### 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.

## 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?