The Architect

47Through 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.

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11 Responses to “The Architect”


  1. 1 1 ted

    I like this funeral speech.

  2. 2 2 Harold

    Mathematics is not the most appreciated by the public at large. If his acheivements were in physics, he would probably be more widely acknowledged.

  3. 3 3 Matthew

    More people would remember him if he went around introducing himself as Daniel Fucking Quillen.

  4. 4 4 RGV

    Can you write a biographical post on how you got to working on economics starting in mathematics? Just curious.

    Thanks!

  5. 5 5 John Faben

    “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.”

    If I were running the universe then “being human” would be the very highest I would consider setting the bar for not-dying. Death is a Bad Thing. As far as obscurity, I might have to raise my standards a little.

  6. 6 6 Scott F

    In my universe I’d set the bar extraordinarily low… but then make a kind of automatic ejection button for extraordinarily stupid acts, perhaps with some sort of three strikes policy.
    That said, I’m not sure how I would deal with the misrepresented math genius issue.

  7. 7 7 Cynthia (Quillen) Cohen

    Thanks for your post, I think my Dad would have liked it. Though he wouldn’t have understood your outrage. He was an exceptionally humble person, which was particularly striking given that he had every reason not to be so. He was quite happy to shuffle around quietly in torn jeans and I am quite sure that the majority of people who he met in his life had no idea of what they were dealing with.

    To those who were fortunate enough to be close to him, as well as being a kind, generous, gentle person he had a mind that was as beautiful as the mathematics he pursued. I had the enviable position of having him as my private math tutor whenever I wished, we used to call him “MatDad” when I was in college… Anyway thanks for your post.

  8. 8 8 Steve Landsburg

    Cynthia: Thanks for visiting, and for sharing this.

  9. 9 9 Ken B

    And round that early-laurelled head
    Will flock to gaze the strengthless dead,
    And find unwithered on its curls
    The garland briefer than a girl’s.

  10. 10 10 gaddeswarup
  11. 11 11 Fred F.

    For some reason, I searched for Quillen today. I don’t know why. And discovered he’d just recently passed.

    He was my professor for “abstract algebra” at MIT in the early 80s. I’ll never forget him: he was so kind, thoughtful, and humble. Once, he got lost in the middle of a proof, and said something like that the proof was too hard for him; the class laughed a bit, then applauded, as they knew his accomplishments.

    And I do agree that it’s absurd that a FIELDS MEDALIST would receive so little notice on his passing. There are surely hundreds of students like myself who feel in his debt. I still have the notes from that class.

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