A mathematician who is a giant star of 20th century mathematical sciences, whose remarkable achievements through pioneering works in a wide range of subjects, including number theory and algebraic geometry, have contributed greatly to the rapid development of this field.
＊This field then was Field of Mathematical Sciences.
Foundations of algebraic geometry. Amer. Math. Soc. Colleg. Publ. Vol. XXIX(Second edition 1962), 1946.
Dr. André Weil is a renowned mathematician who pioneered research in a broad range of mathematics and has thereby become the most significant contributor to the drastic development of pure mathematics in this century.
Dr. Weil’s own personal contributions are broadly eminent. He conjectured innovative hypotheses and concepts to correlate multiple fields of mathematics and dramatically extend individual fields by breaking down barriers. Examples abound where his works acted as the latent catalysts for many fruitful research studies. Dr. Weil’s penetrating insights and original ideas have played an especially important role in relating number theory to geometry. This served as the basis for many subsequent findings and solutions of remarkable correlations across the traditional boundaries.
In the 1940’s, Dr. Weil completed the foundation for abstract algebraic geometry supported by the abstraction of intersection theory; and utilized it to build the basis for research to relate number theory to algebraic geometry. He then succeeded in inventing a purely algebraic theory of Abelian varieties. This, in turn, led to the proof of the Riemann hypothesis on congruence zeta functions of algebraic curves and Abelian varieties. In 1949, Dr. Weil proposed a detailed hypotheses extending his results on the congruence zeta functions to algebraic varieties of higher dimensions.
This Weil Hypotheses is not a simple generalization, but a formulation born of the deep insights that Dr. Weil had in the topology of abstract algebraic varieties. The hypotheses served as an important guiding principle in later breakthroughs over the entire realms of algebra and geometry.
Dr. Weil has contributed greatly to the development of number theory, by establishing number theory related to algebraic groups; by building the research foundation for automorphic representations; by conducting a global study on zeta functions of algebraic varieties over a number field (known as Hasse-Weil Functions); and by researching the means to combine automorphic functions and algebraic geometry form the standpoint of number theory.
Dr. Weil also contributed to the development of the field of geometry, by studying the harmonic analysis of topological groups; by analyzing characteristic classes; by building the foundation for Kähler geometry; and by conducting geometric studies of theta functions.
Dr. Weil’s mathematical ideology is pure and universal. His influences are felt in many fields of mathematics. Immeasurable is the ideological influence that Dr. Weil has given to researchers in fields such as functional analysis, several complex variables, topology, differential geometry, complex manifolds, Lie group theory, number theory, and algebraic geometry.
In light of these achievements, Dr. André Weil is awarded the 1994 Kyoto Prize in Basic Sciences.
The purpose of the lecture is to give a brief sketch of André Weil’s career as a mathematician, including one important episode the creation of Bourbaki.
Many mathematicians are precocious: there are anecdotes showing the appearance of mathematical gifts at an early age. This was the case with André Weil whose devotion to mathematics appeared about the age of seven. Travels and the influence of foreign cultures also made themselves felt soon enough. Most of his mathematical education was acquired at the Ecole Normale Superieure in Paris, an institution dating back to the French Revolution, which has produced many of the most prominent Scientists in France. It recruits itself through competitive examinations (both in scientific and humanistic subjects) and is remarkable through the spirit of friendship it nurtures among its students and alumni.
This played a role in the creation of a group which, beginning in the 1930’s dedicated itself, under the assumed name of Bourbaki, to the production of a collective work, providing up-to-date foundations for the whole of modern mathematical science. This originated in Strasbourg where André Weil and Henri Cartan, for several years, were jointly in charge of the basic calculus course and the two of them, together with a number of colleagues, all young men from the Ecole Normale, joined forces together for such collective work.