In 1970, at the age of 42, Grothendieck started to turn away from mathematics and later from society in general. His techniques were a necessary tool in the work done by Maryam Mirzakhani that earned her the historic first Fields Medal awarded to a woman earlier this summer. Grothendieck's reinvention of the foundations of algebraic geometry led to countless discoveries in the field in the last half century.
The techniques and generalizations originally developed by Grothendieck became the main set of tools used by mathematicians working in algebraic geometry for the last fifty years. In the 1960s, Grothendieck and his contemporaries revolutionized algebraic geometry by establishing a powerful and abstract foundation for the subject.
