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André Weil should not be confused with two other mathematician with similar names:

André Weil (May 6, 1906 - August 6, 1998) (pronounced [ɑ̃dʁe vɛj][1]) was one of the greatest mathematicians of the 20th century, renowned for the breadth and quality of his research output, its influence on future work, and the elegance of his exposition. Sir Andrew John Wiles KBE FRS (born 11 April 1953 is a British Mathematician and a professor at Princeton University Fermat's Last Theorem is the name of the statement in Number theory that It is impossible to separate any power higher than the second into two like In Mathematics, the modularity theorem establishes an important connection between Elliptic curves over the field of Rational numbers and Modular forms In Mathematics, an elliptic curve is a smooth, projective Algebraic curve of genus one on which there is a specified point O Events 1527 - Spanish and German troops sack Rome; some consider this the end of the Renaissance. Year 1906 ( MCMVI) was a Common year starting on Monday (link will display full calendar of the Gregorian calendar (or a Common year starting Events 1538 - Bogotá, Colombia, is founded by Gonzalo Jiménez de Quesada. Year 1998 ( MCMXCVIII) was a Common year starting on Thursday (link will display full 1998 Gregorian calendar) A mathematician is a person whose primary area of study and research is the field of Mathematics. He is especially known for his foundational work in number theory and algebraic geometry. Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes Algebraic geometry is a branch of Mathematics which as the name suggests combines techniques of Abstract algebra, especially Commutative algebra, with He was a founding member and the de facto early leader of the influential Bourbaki group. Nicolas Bourbaki is the collective Pseudonym under which a group of (mainly French) 20th-century Mathematicians wrote a series of books presenting an exposition The philosopher Simone Weil was his sister. Philosophy is the study of general problems concerning matters such as existence knowledge truth beauty justice validity mind and language Simone Weil (simɔn vɛj February 3, 1909 in Paris, France &ndash August 24, 1943 in Ashford Kent,

Contents

Life

Weil (1992), his autobiography, was written more for his American descent than his fellow mathematicians. An autobiography, from the Greek αὐτός autos "self" βίος bios "life" and γράφειν graphein "to write" It also says almost nothing about his life after he and his family settled in the USA for good, in 1947.

Born in Paris to Alsatian Jewish parents who fled the annexation of Alsace-Lorraine to Germany, Weil studied in Paris, Rome and Göttingen and received his doctorate in 1928. Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city Alsace (Alsace alzas Alsatian and Elsass pre-1996 German: Elsaß; Alsatia is one of the 26 Regions of France, located on the eastern PLEASE TAKE NOTE************ Alsace-Lorraine (Reichsland Elsaß-Lothringen generally Elsass - Lothringen) was a territorial entity created by the German Empire in 1871 Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. Rome ( Roma ˈroma Roma is the capital city of Italy and Lazio, and is Italy's largest and most populous city with more than 2 Göttingen ( ˈgœtɪŋən, Low German: Chöttingen is a College town in Lower Saxony, Germany. "PhD" redirects here for other uses see PhD (disambiguation. While in Germany, he befriended Carl Ludwig Siegel. Carl Ludwig Siegel ( December 31 1896 &ndash April 4 1981) was a Mathematician specialising in Number theory. He spent two academic years at Aligarh Muslim University from 1930. Aligarh Muslim University is a Residential Academic Institution which was established in 1875 Sanskrit literature was a life-long interest. Literature in Sanskrit begins with the Vedas, and continues with the Sanskrit Epics of Iron Age India; the golden age of Classical After one year in Marseilles, he taught six years in Strasbourg. Marseille, ( English alt Marseilles mɑrˈseɪ — French: maʁsɛj locally — Provençal Occitan: Marselha maʀˈsijɔ Strasbourg (Strasbourg stʁazbuʁ Alsatian: Strossburi,; Straßburg) is the capital and principal City of the Alsace région He married Eveline in 1937.

Weil was in Finland when World War II broke out; he had been traveling in Scandinavia since April 1939. Finland, officially the Republic of Finland ( is a Nordic country situated in the Fennoscandian region of northern Europe. World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including Eveline returned to France without him. The following anecdote is taken from his autobiography: after having been arrested under suspicion of espionage in Finland, when the USSR attacked on 30 November 1939, he was saved from being shot only by the intervention of Rolf Nevanlinna. An autobiography, from the Greek αὐτός autos "self" βίος bios "life" and γράφειν graphein "to write" Events 1700 - Battle of Narva — A Swedish army of 8500 men under Charles XII defeats Year 1939 ( MCMXXXIX) was a Common year starting on Sunday (link will display the full calendar of the Gregorian calendar. Rolf Herman Nevanlinna ( October 22, 1895, Joensuu, Eastern Finland - May 28, 1980, Helsinki) is perhaps the This is the version that Nevanlinna propagated after the war. However, such a story is a bit too good to be true. In 1992, the Finnish mathematician Osmo Pekonen went to the archives to check the facts. Based on the documents, he established that Weil was not really going to be shot, even if he was under arrest, and that Nevanlinna probably didn't do - and didn't need to do - anything to save him. Pekonen published a paper[2] on this with an afterword by André Weil himself. Nevanlinna's motivation for concocting such a story of himself as the rescuer of a famous Jewish mathematician probably was the fact that he had been a Nazi sympathizer during the war. The story also appears in Nevanlinna's autobiography, published in Finnish, but the dates don't match with real events at all. It is true, however, that Nevanlinna housed Weil in the summer of 1939 at his summer residence Korkee at Lohja in Finland - and offered Hitler's Mein Kampf as bedside reading. Culture Lohja is a town famed for its cultural events More than a hundred different events are arranged in the town each year by its residents and organizations Hi and welcome to Wikipedia! Please understand that this article is frequently vandalized and vandalism is reverted immediately Mein Kampf ( English: My Struggle/My Battle) is a book by Adolf Hitler. Weil signed 'Bourbaki' in Nevanlinna's guestbook. Nicolas Bourbaki is the collective Pseudonym under which a group of (mainly French) 20th-century Mathematicians wrote a series of books presenting an exposition

Weil returned to France via Sweden and the United Kingdom, and was detained at Le Havre in January 1940. Le Havre is a city in the northwest region of France situated on the right bank of the mouth of the Seine River as it outlets into the Bay of the Seine He was charged with failure to report for duty, and was imprisoned in Le Havre and then Rouen. Rouen (ʁwɑ̃ in French) is the historical capital city of Normandy, in northwestern France on the River Seine, and currently the capital It was in the military prison in Bonne-Nouvelle, a district of Rouen, from February to May, that he did the work that made his reputation. He was tried on May 3, 1940. Events 1491 - Kongo monarch Nkuwu Nzinga is baptised by Portuguese missionaries adopting the baptismal name of João Year 1940 ( MCMXL) was a Leap year starting on Monday (link will display the full 1940 calendar of the Gregorian calendar. Sentenced to five years, he asked to be sent to a military unit instead, and joined a regiment in Cherbourg. After the fall of France, he met up with his family in Marseilles, where he arrived by sea. In World War II, the Battle of France, also known as the Fall of France, was the German invasion of France and the Low Countries He then went to Clermont-Ferrand, where he managed to join Eveline, who had been in German-occupied France. Clermont-Ferrand ( Auvergnat dialect of Occitan: Clarmont-Ferrand / Clarmont d'Auvèrnhe) is a city and commune of France

In January 1941, Weil and his family sailed from Marseilles to New York. Marseille, ( English alt Marseilles mɑrˈseɪ — French: maʁsɛj locally — Provençal Occitan: Marselha maʀˈsijɔ He spent the war in the United States, where he was supported by the Rockefeller Foundation and Guggenheim Foundation. The Rockefeller Foundation (RF is a prominent Philanthropic organization and Private foundation based at 420 Fifth Avenue New York City. For two years, he unhappily taught undergraduate mathematics at Lehigh University. Lehigh University is a private, co-educational University located in Bethlehem, Pennsylvania, in the Lehigh Valley region of He taught at the Universidade de São Paulo, 1945-47, where he worked with Oscar Zariski. The University of São Paulo (in Portuguese Universidade de São Paulo; USP) is one of the three public universities funded by the State of São Paulo. Oscar Zariski (born Oscher Zaritsky 24 April 1899 in Kobrin, Poland (today Belarus) died 4 July He taught at the University of Chicago from 1947 to 1958, before spending the remainder of his career at the Institute for Advanced Study. The University of Chicago is a Private university located principally in the Hyde Park neighborhood of Chicago. The Institute for Advanced Study, located in Princeton New Jersey, United States is a center for theoretical research In 1979, he shared the second Wolf Prize in Mathematics.

