He is known for being the "prime architect" of higher algebraic K-theory, for which he was awarded the Cole Prize in 1975 and the Fields Medal in 1978.
He entered Harvard University, where he earned both his AB, in 1961, and his PhD in 1964; the latter completed under the supervision of Raoul Bott, with a thesis in partial differential equations.
In 1969–70, he was a visiting member of the Institute for Advanced Study in Princeton, where he came under the influence of Michael Atiyah.
In 1978, Quillen received a Fields Medal at the International Congress of Mathematicians held in Helsinki.
[4] Quillen's best known contribution (mentioned specifically in his Fields medal citation) was his formulation of higher algebraic K-theory in 1972.