[From: wilbur jonsson] Daniel Quillen obituary (fwd)

[From: wilbur jonsson] Daniel Quillen obituary (fwd)

[Michael Barr]

This should be interesting to a general categorical audience.

Mike

---------- Forwarded message ----------
Date: Fri, 24 Jun 2011 22:13:26 +0100 (BST)
From: guardian.co.uk <noreply@guardian.co.uk>
To: barr@math.mcgill.ca
Subject: [From: wilbur jonsson] Daniel Quillen obituary

wilbur jonsson spotted this on the guardian.co.uk site and thought you should see it.

-------
Note from wilbur jonsson:

Rather better and more thoughtful than the previous obit

W
-------

To see this story with its related links on the guardian.co.uk site, go to 
http://www.guardian.co.uk/science/2011/jun/23/daniel-quillen-obituary

Daniel Quillen obituary

A US mathematician, he developed a key algebraic theory

Graeme Segal
Friday June 24 2011
The Guardian


http://www.guardian.co.uk/science/2011/jun/23/daniel-quillen-obituary


The most important steps forward in mathematics come less often from 
solving a particular problem than from finding a new way of&nbsp;looking 
at a class of&nbsp;problems. The work of the American mathematician Daniel 
Quillen, who has died aged 70 after suffering from Alzheimer's disease, 
was of that rare kind. He transformed whole areas of his subject in a 
career spent first at the Massachusetts Institute of&nbsp;Technology 
(MIT), and then at Oxford.

His most distinctive contributions came in a torrent of exciting work 
produced at the Institute for Advanced Study in Princeton, New Jersey, in 
1969-70. His proof of the Adams conjecture in topology, relating to the 
classification of mappings of one sphere on to another, made crucial use 
of Alexander Grothendieck's work in algebraic geometry. It led on to his 
creation of&nbsp;algebraic K-theory, nowadays a very active subfield of 
algebra and number theory, far from its roots in topology.

The conjecture was almost simultaneously proved by Dennis Sullivan, also 
using Grothendieck's theory, but in a quite different way. His proof 
opened up an unrelated new area of mathematics. By a quirk of history, a 
few years later a much more elementary proof of the Adams conjecture was 
found, not using Grothendieck's theory. Had this happened earlier, a lot 
of current mathematics might not have been invented.

Born in Orange, New Jersey, Quillen won scholarships to Newark academy, 
and then to Harvard, where as a graduate student he worked under Raoul 
Bott, before going to a&nbsp;post at&nbsp;MIT. From the warm, outgoing 
Bott, Quillen learned that one did not have to be quick to be an 
outstanding mathematician. Unlike Bott, who always insisted on having 
everything explained to him many times, Quillen did not seem slow to 
others, but he saw himself as a person who had to think everything out 
very carefully from first principles, and work hard for every scrap of 
progress. Charmingly modest about his abilities, he was nonetheless 
ambitious and driven.

Bott was a universal mathematician, contributing to many different areas 
of&nbsp;the subject while always preserving the perspective of a geometer, 
and Quillen, too, never confined himself to a&nbsp;"field". His most 
famous achievements were in algebra, but he somehow came at it from the 
outside. He was interested in almost all of mathematics, and in a lot of 
physics as well.

Grothendieck, Quillen's second great influence, is famous for his mystical 
conviction that a mathematical problem will solve itself when one has 
found by sufficient humble attentiveness exactly its right context and 
formulation. He&nbsp;opened up one of the most magical panoramas of modern 
mathematics, connecting number theory and geometry, and his influence, as 
well as that of the MIT topologist Daniel Kan, showed in Quillen's first 
lastingly famous work.

This was published in 1967, soon after he had completed his PhD thesis on 
partial differential equations, but in a quite different area. In the 
previous two decades it had been discovered that "shapes" ? the technical 
term is&nbsp;homotopy types ? could be attributed to many algebraic and 
combinatorial structures with, at first sight, nothing geometrical about 
them. The way this had been done, however, remained piecemeal and ad hoc.

Quillen produced a systematic theory of what kinds of structures have 
homotopy types, and how they can be studied. At the time, these ideas 
attracted little attention outside a small band of enthusiasts. Most 
mathematicians thought he was carrying abstraction too far. But 30 years 
later, the theory was becoming widely used, and it remains central on the 
mathematical stage today.

Before his year at the Institute for Advanced Study, Quillen spent 1968-69 
at its Parisian equivalent, the Institut des Hautes ?tudes Scientifiques, 
where Grothendieck was a central figure. Quillen's work, though much 
influenced by Grothendieck's, has a different flavour. Both aimed for 
simplicity, but Grothendieck found it in generality, while Quillen's 
guiding conviction was that to understand a mathematical phenomenon one 
must seek out its very simplest concrete manifestation. He&nbsp;felt he 
was not good with words, but his mathematical writings, produced by long 
agonised struggles to devise accounts that others would understand, are 
models of lucid, accurate, concise expression. Throughout his life he kept 
a beautifully written record of the mathematical thoughts he had each day, 
and they form an extraordinary archive.

In 1978 Quillen was awarded a Fields medal, the discipline's highest 
honour. By then his interests had shifted back towards global geometry and 
analysis. His goal was to show that Alain Connes's non-commutative 
geometry, in particular his cyclic homology, then becoming important in 
analysis and quantum theory, can be understood by&nbsp;traditional 
geometry and topology. This task, in many different guises, occupied the 
rest of his career.

In the 1980s, Quillen made at least three outstanding contributions that 
will continue to shape mathematics: the concept of a "superconnection" in 
differential geometry and analysis, the invention of the "determinant 
line" as a tool in index theory, and the Loday-Quillen theorem relating 
cyclic homology to algebraic K-theory.

Early in the decade, Quillen decided that he wanted to be at Oxford, 
attracted especially by its leading mathematician, Michael Atiyah. After 
spending 1982-83 there, in 1984 he moved from MIT to Oxford as Waynflete 
professor, where he remained until retirement in 2006. (A joke at the time 
of his appointment had an MIT dean rushing to him with an&nbsp;offer to 
halve his salary.)

Quillen loved music, especially Bach, and met his wife, Jean, in the 
Harvard orchestra. They had two children before he completed his PhD, and 
went on to have another four. Although his hair turned white in his 20s, 
he never lost the look or the manner of a boy. He is survived by Jean, 
their four daughters and two sons, 20 grandchildren, and one 
great-grandchild.

? Daniel Gray Quillen, mathematician, born 22 June 1940; died 30 April 2011



[For admin and other information see: http://www.mta.ca/~cat-dist/ ]