André Bloch

André Bloch (20 November 1893 – 11 October 1948) was a French mathematician 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 for 31 years, during which all of his mathematical output was produced.

Early life André Bloch was born in 1893 to a Jewish family in Besançon, France. He was the eldest son in his family, his younger brother is Georges Bloch and his youngest brother is Henry Bloch. According to one of his teachers, Georges Valiron, both André Bloch and his younger brother Georges Bloch 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 to give him an oral exam. The exam convinced Vessiot of Andre's talent and both André and Georges entered the École Polytechnique.

Both brothers served for a year in the military prior to World War I. Both André and Georges studied for only one year at the École Polytechnique before the outbreak of the war. 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 act, in order to eliminate branches of his family affected by mental illness. 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.) 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 in 1980, and the related research started a new area which is called holomorphic curves in Abelian varieties (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.