Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Daniel Gray "Dan" Quillen was an American mathematician. From 1984 to 2006, he was the Waynflete Professor of Pure Mathematics at Magdalen College, Oxford. He is renowned 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. Quillen was born in Orange, New Jersey, and attended Newark Academy. He entered Harvard University, where he earned both his BA and his PhD, the latter of which was completed under the supervision of Raoul Bott with a thesis in partial differential equations. He was a Putnam Fellow in 1959. Quillen obtained a position at the Massachusetts Institute of Technology after completing his doctorate. However, he also spent a number of years at several other universities