André Weil
Encyclopedia
André Weil (ɑ̃dʁe vɛj) was an influential mathematician
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. He is especially known for his foundational work in number theory
and algebraic geometry
. He was a founding member and the de facto early leader of the influential Bourbaki group. The philosopher Simone Weil
was his sister.
to Alsatian
agnostic
Jewish parents who fled the annexation of Alsace-Lorraine
to Germany
. His only sibling was Simone Weil
, a famous philosopher. Weil studied in Paris, Rome
and Göttingen
and received his doctorate
in 1928. While in Germany, he befriended Carl Ludwig Siegel
. He spent two academic years at Aligarh Muslim University
from 1930. Hinduism
and Sanskrit literature
were his life-long interests. After one year in Marseille
, he taught six years in Strasbourg
. He married Éveline in 1937.
Weil was in Finland
when World War II
broke out; he had been traveling in Scandinavia since April 1939. Éveline returned to France without him. Weil was mistakenly arrested in Finland at the outbreak of the Winter War
suspected of spying; however, accounts of his life having been at danger have been shown to be exaggerated. Weil returned to France via Sweden and the United Kingdom, and was detained at Le Havre
in January 1940. He was charged with failure to report for duty, and was imprisoned in Le Havre and then Rouen
. 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 3 May 1940. 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 Marseille, where he arrived by sea. He then went to Clermont-Ferrand
, where he managed to join Éveline, who had been in German-occupied France.
In January 1941, Weil and his family sailed from Marseille
to New York. He spent the war in the United States, where he was supported by the Rockefeller Foundation
and Guggenheim Foundation
. For two years, he taught undergraduate mathematics at Lehigh University
. He taught at the Universidade de São Paulo, 1945–47, where he worked with Oscar Zariski
. He taught at the University of Chicago
from 1947 to 1958, before spending the remainder of his career at the Institute for Advanced Study
. In 1979, he shared the second Wolf Prize in Mathematics
.
and number theory
. This began in his doctoral work leading to the Mordell–Weil theorem
(1928, and shortly applied in Siegel's theorem on integral points). 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. Both aspects have steadily developed into substantial theories.
Among his major accomplishments were the 1940 proof, of the Riemann hypothesis
for zeta-functions of curves over finite fields, and his subsequent laying of proper foundations for algebraic geometry to support that result (from 1942 to 1946, most intensively). 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.
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). His 'matrix divisor' (vector bundle
avant la lettre) Riemann–Roch theorem from 1938 was a very early anticipation of later ideas such as moduli spaces of bundles. The Weil conjecture on Tamagawa numbers
proved resistant for many years. Eventually the adelic approach became basic in automorphic representation theory. He picked up another credited Weil conjecture, around 1967, which later under pressure from Serge Lang
(resp. of Serre) became known as the Taniyama–Shimura conjecture (resp. Taniyama-Weil conjecture) based on a roughly formulated question of Taniyama at the 1955 Nikkō conference. His attitude towards conjectures was that one should not dignify a guess as a conjecture lightly, and in the 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. He introduced the concept of a uniform space
in general topology
, as a by-product of his collaboration with Nicolas Bourbaki (of which he was a Founding Father). 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.
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 form
s. This was also a beginning of a substantial development by others, connecting representation theory
and theta-functions.
He also wrote several books on the history of Number Theory.
.
He says in the page 114 of his autobiography that he was responsible for the null set symbol (Ø) and it came from the Norwegian alphabet, with which he alone among the Bourbaki group was familiar.
to justify his stand: he said his true dharma
was the pursuit of mathematics and that was what he should be doing, not assisting in the war effort, however just the cause.
His Collected Papers:
His autobiography
:
Memoir by his daughter:
At Home with Andre and Simone Weil by Sylvie Weil, translated by Benjamin Ivry
; ISBN 978-0810127043, Northwestern University Press
, 2010.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
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. He is especially known for his foundational work in number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
and algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
. He was a founding member and the de facto early leader of the influential Bourbaki group. The philosopher Simone Weil
Simone Weil
Simone Weil , was a French philosopher, Christian mystic, and social activist.-Biography:Weil was born in Paris to Alsatian agnostic Jewish parents who fled the annexation of Alsace-Lorraine to Germany. She grew up in comfortable circumstances, and her father was a doctor. Her only sibling was...
was his sister.
