 8 September 1882) was a French mathematician and engineer.
Life and work
He was born in Saint-Omer in France on 24 March 1809. His parents were Claude-Joseph Liouville (an army officer) and Thérèse ...
(1833). In December 1834 he was expelled along with most of the students in his year for political reasons;
November 1834
/ref> he resumed his studies in January 1835, graduated that summer, and went on to teach at Châlons-sur-Marne. Catalan came back to the École Polytechnique, and, with the help of Liouville, obtained his degree in mathematics in 1841. He went on to Charlemagne College to teach descriptive geometry. Though he was politically active and strongly left-wing, leading him to participate in the 1848 Revolution
The Revolutions of 1848, known in some countries as the Springtime of the Peoples or the Springtime of Nations, were a series of political upheavals throughout Europe starting in 1848. It remains the most widespread revolutionary wave in Europea ...
, he had an animated career and also sat in the France's Chamber of Deputies. Later, in 1849, Catalan was visited at his home by the French Police, searching for illicit teaching material; however, none was found.
The University of Liège
The University of Liège (french: Université de Liège), or ULiège, is a major public university of the French Community of Belgium based in Liège, Wallonia, Belgium. Its official language is French. As of 2020, ULiège is ranked in the 301� ...
appointed him chair of analysis in 1865. In 1879, still in Belgium, he became journal editor where he published as a foot note Paul-Jean Busschop's theory after refusing it in 1873 - letting Busschop know that it was too empirical. In 1883, he worked for the Belgian Academy of Science in the field of number theory. He died in Liège, Belgium where he had received a chair.
Work
He worked on continued fraction
In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integ ...
s, descriptive geometry, number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...
and combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...
. He gave his name to a unique surface (periodic minimal surface in the space ) that he discovered in 1855. Before that, he had stated the famous Catalan's conjecture
Catalan's conjecture (or Mihăilescu's theorem) is a theorem in number theory that was conjectured by the mathematician Eugène Charles Catalan in 1844 and proven in 2002 by Preda Mihăilescu at Paderborn University. The integers 23 and 32 are ...
, which was published in 1844 and was eventually proved in 2002, by the Romania
Romania ( ; ro, România ) is a country located at the crossroads of Central, Eastern, and Southeastern Europe. It borders Bulgaria to the south, Ukraine to the north, Hungary to the west, Serbia to the southwest, Moldova to the east, a ...
n mathematician Preda Mihăilescu. He introduced the Catalan number
In combinatorial mathematics, the Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named after the French-Belgian mathematician Eugène Charles C ...
s to solve a combinatorial problem
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business an ...
.
Selected publications
*Théorèmes et Problèmes Géométrie élémentaire, Brussels, 2nd edition 1852
6th edition 1879
*Éléments de géométrie, 1843
2nd printing 1847
*Traité élémentaire de géométrie descriptive, 2 volumes 1850, 1852
3rd edition 1867/1868
5th edition 1881
*Nouveau manuel des aspirants au baccalauréat ès sciences, 1852 (12 editions published)
*Solutions des problèmes de mathématique et de physique donnés à la Sorbonne dans les compositions du baccalauréat ès sciences, 1855/56
*Manuel des candidats à l'École Polytechnique, 2 volumes, 1857–58
*Notions d'astronomie, 1860 (6 editions published)
Traité élémentaire des séries
1860
*Histoire d'un concours, 1865, 2nd edition 1867
*Cours d'analyse de l'université de Liège, 1870, 2nd edition 1880
Intégrales eulériennes ou elliptiques
1892
See also
* Catalan pseudoprime
*Catalan's triangle In combinatorial mathematics, Catalan's triangle is a number triangle whose entries C(n,k) give the number of strings consisting of ''n'' X's and ''k'' Y's such that no initial segment of the string has more Y's than X's. It is a generalization of ...
* Catalan–Dickson conjecture
* Catalan–Mersenne number conjecture
* Catalan beta function
* Fermat–Catalan conjecture
* Fuss–Catalan number
References
External links
*
*
Catalan
{{DEFAULTSORT:Catalan, Eugene Charles
1814 births
1894 deaths
Scientists from Bruges
University of Liège faculty
19th-century Belgian mathematicians
Corresponding members of the Saint Petersburg Academy of Sciences
Combinatorialists
Number theorists
19th-century French mathematicians