Work

He made substantial contributions in many areas, the most important being his discovery of profound connections between algebraic geometry and number theory. Algebraic geometry is a branch of Mathematics which as the name suggests combines techniques of Abstract algebra, especially Commutative algebra, with Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes This began in his doctoral work leading to the Mordell-Weil theorem (1928, and shortly applied in Siegel's theorem on integral points). In Mathematics, the Mordell–Weil theorem states that for an Abelian variety A over a Number field K, the group A ( In Mathematics, Siegel's theorem on integral points is the 1929 result of Carl Ludwig Siegel, that for an Algebraic curve C of genus Mordell's theorem had an ad hoc proof; Weil began the separation of the infinite descent argument into two types of structural approach, by means of height functions for sizing rational points, and by means of Galois cohomology, which was not to be clearly named as that for two more decades. In Mathematics, the Mordell–Weil theorem states that for an Abelian variety A over a Number field K, the group A ( In Mathematics, a proof by infinite descent is a particular kind of proof by Mathematical induction. This is a glossary of arithmetic and Diophantine geometry in Mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts In Mathematics, Galois cohomology is the study of the Group cohomology of Galois modules that is the application of Homological algebra to Both aspects have steadily developed into substantial theories.

Among his major accomplishments were the 1940 proof, while in prison, of the Riemann hypothesis for local zeta-functions, and his subsequent laying of proper foundations for algebraic geometry to support that result (from 1942 to 1946, most intensively). The Riemann hypothesis (also called the Riemann zeta-hypothesis) first formulated by Bernhard Riemann in 1859 is one of the most famous and important unsolved In Number theory, a local zeta-function is a Generating function Z ( t) for the number of solutions of a set of equations By modern standards his claim to have a proof had a very easy ride, but wartime conditions were one factor, and the fact that the German experts made little or no comment another. The so-called Weil conjectures were hugely influential from around 1950; they were later proved by Bernard Dwork, Alexander Grothendieck, Michael Artin, and Pierre Deligne, who completed the most difficult step in 1973. In Mathematics, the Weil conjectures, which had become theorems by 1974 were some highly-influential proposals from the late 1940s by André Weil on the Bernard Morris Dwork ( May 27, 1923 &ndash May 9, 1998) was an American mathematician known for his application of P-adic analysis Experimental infobox see Wikipedia talkPersondata before changing --> Alexander Grothendieck (born March 28, 1928 in Berlin, Germany Michael Artin (born 1934 is an American Mathematician and a professor at MIT, known for his contributions to Algebraic Pierre René Viscount Deligne (born 3 October 1944 in Brussels) is a Belgian Mathematician.

