**Dan Quillen** was an American mathematician who won a Fields medal for his work in algebraic topology.

- As a Harvard University student, Quillen took part in the 20th Individual and Team Putnam Competition in 1959 and was named as a Putnam Fellow.
- Quillen felt that Bott had played a huge part in his development as a mathematician.
- Unlike Bott, who made a performance of having everything explained to him many times over, Quillen did not seem at all slow to others, yet he saw himself as someone who had to think things out very slowly and carefully from first principles and had to work hard for every scrap of progress he made.
- Michael Atiyah first met Quillen when he was working for his Ph.D. at Harvard.
- They first saw each other when Quillen took a first year chemistry class in his second year of undergraduate study, but it was their common love of music that brought them together for they met regularly through the Harvard orchestra.
- Jean played the viola and Quillen always claimed that he played the triangle.
- Jean, however, always claimed that Quillen was the orchestra's librarian and occasional trumpeter.
- In 1964, Quillen was awarded his Ph.D. for his thesis on partial differential equations entitled Formal Properties of Over-Determined Systems of Linear Partial Differential Equations.
- After receiving his doctorate, Quillen was appointed to the faculty of Massachusetts Institute of Technology.
- In that brilliant, and often flamboyant, mathematical milieu, Quillen seemed to listen more than he spoke, and he spoke only when he had something substantial to say.
- Quillen was a visiting member of the Institute for Advanced Study at Princeton during 1969-70 when he was strongly influenced by Michael Atiyah, and a Guggenheim Fellow, again at the Institut des Hautes Études Scientifiques in Paris, during 1973-74.
- In the 1960s, Quillen described how to define the homology of simplical objects over many different categories, including sets, algebras over a ring, and unstable algebras over the Steenrod algebra.
- Frank Adams had formulated a conjecture in homotopy theory which Quillen worked on.
- Quillen approached the Adams conjecture with two quite distinct approaches, namely using techniques from algebraic geometry and also using techniques from the modular representation theory of groups.
- Both approaches proved successful, the proof in the first approach being completed by one of Quillen's students, the second approach leading to a proof by Quillen himself.
- The techniques using modular representation theory of groups were used by Quillen to great effect in later work on cohomology of groups and algebraic K-theory.
- The work on cohomology led to Quillen giving a structure theorem for mod p cohomology rings of finite groups, this structure theorem solving a number of open questions in the area.
- Quillen received a Fields Medal at the International Congress of Mathematicians held in Helsinki in 1978.
- Clearly Quillen's year spent in Paris under Grothendieck's influence and at Princeton working with Atiyah were important factors in Quillen's development of algebraic K-theory.
- Jeanne Duflot was undertaking research for her Ph.D. with Quillen as her advisor when he learnt that he would receive the Fields medal.
- It is with rare cases like Quillen that one has the satisfaction of seeing hard, concrete problems solved with general ideas of great force and scope and by the unification of methods from diverse fields of mathematics.
- Quillen has had a deep impact on the perceptions and the very thinking habits of a whole generation of young algebraists and topologists.
- From 1984 to 2006 Quillen was the Waynflete Professor of Pure Mathematics at Magdalen College, Oxford.
- In 2000 the journal K-Theory issued a special part dedicated to Quillen on the occasion of his sixtieth birthday.
- On 22 May 2006 the '39th K-theory Day' at Oxford was set up to celebrate Quillen's 65th birthday.
- Having reached the age of 65, Quillen retired in 2006.
- Quillen's death came after an extremely sad number of years during which Alzheimer's disease took an increasing toll on him.
- Daniel Gray Quillen, 69, may have been heading toward Westside Park ...
- officers were in the area looking for Quillen, who is described as 5-foot-6, 160 pounds with thinning gray hair.
- Police provided a clothing description that said Quillen should be wearing a green plaid shirt, khaki shorts and sandals.
- Among the many honours given to Quillen, in addition to the Fields Medal, we mention that he was a plenary speaker at the International Congress of Mathematicians at Vancouver in August 1974 when he gave the lecture 'Higher Algebraic KKK-Theory'.
- As editors devoted to the subject that Quillen largely created, we are highly appreciative of his crucial support for the journal "K-Theory" and its successor the "Journal of K-Theory", and of all that he has done for our area of mathematics.

Born 27 June 1940, Orange, New Jersey, USA. Died 30 April 2011, Gainsville, Florida, USA.

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Prize Fields Medal, Origin Usa

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive