Daniel Quillen Eric Friedlander and Daniel Grayson

Daniel Quillen, 1940–2011, Fields Medalist, transformed many aspects of algebra, geometry, and topology. Especially in a succession of remarkable papers during the ten-year period of 1967–1977, Quillen created astonishing mathematics which continues to inspire current research in many fields. Quillen’s mathematical exposition serves as the ultimate model of clarity. Despite his brilliance, those who knew Quillen were regularly impressed by his generosity and modesty. It has been our privilege to have been mentored by Quillen and to study his remarkable achievements. We feel a deep personal loss at his passing. In this memorial article we assemble twelve contributions from Quillen’s colleagues, collaborators, students, and family. Graeme Segal’s contribution is a broad mathematical biography of Quillen which emphasizes the scope and breadth of his work. Hyman Bass surveys Quillen’s stunning contributions to algebraicK-theory. Quillen’s collaborators Joachim Cuntz and Jean-Louis Loday discuss their work with Quillen on cyclic homology. Michael Atiyah and Ulrike Tillmann, colleagues at Oxford, and Barry Mazur, of Harvard, offer their remembrances. Dennis Sullivan and Andrew Ranicki recall their early mathematical interactions with Quillen. Ken Brown and Jeanne Duflot reflect upon their experiences as students of Quillen. The final contribution, from Quillen’s wife and the mother of their six children, Jean Quillen, gives a glimpse of the shy family man who created such beautiful mathematics.