Grothendieck tells you how to solve every problem. - John L. Rhodes
Grothendieck revealed the importance of covering in algebra. Philosophically, the set of all covers encodes every possible way of thinking about, unraveling, and understanding an algebraic structure.
The French mathematician extended the work of Weil & Zariski, revolutionized our understanding of algebraic geometry and homological algebra, and introduced K-theory. He was awarded the Fields Medal in 1966. The importance of his ideas for mathematics is only beginning to be felt.