André Bloch (mathematician)

André Bloch (born November 20, 1893 in Besançon , † October 11, 1948 in Paris ) was a French mathematician who is known for his work on function theory.

Life

André Bloch's parents died early. His father was a watchmaker originally from Alsace . Bloch had excellent grades at grammar school and passed the entrance exams for the École polytechnique in Paris in 1912 at the same time as his brother Georges, who was a year younger. However, he was only able to attend university for about a year (like his brother he had to do a year of military service before the war), so that his mathematics skills were largely self-taught . In 1914 he was drafted as a second lieutenant in the artillery , but after a few months after a near direct hit at his observation post he was released for psychological reasons.

After he had one of his brothers (who had also been discharged from the military in 1917 after a head injury that cost him an eye), an uncle and an aunt, killed with an ax at a family meal on November 17, 1917 he arrested without resistance and was in the psychiatry ( Hôpital Saint Maurice, also Maison de Charenton called ) briefed. There he spent the rest of his life as an exemplary patient devoted entirely to mathematics. He was popular with the caretakers for his politeness, did not go out like the others in the park, but only relaxed playing chess . He was in correspondence with important analysts such as Jacques Hadamard , Gösta Mittag-Leffler , George Pólya , Émile Picard , Paul Montel and Henri Cartan , some of whom were ignorant of his particular fate. During the time of the German occupation, his seclusion avoided the fate of many Jews in what was then France (he published during this time under the pseudonym Marcel Segond). Rolf Nevanlinna is one of his rare mathematicians . Bloch died in a hospital where he was going to have an operation for leukemia .

plant

André Bloch is best known for Bloch's theorem. In this context, Bloch's constant is also named after him. The Bloch space , also named after him, consists of all holomorphic functions in the complex unit disk for which ${\displaystyle \mathbb {D} }$ ${\displaystyle f}$

${\displaystyle \sup _{z\in \mathbb {D} }(1-|z|^{2})|f^{\prime }(z)|<\infty .}$

The subset of functions for which ${\displaystyle f}$

${\displaystyle \lim _{|z|\to 1}(1-|z|^{2})|f^{\prime }(z)|=0}$

is also called a small Bloch space. In the theory of normal families , which goes back to Paul Montel , the heuristic Bloch principle is important.

In addition to work on function theory , he also wrote works z. B. on geometry , kinematics, equation theory and number theory . He also wrote an astronomical essay on ebb and flow, which was lost (after Montel refused to publish it), and essays on the didactics of mathematics. With the President Raymond Poincaré he corresponded about the state finances. He mostly published in the Bulletin des Sciences Mathématiques , to which he also subscribed. With another mathematician, G.Guillaumin, who was temporarily treated in Saint Maurice, he wrote a book on integral geometry that appeared in 1949 with a foreword by Élie Cartan .

Bloch also proved a theorem about the hyperbolicity of the sub-varieties of complex tori in 1926 and made a conjecture that was proven by Mark Green , Phillip Griffiths from the 1970s and by Michael McQuillan in the 1990s .

In 1948 he received the Becquerel Prize from the Académie des Sciences .

motive

When asked by his doctor about the reason for his bloody act, Bloch replied at the end of his life, one day after the visit of his third and youngest brother, from whom he was instructed about the remaining family: “It is a matter of mathematical logic. There have been cases of mental illness in my family. The destruction of this branch of the family came naturally. I began my work at the time of this famous meal ” (quoted in the essay by Cartan, Ferrand). When the doctor objected to this argument, Bloch said: “You are using emotional language. At the top there is mathematics and its laws. You know very well that my philosophy is inspired by pragmatism and absolute rationalism. I applied the example and principles of the famous mathematician Hypatia from Alexandria. ” Cartan and Ferrand suggest that Bloch was referring to a passage in Charles Kingsley's biography, Hypatias , in which Hypatia remains calm at the sight of a massacre in the gladiatorial arena so that a philosophical indifference towards death can be recognized, which results from the belief in an eternal cycle. According to Henri Baruk (1897–1999, director of Saint Maurice from 1932) Bloch suffered from a “morbid rationalism”: he had eliminated that part of his family that he considered to be hereditary with mental illnesses.

literature

• Henri Cartan, Jacqueline Ferrand : The case of Andre Bloch . Mathematical Intelligencer Vol. 10, 1988
• D. Campbell: Beauty and the beast: The Strange Case of André Bloch . Mathematical Intelligencer Vol. 7, 1985, No. 4
• Georges Valiron : The théorèmes de Bloch aux travaux de Ahlfors . Bulletin des Sciences Mathématiques Vol. 73, 1949, pp. 152-162
• Henri Baruk (his attending psychiatrist): People like us . Econ 1979, (French 1975 from Robert Laffont)

Web links

• John J. O'Connor, Edmund F. Robertson :  André Bloch. In: MacTutor History of Mathematics archive .
• Henri Cartan, Jacqueline Ferrand: Le cas André Bloch, Cahiers du séminaire d'histoire des mathématiques 9, 1988, pp. 211-219 (French version of the Mathematical Intelligencer article, with a list of his writings)
• Some of his essays
• Author profile in the database zbMATH