André Bloch (20 November 1893 – 11 October 1948) was a French
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 ...
who is best remembered for his fundamental contribution to
complex analysis.
Bloch killed three of his family members, for which he was
institutionalized in a
mental asylum
The lunatic asylum (or insane asylum) was an early precursor of the modern psychiatric hospital.
The fall of the lunatic asylum and its eventual replacement by modern psychiatric hospitals explains the rise of organized, institutional psychiatry ...
for 31 years, during which all of his mathematical output was produced.
Early life
Bloch was born in 1893 in
Besançon
Besançon (, , , ; archaic german: Bisanz; la, Vesontio) is the prefecture of the department of Doubs in the region of Bourgogne-Franche-Comté. The city is located in Eastern France, close to the Jura Mountains and the border with Switzer ...
,
France
France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of overseas regions and territories in the Americas and the Atlantic, Pacific and Indian Oceans. Its metropolitan area ...
. According to one of his teachers,
Georges Valiron, both André Bloch and his younger brother Georges were in the same class in October 1910. Valiron believed Georges to have the better talent, and due to lack of preparation, André finished last in the class. André was spared from failing the class by convincing
Ernest Vessiot
Ernest Vessiot (; 8 March 1865 – 17 October 1952) was a French mathematician. He was born in Marseille, France, and died in La Bauche, Savoie, France. He entered the École Normale Supérieure in 1884.
He was Maître de Conférences at Lille ...
to give him an oral exam. The exam convinced Vessiot of Andre's talent and both André and Georges entered the
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 flowing in région Île-de-France
* École, Savoi ...
.
[G. Valiron, Des Théorèmes de Bloch aux Théories d'Ahlfors, Bulletin des Sciences Mathematiques 73 (1949) 152–162.][D. Campbell, Beauty and the beast: The strange case of André Bloch, The Mathematical Intelligencer 7 (1985) 36–38.]
Both brothers served for a year in the military prior to
World War I
World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
.
Both André and Georges studied for only one year at the
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 flowing in région Île-de-France
* École, Savoi ...
before the outbreak of the war.
World War I
Upon the outbreak of
World War I
World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
in 1914, André and Georges Bloch were drafted. André, as a second-lieutenant in the artillery, was assigned to the headquarters of
General De Castelnau in
Nancy.
Both Bloch brothers were injured: André suffered a fall from an observation post, while Georges sustained a head wound which cost him an eye.
Georges was released from service and returned to the École Polytechnique on 7 October 1917.
André, however, was allowed to convalesce but not released from duty.
Murder
On 17 November 1917, while on convalescent leave from service in
World War I
World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with fightin ...
, Bloch killed his brother Georges and his aunt and uncle.
Several conjectures about the motives for Bloch's crime exist among mathematicians.
[See the article by Campbell for several anecdotal examples. Henri Cartan and ]Jacqueline Ferrand
Jacqueline Lelong-Ferrand (17 February 1918, Alès, France – 26 April 2014, Sceaux, France) was a French mathematician who worked on conformal representation theory, potential theory, and Riemannian manifolds. She taught at universities in ...
note that "certain of these conjectures are outrageously eccentric". Steven G. Krantz
Steven George Krantz (born February 3, 1951) is an American scholar, mathematician, and writer. He has authored more than 350 research papers and published more than 150 books. Additionally, Krantz has edited journals such as the ''Notices of th ...
("Mathematical Apocrypha: Stories and Anecdotes of Mathematicians and the Mathematical", American Mathematical Society, 2002) also lists some conjectures. However, Cartan and Ferrand quote
Henri Baruk, who was the medical head of the asylum where Bloch was confined. Bloch told Baruk that the murders were a
eugenic
Eugenics ( ; ) is a fringe set of beliefs and practices that aim to improve the genetic quality of a human population. Historically, eugenicists have attempted to alter human gene pools by excluding people and groups judged to be inferior or ...
act, in order to eliminate branches of his family affected by mental illness.
Commitment and mathematical career
After the murders, Bloch was committed to the
asylum at Charenton in
Saint Maurice
Saint Maurice (also Moritz, Morris, or Mauritius; ) was an Egyptian military leader who headed the legendary Theban Legion of Rome in the 3rd century, and is one of the favorite and most widely venerated saints of that martyred group. He is the ...
,
a suburb of
Paris
Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, 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), ma ...
. Bloch continued his mathematical career while confined. All of his publications, including those relating to
Bloch's constant, were written while he was committed. Bloch corresponded with several
mathematicians, including
Georges Valiron,
George Pólya
George Pólya (; hu, Pólya György, ; December 13, 1887 – September 7, 1985) was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamenta ...
,
Jacques Hadamard
Jacques Salomon Hadamard (; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex analysis, differential geometry and partial differential equations.
Biography
The son of a teac ...
and others,
giving his return address as only "57 Grande rue, Saint-Maurice", never mentioning that this was a psychiatric hospital. Several of his correspondents were thus unaware of his confinement.
