Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

July 14, 2007

George Mackey

Posted by David Corfield

The latest edition of the Notices of the American Mathematical Society is out, and it contains reminiscences about the life and work of George Mackey.

For a long time I’ve been attracted by big mathematical visions. While I was PhD student I’d hunt out the informal writings of people like Atiyah and MacLane. But I think my favourite author at the time was Mackey, in particular the story of maths he had told in ‘The scope and history of commutative and noncommutative harmonic analysis’.

As Caroline Series puts it

I do not know any other writer with quite his gift of sifting out the essentials and exposing the bare bones of a subject. There is no doubt that his unique ability to cut through the technicalities and draw diverse strands together into one grand story has been a hugely wide and enduring influence. (p. 21)

Later when carrying out research on the rise of the groupoid concept, I decided to contact him to ask him about his role and about how he saw groupoids fitting into the big picture. His reply included the remark:

At the moment I am occupied with developing some recent ideas I have had on a possible extensive development of my methods to apply to a much larger part of mathematics and produce more unification. I will explain more fully when I have made a bit more progress in seeking the proper formulation.

He spoke of some manuscripts he had written along these lines.

Caroline Series, again:

Mackey had the habit of writing lengthy letters about his latest discoveries. Long after retirement, indeed right up to a couple of years before his death, he continued working on various projects which between them seemed to involve nothing less than unravelling the entire mathematical history of the twentieth century. Subjects expanded to include statistical mechanics, number theory, complex analysis, probability, and more. (p. 24)

Someone could do us a great service by collecting these writings and publishing them.

Posted at July 14, 2007 3:00 PM UTC

TrackBack URL for this Entry:

2 Comments & 0 Trackbacks

Re: George Mackey

I may have first heard of and read George Mackey when I grappled with group representations, and with von Neumann Algebras.

It is interesting to me that he, in some sense, started in Chemistry and Chemical Engineering, as my Honorable Mention in the Westinghouse Science Talent Search seemed to suggest that I would follow Linus Pauling in that endeavor.

He may have been mentioned again to me in regards to the Putnam exam, where Caltech often placed people at or near the top. I need not mention how important Marshall Stone was at Caltech and radiating to the universe therefrom.

I heard about, and was influenced by, some of Mackey’s students, such as John Kalman.

I don’t understand the essence of Operator Algebras at his breakthrough level, but do see that it is crucial to to the foundations of quantum mechanics. I would love to understand his semidirect product/ergodicity results.

What is the recent take on his imprimitivity Hilbert space work?

What did he say about Yang-Mills, and why?

What are we to make of his parallelism with Feynman on the metaphysics of Math?

Was he really incluenced by Bourbaki?
Borel? Singer?

And, for this blog, how deeply is he in the Groupoidification program?

Posted by: Jonathan Vos Post on July 15, 2007 7:49 PM | Permalink | Reply to this

Re: George Mackey

Mackey may not have cared much about groupoidification, but groupoidification cares a lot about him! Induced representations reign supreme!

Posted by: John Baez on July 15, 2007 10:48 PM | Permalink | Reply to this

Post a New Comment