Life
Born in ParisParis
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
to Alsatian
Alsace
Alsace is the fifth-smallest of the 27 regions of France in land area , and the smallest in metropolitan France. It is also the seventh-most densely populated region in France and third most densely populated region in metropolitan France, with ca. 220 inhabitants per km²...
agnostic
Agnosticism
Agnosticism is the view that the truth value of certain claims—especially claims about the existence or non-existence of any deity, but also other religious and metaphysical claims—is unknown or unknowable....
Jewish parents who fled the annexation of Alsace-Lorraine
Alsace-Lorraine
The Imperial Territory of Alsace-Lorraine was a territory created by the German Empire in 1871 after it annexed most of Alsace and the Moselle region of Lorraine following its victory in the Franco-Prussian War. The Alsatian part lay in the Rhine Valley on the west bank of the Rhine River and east...
to Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
. His only sibling was Simone Weil
Simone Weil
Simone Weil , was a French philosopher, Christian mystic, and social activist.-Biography:Weil was born in Paris to Alsatian agnostic Jewish parents who fled the annexation of Alsace-Lorraine to Germany. She grew up in comfortable circumstances, and her father was a doctor. Her only sibling was...
, a famous philosopher. Weil studied in Paris, Rome
Rome
Rome is the capital of Italy and the country's largest and most populated city and comune, with over 2.7 million residents in . The city is located in the central-western portion of the Italian Peninsula, on the Tiber River within the Lazio region of Italy.Rome's history spans two and a half...
and Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
and received his doctorate
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
in 1928. While in Germany, he befriended Carl Ludwig Siegel
Carl Ludwig Siegel
Carl Ludwig Siegel was a mathematician specialising in number theory and celestial mechanics. He was one of the most important mathematicians of the 20th century.-Biography:...
. He spent two academic years at Aligarh Muslim University
Aligarh Muslim University
Aligarh Muslim University ,is a residential academic university, established in 1875 by Sir Syed Ahmed Khan as Mohammedan Angelo-Oriental College and later granted the status of Central University by an Act of the Indian Parliament in 1920...
from 1930. Hinduism
Hinduism
Hinduism is the predominant and indigenous religious tradition of the Indian Subcontinent. Hinduism is known to its followers as , amongst many other expressions...
and Sanskrit literature
Sanskrit literature
Literature in Sanskrit begins with the Vedas, and continues with the Sanskrit Epics of Iron Age India; the golden age of Classical Sanskrit literature dates to late Antiquity . Literary production saw a late bloom in the 11th century before declining after 1100 AD...
were his life-long interests. After one year in Marseille
Marseille
Marseille , known in antiquity as Massalia , is the second largest city in France, after Paris, with a population of 852,395 within its administrative limits on a land area of . The urban area of Marseille extends beyond the city limits with a population of over 1,420,000 on an area of...
, he taught six years in Strasbourg
Strasbourg
Strasbourg is the capital and principal city of the Alsace region in eastern France and is the official seat of the European Parliament. Located close to the border with Germany, it is the capital of the Bas-Rhin département. The city and the region of Alsace are historically German-speaking,...
. He married Éveline in 1937.
Weil was in Finland
Finland
Finland , officially the Republic of Finland, is a Nordic country situated in the Fennoscandian region of Northern Europe. It is bordered by Sweden in the west, Norway in the north and Russia in the east, while Estonia lies to its south across the Gulf of Finland.Around 5.4 million people reside...
when World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
broke out; he had been traveling in Scandinavia since April 1939. Éveline returned to France without him. Weil was mistakenly arrested in Finland at the outbreak of the Winter War
Winter War
The Winter War was a military conflict between the Soviet Union and Finland. It began with a Soviet offensive on 30 November 1939 – three months after the start of World War II and the Soviet invasion of Poland – and ended on 13 March 1940 with the Moscow Peace Treaty...
suspected of spying; however, accounts of his life having been at danger have been shown to be exaggerated. Weil returned to France via Sweden and the United Kingdom, and was detained at Le Havre
Le Havre
Le Havre is a city in the Seine-Maritime department of the Haute-Normandie region in France. It is situated in north-western France, on the right bank of the mouth of the river Seine on the English Channel. Le Havre is the most populous commune in the Haute-Normandie region, although the total...
in January 1940. He was charged with failure to report for duty, and was imprisoned in Le Havre and then Rouen
Rouen
Rouen , in northern France on the River Seine, is the capital of the Haute-Normandie region and the historic capital city of Normandy. Once one of the largest and most prosperous cities of medieval Europe , it was the seat of the Exchequer of Normandy in the Middle Ages...