During the
German occupation of France
The Military Administration in France (german: Militärverwaltung in Frankreich; french: Occupation de la France par l'Allemagne) was an interim occupation authority established by Nazi Germany during World War II to administer the occupied zo ...
, Bloch (who was
Jewish
Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...
) wrote under
aliases
A pseudonym (; ) or alias () is a fictitious name that a person or group assumes for a particular purpose, which differs from their original or true name ( orthonym). This also differs from a new name that entirely or legally replaces an individu ...
, in order to avoid advertising his presence to
Nazi
Nazism ( ; german: Nazismus), the common name in English for National Socialism (german: Nationalsozialismus, ), is the far-right totalitarian political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in ...
occupiers. In particular, Bloch is known to have authored papers under the names of René Binaud and Marcel Segond during this time.
According to Pólya, Bloch had the habit of dating his letters with 1 April,
regardless of when they were written.
Bloch was transferred to the
Sainte-Anne Hospital in Paris on 21 August 1948 for an operation. He died from
leukemia
Leukemia ( also spelled leukaemia and pronounced ) is a group of blood cancers that usually begin in the bone marrow and result in high numbers of abnormal blood cells. These blood cells are not fully developed and are called ''blasts'' or ...
in Paris on 11 October 1948.
Mathematical work
Most important works of Bloch belong to
complex analysis.
His early contribution is known as
Bloch's theorem
In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential take the form of a plane wave modulated by a periodic function. The theorem is named after the physicist Felix Bloch, who d ...
. This theorem asserts the existence of a certain absolute constant which is called the
Bloch constant. The exact value of the Bloch constant is still unknown . Research originating from this theorem led to introduction of Bloch's functions which form the so-called
Bloch space. (This usage should not be confused with
Bloch's functions of Swiss physicist
Felix Bloch
Felix Bloch (23 October 1905 – 10 September 1983) was a Swiss-American physicist and Nobel physics laureate who worked mainly in the U.S. He and Edward Mills Purcell were awarded the 1952 Nobel Prize for Physics for "their development of new ...
.)
Bloch formulated two important philosophical principles which proved to be useful in research in complex analysis. The more famous of these two is the so-called
Bloch's principle Bloch's Principle is a philosophical principle in mathematics
stated by André Bloch.
Bloch states the principle in Latin as: ''Nihil est in infinito quod non prius fuerit in finito,'' and explains this as follows: Every proposition in whose sta ...
.
In Bloch's own words it is formulated (in Latin) as follows:
"Nihil est in infinito quod non prius fuerit in finito", translated as "There is nothing in the infinite that did not exist before in the finite". Guided by this principle, Bloch was able to discover several important facts which were later proved by other mathematicians, for example, the
five-island theorem. There is an intensive current research related to Bloch's principle.
Bloch's ideas stimulated much of the research on
holomorphic curves in the 20th century and remain central in this subfield. He stated a fundamental theorem on holomorphic curves in complex manifolds whose irregularity exceeds dimension. (This can be considered as a deep and far-reaching generalization of
Picard's theorem
In complex analysis, Picard's great theorem and Picard's little theorem are related theorems about the range of an analytic function. They are named after Émile Picard.
The theorems
Little Picard Theorem: If a function f: \mathbb \to\mathbb ...
.) His proof of this theorem contained gaps (which he recognized), and later the theorem was known as "Bloch's conjecture". Bloch's conjecture, as stated, was proved by Takushiro Ochiai, Pit Man Wong, and simultaneously by
Yujiro Kawamata
Yujiro Kawamata (born 1952) is a Japanese mathematician working
in algebraic geometry.
Career
Kawamata completed the master's course at the University of Tokyo in 1977. He was an Assistant at the University of Mannheim from 1977 to 1979 and a M ...
in 1980, and the related research started a new area which is called holomorphic curves in
Abelian varieties
In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a Algebraic variety#Projective variety, projective algebraic variety that is also an algebraic group, i.e., has a group law th ...
(and semi-Abelian varieties).
Bloch was the first (jointly with
Pólya) to consider the distribution of roots of random polynomials,
which is another area of research which is intensively developing
since the middle of 20th century.
References
External links
Bloch's Constantat
PlanetMath
PlanetMath is a free, collaborative, mathematics online encyclopedia. The emphasis is on rigour, openness, pedagogy, real-time content, interlinked content, and also community of about 24,000 people with various maths interests. Intended to be c ...
Bloch's Theoremat
PlanetMath
PlanetMath is a free, collaborative, mathematics online encyclopedia. The emphasis is on rigour, openness, pedagogy, real-time content, interlinked content, and also community of about 24,000 people with various maths interests. Intended to be c ...
{{DEFAULTSORT:Bloch, Andre
1893 births
1948 deaths
Jewish French scientists
Scientists from Besançon
19th-century French Jews
20th-century French mathematicians
Complex analysts
French military personnel of World War I
Deaths from leukemia
French people convicted of murder
Fratricides