Alexander Grothendieck: a visionary who did pioneering work in algebraic geometry

Alexander Grothendieck, one of the greatest mathematical minds of the twentieth century, died on November 13

Alexander Grothendieck, one of the greatest mathematical minds of the twentieth century, died last Thursday (November 13).

A recipient of the most prestigious honour in mathematics, the Fields medal, in 1966, he was a visionary who set up several ideas in algebraic geometry for mathematicians who followed.

Though his early work was on Functional analysis, he became interested in algebraic geometry in the mid-1950s, as did many brilliant minds of that period. “He brought in a completely new universal perspective, a new language and thought, using which he solved existing concrete problems and set up a whole superstructure indispensible for generations to come,” says Prof. V. Balaji, algebraic geometer from Chennai Mathematical Institute.

The Grothendieck-Riemann-Roch theorem was one striking result to emerge in this time. His work laid the foundation for many important results, including the solution of the Weil conjectures and Fermat’s last theorem and applications in diverse fields as robotics and cryptography.

Born in 1928, in Germany, Grothendieck witnessed rebellion early. When he was five, his parents left him with a family in Hamburg and moved to France. In 1942, he attended school, at Collège Cévénol, and then went on to study in Paris. He took up a position at Institut des Hautes Etudes Scientifique, near Paris, where he did phenomenal work.

In his own words, taken from his autobiographical work Récoltes et Semailles: “In our acquisition of knowledge of the Universe (whether mathematical or otherwise) that which renovates the quest is nothing more nor less than complete innocence ... Although so often the object of our contempt and of our private fears, it is always in us. It alone can unite humility with boldness so as to allow us to penetrate to the heart of things, or allow things to enter us and take possession of us. This unique power is in no way a privilege given to ‘exceptional talents’ — persons of incredible brain power (for example)... Yet it is not these gifts, nor the most determined ambition combined with irresistible will power that enables one to surmount the ‘invisible yet formidable boundaries’ that encircle our universe. Only innocence can surmount them...”