He had introduced the adele ring in the late 1930s, following Claude Chevalley's lead with the ideles, and given a proof of the Riemann-Roch theorem with them (a version appeared in his Basic Number Theory in 1967). In Number theory, the adele ring is a Topological ring which is built on the field of Rational numbers (or more generally any Algebraic Claude Chevalley ( 11 February 1909, Johannesburg, South Africa - 28 June 1984, Paris) was a French In Mathematics, an adelic algebraic group is a Topological group defined by an Algebraic group G over a Number field K In Mathematics, specifically in Complex analysis and Algebraic geometry, the Riemann–Roch theorem is an important tool in the computation of the dimension His 'matrix divisor' (vector bundle avant le jour) Riemann-Roch theorem from 1938 was a very early anticipation of later ideas such as moduli spaces of bundles. In Mathematics, a vector bundle is a topological construction which makes precise the idea of a family of Vector spaces parameterized by another space The Weil conjecture on Tamagawa numbers proved resistant for many years. In Mathematics, the Weil conjecture on Tamagawa numbers was formulated by André Weil in the late 1950s and proved in 1989 Eventually the adelic approach became basic in automorphic representation theory. In Mathematics, the general notion of automorphic form is the extension to Analytic functions perhaps of Several complex variables, of the theory of He picked up another credited Weil conjecture, around 1970, which later under pressure from Serge Lang became known as the Taniyama-Shimura conjecture based on the presentation of the basic ideas at the 1955 Nikkō conference. Serge Lang ( May 19, 1927 – September 12, 2005) was a French -born American Mathematician. In Mathematics, the modularity theorem establishes an important connection between Elliptic curves over the field of Rational numbers and Modular forms His attitude towards conjectures struck many in the field as oblique; he wrote that one should not dignify a guess as a conjecture lightly, and in the Shimura-Taniyama case, the evidence was only there after extensive computational work carried out from the late 1960s.

Other significant results were on Pontryagin duality and differential geometry. In Mathematics, in particular in Harmonic analysis and the theory of Topological groups Pontryagin duality explains the general properties of the Fourier Differential geometry is a mathematical discipline that uses the methods of differential and integral Calculus to study problems in Geometry He introduced the concept of uniform space in general topology. In the Mathematical field of Topology, a uniform space is a set with a uniform structure. In Mathematics, general topology or point-set topology is the branch of Topology which studies properties of Topological spaces and structures His work on sheaf theory hardly appears in his published papers, but correspondence with Henri Cartan in the late 1940s, and reprinted in his collected papers, proved most influential. In Mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the Open sets of a Topological space. Henri Paul Cartan ( July 8, 1904 &ndash August 13, 2008) was a son of Élie Cartan, and was as his father was a distinguished

He discovered that the so-called Weil representation, previously introduced in quantum mechanics by Irving Segal and Shale, gave a contemporary framework for understanding the classical theory of quadratic forms. In Mathematics, the metaplectic group Mp 2 n is a Double cover of the Symplectic group Sp 2 n. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons Irving Ezra Segal ( September 13, 1918 – December 24, 1998) was a mathematician known for work on theoretical Quantum mechanics. In Mathematics, a quadratic form is a Homogeneous polynomial of degree two in a number of variables This was also a beginning of a substantial development by others, connecting representation theory and theta-functions. In the mathematical field of Representation theory, group representations describe abstract groups in terms of Linear transformations of In Mathematics, theta functions are Special functions of Several complex variables.

As expositor

Weil's ideas made an important contribution to the writings and seminars of Bourbaki, before and after WWII. Nicolas Bourbaki is the collective Pseudonym under which a group of (mainly French) 20th-century Mathematicians wrote a series of books presenting an exposition World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including His books had an important influence on research, and exceptional situation in mathematics. (In one famous case, the influence was possibly negative: Alexander Grothendieck is said to have complained of the 'aridity' of Weil's Foundations of Algebraic Geometry. Experimental infobox see Wikipedia talkPersondata before changing --> Alexander Grothendieck (born March 28, 1928 in Berlin, Germany ) The style of his books is clearly demarcated from that of his research papers.

He invented the notation "Ø" for the empty set (q. In Mathematics, and more specifically Set theory, the empty set is the unique set having no ( Zero) members v. ).

Books

His autobiography:

Quotations

See also

Notes

  1. ^ In English, "Weil" is pronounced /ˈveɪ/ vay, while "Weyl" is /ˈvaɪl/ vial and "Wiles" is /ˈwaɪlz/ why-ulz. Hermann Klaus Hugo Weyl ( 9 November 1885 – 8 December 1955) was a German Mathematician. However, in Russian the names Weil and Weyl are pronounced in the same way (as [vʲejlʲ] vail).
  2. ^ Osmo Pekonen: L'affaire Weil à Helsinki en 1939, Gazette des mathématiciens 52 (avril 1992), pp. 13—20. With an afterword by André Weil.

External links

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