. 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 3 May 1940. Sentenced to five years, he asked to be sent to a military unit instead, and joined a regiment in Cherbourg
Cherbourg-Octeville
-Main sights:* La Glacerie has a race track.* The Cité de la Mer is a large museum devoted to scientific and historical aspects of maritime subjects.* Cherbourg Basilica* Jardin botanique de la Roche Fauconnière, a private botanical garden.* Le Trident theatre...
. After the fall of France, he met up with his family in Marseille, where he arrived by sea. He then went to Clermont-Ferrand
Clermont-Ferrand
Clermont-Ferrand is a city and commune of France, in the Auvergne region, with a population of 140,700 . Its metropolitan area had 409,558 inhabitants at the 1999 census. It is the prefecture of the Puy-de-Dôme department...
, where he managed to join Éveline, who had been in German-occupied France.
In January 1941, Weil and his family sailed from Marseille
Marseille
Marseille , known in antiquity as Massalia , is the second largest city in France, after Paris, with a population of 852,395 within its administrative limits on a land area of . The urban area of Marseille extends beyond the city limits with a population of over 1,420,000 on an area of...
to New York. He spent the war in the United States, where he was supported by the Rockefeller Foundation
Rockefeller Foundation
The Rockefeller Foundation is a prominent philanthropic organization and private foundation based at 420 Fifth Avenue, New York City. The preeminent institution established by the six-generation Rockefeller family, it was founded by John D. Rockefeller , along with his son John D. Rockefeller, Jr...
and Guggenheim Foundation
John Simon Guggenheim Memorial Foundation
The John Simon Guggenheim Memorial Foundation was founded in 1925 by Mr. and Mrs. Simon Guggenheim in memory of their son, who died April 26, 1922...
. For two years, he taught undergraduate mathematics at Lehigh University
Lehigh University
Lehigh University is a private, co-educational university located in Bethlehem, Pennsylvania, in the Lehigh Valley region of the United States. It was established in 1865 by Asa Packer as a four-year technical school, but has grown to include studies in a wide variety of disciplines...
. He taught at the Universidade de São Paulo, 1945–47, where he worked with Oscar Zariski
Oscar Zariski
Oscar Zariski was a Russian mathematician and one of the most influential algebraic geometers of the 20th century.-Education:...
. He taught at the University of Chicago
University of Chicago
The University of Chicago is a private research university in Chicago, Illinois, USA. It was founded by the American Baptist Education Society with a donation from oil magnate and philanthropist John D. Rockefeller and incorporated in 1890...
from 1947 to 1958, before spending the remainder of his career at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
. In 1979, he shared the second Wolf Prize in Mathematics
Wolf Prize in Mathematics
The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts...
.
Work
He made substantial contributions in many areas, the most important being his discovery of profound connections between algebraic geometryAlgebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
and number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
. This began in his doctoral work leading to the Mordell–Weil theorem
Mordell–Weil theorem
In mathematics, the Mordell–Weil theorem states that for an abelian variety A over a number field K, the group A of K-rational points of A is a finitely-generated abelian group, called the Mordell-Weil group...
(1928, and shortly applied in Siegel's theorem on integral points). Mordell's theorem had an ad hoc proof; Weil began the separation of the infinite descent
Infinite descent
In mathematics, a proof by infinite descent is a particular kind of proof by contradiction which relies on the fact that the natural numbers are well ordered. One typical application is to show that a given equation has no solutions. Assuming a solution exists, one shows that another exists, that...
argument into two types of structural approach, by means of height functions for sizing rational points, and by means of Galois cohomology
Galois cohomology
In mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups...
, which was not to be clearly named as that for two more decades. Both aspects have steadily developed into substantial theories.
Among his major accomplishments were the 1940 proof, of the Riemann hypothesis
Riemann hypothesis
In mathematics, the Riemann hypothesis, proposed by , is a conjecture about the location of the zeros of the Riemann zeta function which states that all non-trivial zeros have real part 1/2...
for zeta-functions of curves over finite fields, and his subsequent laying of proper foundations for algebraic geometry to support that result (from 1942 to 1946, most intensively). The so-called Weil conjectures
Weil conjectures
In mathematics, the Weil conjectures were some highly-influential proposals by on the generating functions derived from counting the number of points on algebraic varieties over finite fields....
were hugely influential from around 1950; they were later proved by Bernard Dwork
Bernard Dwork
Bernard Morris Dwork was an American mathematician, known for his application of p-adic analysis to local zeta functions, and in particular for the first general results on the Weil conjectures. Together with Kenkichi Iwasawa he received the Cole Prize in 1962.Dwork received his Ph.D. at Columbia...
, Alexander Grothendieck
Alexander Grothendieck
Alexander Grothendieck is a mathematician and the central figure behind the creation of the modern theory of algebraic geometry. His research program vastly extended the scope of the field, incorporating major elements of commutative algebra, homological algebra, sheaf theory, and category theory...
, Michael Artin
Michael Artin
Michael Artin is an American mathematician and a professor emeritus in the Massachusetts Institute of Technology mathematics department, known for his contributions to algebraic geometry. and also generally recognized as one of the outstanding professors in his field.Artin was born in Hamburg,...
, and Pierre Deligne
Pierre Deligne
- See also :* Deligne conjecture* Deligne–Mumford moduli space of curves* Deligne–Mumford stacks* Deligne cohomology* Fourier–Deligne transform* Langlands–Deligne local constant- External links :...
, who completed the most difficult step in 1973.
He had introduced the adele ring
Adele ring
In algebraic number theory and topological algebra, the adele ring is a topological ring which is built on the field of rational numbers . It involves all the completions of the field....
in the late 1930s, following Claude Chevalley
Claude Chevalley
Claude Chevalley was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory, and the theory of algebraic groups...
's lead with the ideles, and given a proof of the Riemann–Roch theorem
Riemann–Roch theorem
The Riemann–Roch theorem is an important tool in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles...
with them (a version appeared in his Basic Number Theory in 1967). His 'matrix divisor' (vector bundle
Vector bundle
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X : to every point x of the space X we associate a vector space V in such a way that these vector spaces fit together...
avant la lettre) Riemann–Roch theorem from 1938 was a very early anticipation of later ideas such as moduli spaces of bundles. The Weil conjecture on Tamagawa numbers
Weil conjecture on Tamagawa numbers
In mathematics, the Weil conjecture on Tamagawa numbers is a result about algebraic groups formulated by André Weil in the late 1950s and proved in 1989...
proved resistant for many years. Eventually the adelic approach became basic in automorphic representation theory. He picked up another credited Weil conjecture, around 1967, which later under pressure from Serge Lang
Serge Lang
Serge Lang was a French-born American mathematician. He was known for his work in number theory and for his mathematics textbooks, including the influential Algebra...
(resp. of Serre) became known as the Taniyama–Shimura conjecture (resp. Taniyama-Weil conjecture) based on a roughly formulated question of Taniyama at the 1955 Nikkō conference. His attitude towards conjectures was that one should not dignify a guess as a conjecture lightly, and in the Taniyama case, the evidence was only there after extensive computational work carried out from the late 1960s.
Other significant results were on Pontryagin duality
Pontryagin duality
In mathematics, specifically in harmonic analysis and the theory of topological groups, Pontryagin duality explains the general properties of the Fourier transform on locally compact groups, such as R, the circle or finite cyclic groups.-Introduction:...
and differential geometry. He introduced the concept of a uniform space
Uniform space
In the mathematical field of topology, a uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure which is used to define uniform properties such as completeness, uniform continuity and uniform convergence.The conceptual difference between...
in general topology
General topology
In mathematics, general topology or point-set topology is the branch of topology which studies properties of topological spaces and structures defined on them...
, as a by-product of his collaboration with Nicolas Bourbaki (of which he was a Founding Father). His work on sheaf theory hardly appears in his published papers, but correspondence with Henri Cartan
Henri Cartan
Henri Paul Cartan was a French mathematician with substantial contributions in algebraic topology. He was the son of the French mathematician Élie Cartan.-Life:...
in the late 1940s, and reprinted in his collected papers, proved most influential.
He discovered that the so-called Weil representation, previously introduced in quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
by Irving Segal
Irving Segal
Irving Ezra Segal was a mathematician known for work on theoretical quantum mechanics.He was at the Massachusetts Institute of Technology...
and Shale, gave a contemporary framework for understanding the classical theory of quadratic form
Quadratic form
In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example,4x^2 + 2xy - 3y^2\,\!is a quadratic form in the variables x and y....
s. This was also a beginning of a substantial development by others, connecting representation theory
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
and theta-functions.
He also wrote several books on the history of Number Theory.
As expositor
Weil's ideas made an important contribution to the writings and seminars of Bourbaki, before and after World War IIWorld War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
.
He says in the page 114 of his autobiography that he was responsible for the null set symbol (Ø) and it came from the Norwegian alphabet, with which he alone among the Bourbaki group was familiar.
