Rouen
Rouen (, ; or ) is a city on the River Seine in northern France. It is the prefecture of the Regions of France, region of Normandy (administrative region), Normandy and the Departments of France, department of Seine-Maritime. Formerly one of ...
– 18 December 1994,
Caen
Caen (, ; nrf, Kaem) is a commune in northwestern France. It is the prefecture of the department of Calvados. The city proper has 105,512 inhabitants (), while its functional urban area has 470,000,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 ...
most remembered for
Apéry's theorem
In mathematics, Apéry's theorem is a result in number theory that states the Apéry's constant ζ(3) is irrational. That is, the number
:\zeta(3) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots = 1.2020569\ldots
cannot be written as a fract ...
, which states that is an
irrational number
In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integ ...
. Here, denotes the
Riemann zeta function
The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for \operatorname(s) > ...
.
Biography
Apéry was born in
Rouen
Rouen (, ; or ) is a city on the River Seine in northern France. It is the prefecture of the Regions of France, region of Normandy (administrative region), Normandy and the Departments of France, department of Seine-Maritime. Formerly one of ...
Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
father. His childhood was spent in
Lille
Lille ( , ; nl, Rijsel ; pcd, Lile; vls, Rysel) is a city in the northern part of France, in French Flanders. On the river Deûle, near France's border with Belgium, it is the capital of the Hauts-de-France Regions of France, region, the Pref ...
until 1926, when the family moved to
Paris
Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...
, where he studied at the Lycée Ledru-Rollin and the
Lycée Louis-le-Grand
The Lycée Louis-le-Grand (), also referred to simply as Louis-le-Grand or by its acronym LLG, is a public Lycée (French secondary school, also known as sixth form college) located on rue Saint-Jacques in central Paris. It was founded in the ...
. He was admitted at 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 1935. His studies were interrupted at the start of
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
; he was mobilized in September 1939, taken
prisoner of war
A prisoner of war (POW) is a person who is held captive by a belligerent power during or immediately after an armed conflict. The earliest recorded usage of the phrase "prisoner of war" dates back to 1610.
Belligerents hold prisoners of wa ...
in June 1940, repatriated with pleurisy in June 1941, and hospitalized until August 1941. He wrote his doctoral thesis in
algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...
under the direction of Paul Dubreil and René Garnier in 1947.
In 1947 Apéry was appointed
Maître de conférences
''Maître'' (spelled ''Maitre'' according to post-1990 spelling rules) is a commonly used honorific for lawyers, judicial officers and notaries in France, Belgium, Switzerland and French-speaking parts of Canada. It is often written in its abbrev ...
(lecturer) at the
University of Rennes
The University of Rennes is a public research university which will be officially reconstituted on 1 January 2023 and located in the city of Rennes, in Upper Brittany, France. The University of Rennes has been divided for almost 50 years, before ...
. In 1949 he was appointed Professor at the
University of Caen
The University of Caen Normandy (French: ''Université de Caen Normandie''), also known as Unicaen, is a public university in Caen, France.
History
The institution was founded in 1432 by John of Lancaster, 1st Duke of Bedford, the first rector ...
, where he remained until his retirement.
In 1979 he published an unexpected proof of the
irrationality
Irrationality is cognition, thinking, talking, or acting without inclusion of rationality. It is more specifically described as an action or opinion given through inadequate use of reason, or through emotional distress or cognitive deficiency. ...
of , which is the sum of the inverses of the cubes of the positive integers. An indication of the difficulty is that the corresponding problem for other odd powers remains unsolved. Nevertheless, many mathematicians have since worked on the so-called Apéry sequences to seek alternative proofs that might apply to other odd powers ( Frits Beukers,
Alfred van der Poorten
Alfred Jacobus (Alf) van der Poorten (16 May 1942 – 9 October 2010) was a Dutch-Australian number theorist, for many years on the mathematics faculties of the University of New South Wales and Macquarie University....
Biography
Van der Poor ...
, Marc Prévost,
Keith Ball
Keith Ball (born 26 October 1940) is an English former footballer. He was a short but agile goalkeeper who made 145 league and cup appearances for Port Vale and enjoyed three spells with Walsall. He also played non-league football for Worceste ...
, Tanguy Rivoal,
Wadim Zudilin
Wadim Zudilin (Вадим Валентинович Зудилин) is a Russian mathematician and number theory, number theorist who is active in studying Hypergeometric series, hypergeometric functions and zeta constants. He studied under Yuri Va ...
, and others).
Apéry was active in politics and for a few years in the 1960s was president of the
Calvados
Calvados (, , ) is a brandy from Normandy in France, made from apples or pears, or from apples with pears.
History In France
Apple orchards and brewers are mentioned as far back as the 8th century by Charlemagne. The first known record of Nor ...
Radical Party of the Left
The Radical Party of the Left (french: Parti radical de gauche, PRG) is a social-liberal political party in France. A party in the Radical tradition, since 1972 the PRG was a close ally of the major party of the centre-left in France, the Soc ...
. He abandoned politics after the reforms instituted by
Edgar Faure
Edgar Jean Faure (; 18 August 1908 – 30 March 1988) was a French politician, lawyer, essayist, historian and memoirist who served as Prime Minister of France in 1952 and again between 1955 and 1956.1968 revolt, when he realised that university life was running against the tradition he had always upheld.
Personal life
Apéry married in 1947 and had three sons, including mathematician François Apéry. His first marriage ended in divorce in 1971. He then remarried in 1972 and divorced in 1977.
In 1994, Apéry died from
Parkinson's disease
Parkinson's disease (PD), or simply Parkinson's, is a long-term degenerative disorder of the central nervous system that mainly affects the motor system. The symptoms usually emerge slowly, and as the disease worsens, non-motor symptoms becom ...
after a long illness in
Caen
Caen (, ; nrf, Kaem) is a commune in northwestern France. It is the prefecture of the department of Calvados. The city proper has 105,512 inhabitants (), while its functional urban area has 470,000,Père Lachaise Cemetery
Père Lachaise Cemetery (french: Cimetière du Père-Lachaise ; formerly , "East Cemetery") is the largest cemetery in Paris, France (). With more than 3.5 million visitors annually, it is the most visited necropolis in the world. Notable figures ...
in Paris. His tombstone has a mathematical inscription stating his theorem.
:
See also
*
Apéry's constant
In mathematics, Apéry's constant is the sum of the reciprocals of the positive cubes. That is, it is defined as the number
:
\begin
\zeta(3) &= \sum_^\infty \frac \\
&= \lim_ \left(\frac + \frac + \cdots + \frac\right),
\end
...
*
Basel problem
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, and read on 5 December 1735 ...