Through the 1970s — which is to say, yesterday — Dan Quillen barraged the field of algebraic topology with a stream of new techniques and concepts that not only invigorated the field, but ramped up its power to solve problems in geometry, arithmetic and other mathematical areas where you might have thought topology had no business sticking its nose.
The greatest of these great accomplishments was Quillen’s development of higher algebraic K-theory, a long-sought holy grail for mathematicians. Pre-Quillen, one had a sense that there ought to be a subject called higher K-theory, and a general sense of what it should look like, and reasons to hope that K-theory, if only we could figure out what it was, would be the great unifying theme behind much of mathematics, and a tool for translating insights in one field into useful techniques in another. Many had tried and failed to lay the foundations of the subject. Then Quillen, in one 63 page paper, not only laid the foundations but brought the subject to a state of maturity that, in the words of Hyman Bass, one normally expects from the efforts of several mathematicians over several years:
The paper…is essentially without mathematical precursors. Reading it for the first time is like landing on a new and friendly mathematical planet. One meets there not only new theorems and new methods, but new mathematical creatures and a complete paradigm of gestures for dealing with them.
Much of my mathematical youth was spent exploring that planet. I met Quillen only once, and very briefly, but great mathematicians, like great poets, reveal so much of themselves in their work that one comes to feel a certain intimacy just by studying them. In that sense, Quillen was my close companion many a year.
Dan Quillen died this week at the age of 70, after a five year battle with Alzheimer’s. Scouring the web for obituaries and other recent mentions, I found very little besides a brief article from a Gainesville newspaper about an Alzheimer’s patient named Daniel Gray Quillen who had gone briefly missing in June, 2010. Followup stories identify the missing man as “a senior citizen with Alzheimer’s”.
“A senior citizen”?!?!?! Part of me wants to scream: “Dammit, this is no generic senior citizen! This is Daniel Fucking Quillen, Fields Medalist, Cole Prize Winner, architect of higher K-theory, conqueror of the Serre conjecture, and one of the intellectual giants of the 20th century!”
Arguably none of that has any place in a short note about a man gone briefly missing, so my gripe is not with the Gainesville Sun. My gripe is with the Universe. If I were running the Universe, there’d be some level of accomplishment that confers immunity from death, deterioration and obscurity. I’m not sure exactly where I’d set that bar, but I’m sure Dan Quillen would have cleared it.