Beliefs
Indian (Hindu) thought had great influence on Weil. In his autobiography, he says that the only religious ideas that appealed to him were those to be found in Hindu philosophical thought. During the second World War, Weil refused to do military service and cited the Bhagavad GitaBhagavad Gita
The ' , also more simply known as Gita, is a 700-verse Hindu scripture that is part of the ancient Sanskrit epic, the Mahabharata, but is frequently treated as a freestanding text, and in particular, as an Upanishad in its own right, one of the several books that constitute general Vedic tradition...
to justify his stand: he said his true dharma
Dharma
Dharma means Law or Natural Law and is a concept of central importance in Indian philosophy and religion. In the context of Hinduism, it refers to one's personal obligations, calling and duties, and a Hindu's dharma is affected by the person's age, caste, class, occupation, and gender...
was the pursuit of mathematics and that was what he should be doing, not assisting in the war effort, however just the cause.
Books
- Arithmétique et géométrie sur les variétés algébriques (1935)
- Sur les espaces à structure uniforme et sur la topologie générale (1937)
- L'intégration dans les groupes topologiques et ses applications (1940) | year=1946}}
- Sur les courbes algébriques et les variétés qui s’en déduisent (1948)
- Variétés abéliennes et courbes algébriques (1948)
- Introduction à l'étude des variétés kählériennes (1958)
- Discontinuous subgroups of classical groups (1958) Chicago lecture notes
- Basic Number Theory (1967)
- Dirichlet Series and Automorphic Forms, Lezioni Fermiane (1971) Lecture Notes in Mathematics, vol. 189,
- Essais historiques sur la théorie des nombres (1975)
- Elliptic Functions According to Eisenstein and Kronecker (1976)
- Number Theory for Beginners (1979) with Maxwell Rosenlicht
- Adeles and Algebraic Groups (1982)
- Number Theory: An Approach Through History From Hammurapi to Legendre (1984)
His Collected Papers:
- Œuvres Scientifiques, Collected Works, three volumes (1979)
His autobiography
Autobiography
An autobiography is a book about the life of a person, written by that person.-Origin of the term:...
:
- French: Souvenirs d’Apprentissage (1991) ISBN 3764325003. Review in English by J. E. Cremona.
- English translation: The Apprenticeship of a Mathematician (1992), ISBN 0817626506
Memoir by his daughter:
At Home with Andre and Simone Weil by Sylvie Weil, translated by Benjamin Ivry
Benjamin Ivry
Benjamin Ivry is an American writer on the arts, broadcaster and translator.Ivry is author of biographies of Francis Poulenc, Arthur Rimbaud, and Maurice Ravel, as well as a poetry collection, Paradise for the Portuguese Queen...
; ISBN 978-0810127043, Northwestern University Press
Northwestern University Press
Northwestern University Press is the university press of Northwestern University in Evanston, Illinois, USA.- History :Northwestern University Press was founded in 1893, at first specializing in legal periodicals. Today, the Press publishes scholarly books of fiction, non-fiction, and literary...
, 2010.
Quotations
- "God exists since mathematics is consistent, and the Devil exists since we cannot prove it."
- Weil's Law of university hiring: "First rate people hire other first rate people. Second rate people hire third rate people. Third rate people hire fifth rate people."
External links
- André Weil, by A.Borel, Bull.AMS 46 (2009), 661-666.
- André Weil: memorial articles in the Notices of AMSNotices of the American Mathematical SocietyNotices of the American Mathematical Society is a membership magazine of the American Mathematical Society, published monthly except for the combined June/July issue. It is the world's most widely read mathematics magazine, sent to the approximately 30,000 AMS members worldwide...
by Armand BorelArmand BorelArmand Borel was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993...
, Pierre CartierPierre Cartier (mathematician)Pierre Cartier is a mathematician. An associate of the Bourbaki group and at one time a colleague of Alexander Grothendieck, his interests have ranged over algebraic geometry, representation theory, mathematical physics, and category theory....
, Komaravolu Chandrasekharan, Shiing-Shen ChernShiing-Shen ChernShiing-Shen Chern was a Chinese American mathematician, one of the leaders in differential geometry of the twentieth century.-Early years in China:...
, and Shokichi Iyanaga - Image of Weil
- A 1940 Letter of André Weil on Analogy in Mathematics
- Artless innocents and ivory-tower sophisticates: Some personalities on the Indian mathematical scene - M. S. Raghunathan
