Eugène Charles Catalan
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Eugène Charles Catalan (; 30 May 1814 – 14 February 1894) was a French and Belgian mathematician who worked on
continued fraction A continued fraction is a mathematical expression that can be written as a fraction with a denominator that is a sum that contains another simple or continued fraction. Depending on whether this iteration terminates with a simple fraction or not, ...
s,
descriptive geometry Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design an ...
,
number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
and
combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...
. His notable contributions included discovering a periodic minimal surface in the space \mathbb^3; 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 ...
, which was eventually proved in 2002; and introducing the
Catalan number The Catalan numbers are a sequence of natural numbers that occur in various Enumeration, counting problems, often involving recursion, recursively defined objects. They are named after Eugène Charles Catalan, Eugène Catalan, though they were p ...
s to solve a combinatorial problem.


Biography

Catalan was born in Brugge (now in
Belgium Belgium, officially the Kingdom of Belgium, is a country in Northwestern Europe. Situated in a coastal lowland region known as the Low Countries, it is bordered by the Netherlands to the north, Germany to the east, Luxembourg to the southeas ...
, then under Dutch rule even though the
Kingdom of the Netherlands The Kingdom of the Netherlands (, ;, , ), commonly known simply as the Netherlands, is a sovereign state consisting of a collection of constituent territories united under the monarch of the Netherlands, who functions as head of state. The re ...
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 (, ; also known as Polytechnique or l'X ) is a ''grande école'' located in Palaiseau, France. It specializes in science and engineering and is a founding member of the Polytechnic Institute of Paris. The school was founded in 1794 by mat ...
, 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 Thérès ...
(1833). In December 1834 he was expelled along with most of the students in his year as part of a crackdown by the
July Monarchy The July Monarchy (), officially the ''Kingdom of France'' (), was a liberalism, liberal constitutional monarchy in France under , starting on 9 August 1830, after the revolutionary victory of the July Revolution of 1830, and ending 26 Februar ...
against republican tendencies among the students. 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 revolutions throughout Europe over the course of more than one year, from 1848 to 1849. It remains the most widespre ...
, 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 (), or ULiège, is a major public university of the French Community of Belgium founded in 1817 and based in Liège, Wallonia, Belgium. Its official language is French (language), French. History The university was foun ...
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 Liège ( ; ; ; ; ) is a City status in Belgium, city and Municipalities in Belgium, municipality of Wallonia, and the capital of the Liège Province, province of Liège, Belgium. The city is situated in the valley of the Meuse, in the east o ...
, Belgium where he had received a chair.


Work

He worked on
continued fraction A continued fraction is a mathematical expression that can be written as a fraction with a denominator that is a sum that contains another simple or continued fraction. Depending on whether this iteration terminates with a simple fraction or not, ...
s,
descriptive geometry Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design an ...
,
number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...
and
combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...
. He gave his name to a unique surface (periodic minimal surface in the space \mathbb^3) 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 ...
, which was published in 1844 and was eventually proved in 2002, by the
Romania Romania is a country located at the crossroads of Central Europe, Central, Eastern Europe, Eastern and Southeast Europe. It borders Ukraine to the north and east, Hungary to the west, Serbia to the southwest, Bulgaria to the south, Moldova to ...
n mathematician
Preda Mihăilescu Preda V. Mihăilescu (born 23 May 1955) is a Romanian mathematician, best known for his proof of the 158-year-old Catalan's conjecture. Biography Born in Bucharest,Stewart 2013 he is the brother of Vintilă Mihăilescu. After leaving Romania i ...
. He introduced the
Catalan number The Catalan numbers are a sequence of natural numbers that occur in various Enumeration, counting problems, often involving recursion, recursively defined objects. They are named after Eugène Charles Catalan, Eugène Catalan, though they were p ...
s to solve a
combinatorial Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...
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 ...
(although these were actually discovered a century earlier by the Chinese
astronomer An astronomer is a scientist in the field of astronomy who focuses on a specific question or field outside the scope of Earth. Astronomers observe astronomical objects, such as stars, planets, natural satellite, moons, comets and galaxy, galax ...
Minggatu).


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 * Catalan–Dickson conjecture * Catalan–Mersenne number conjecture * Catalan beta function *
Fermat–Catalan conjecture In number theory, the Fermat–Catalan conjecture is a generalization of Fermat's Last Theorem and of Catalan's conjecture. The conjecture states that the equation has only finitely many solutions (''a'', ''b'', ''c'', ''m'', ''n'', ''k'') with ...
* Fuss–Catalan number


References


External links

* *
Catalan
{{DEFAULTSORT:Catalan, Eugene Charles 1814 births 1894 deaths Scientists from Bruges Academic staff of the University of Liège 19th-century Belgian mathematicians Corresponding members of the Saint Petersburg Academy of Sciences Combinatorialists Number theorists 19th-century French mathematicians