Alexander Grothendieck
Early Life and Education
Alexander Grothendieck was born on March 28, 1928, in Berlin, Germany. His parents, Hanka Grothendieck and Alexander Schapiro, were anarchists who had moved to Germany from Russia. Grothendieck's early life was marked by the political turmoil of the era, as his father was killed in the Auschwitz during the Second World War.
Grothendieck was primarily raised by foster parents in France and attended the University of Montpellier for his undergraduate studies. He showed an early aptitude for mathematics and was particularly interested in the field of number theory. He completed his Ph.D. at the University of Nancy under the supervision of Laurent Schwartz and Jean Dieudonné, two leading mathematicians of the time.
Career and Contributions to Mathematics
Grothendieck's work revolutionized several areas of mathematics, including algebraic geometry, number theory, and functional analysis. He introduced many concepts and theories that have become fundamental to these fields, such as schemes, topoi, and the étale cohomology.
One of Grothendieck's most significant contributions was his development of the theory of schemes, which generalized the classical concept of algebraic varieties in algebraic geometry. This allowed for a more flexible and powerful approach to geometric problems, and has since become the standard framework for the field.
Grothendieck also made significant contributions to the field of functional analysis, where he developed the theory of nuclear spaces, a class of topological vector spaces. This work was instrumental in the development of the Schwartz distributions, a generalization of the classical notion of a function.
In number theory, Grothendieck introduced the concept of étale cohomology, a tool that has since become indispensable in the study of algebraic varieties over number fields. This work was a key part of his proof of the Weil conjectures, one of the most important achievements in algebraic geometry in the 20th century.
Later Life and Legacy
In the late 1960s, Grothendieck began to withdraw from the mathematical community, and by the 1980s he had largely ceased publishing. He spent the later part of his life in isolation, living in the Pyrenees in southern France.
Despite his withdrawal from public life, Grothendieck's influence on mathematics has been profound. His work has shaped the development of several fields, and his ideas continue to inspire new research. He received many awards for his contributions, including the Fields Medal, often considered the highest honor in mathematics.
Grothendieck passed away on November 13, 2014, but his legacy lives on in the many areas of mathematics that his work transformed.