From: rusin@olympus.math.niu.edu (Dave Rusin)
Subject: Re: Cantor, fun (non-crackpot post)
Date: 8 Apr 1999 17:50:53 GMT
Newsgroups: sci.math
Keywords: Who is "Paul Cohen"?

I had claimed Paul Cohen had no papers in analysis, but either I had
jumped to a conclusion or Math Reviews's "find same author" feature had
bad data when I had collected this information. "My bad", as the kids say.
I checked again, and also looked up the MacTutor history-of-math website entry
on Paul Cohen.

Daniel Grubb wrote:
>
> Paul Cohen was an analyst first. He characterized the idempotents of the
> measure algebra of an LCA group and investigated homomorphisms of the
> group algebras of such groups.
> 
> See Amer J. Math. 82, (1960) pp 191-212 and 213-226.

Jan-Christoph Puchta  <jcp@arcade.mathematik.uni-freiburg.de> wrote:
>
>Just had a look at the Zentralblatt. There are two Paul Cohens, Paul E.
>Cohen and Paul J. Cohen. Paul J. Cohen wrote several papers on analysis
>and two on logic (Comments on the foundations of set theory. (Russian)
>[J] Usp. Mat. Nauk 29, No.5(179), 169-176 (1974) and Automorphisms of
>set theory. (English)
>[CA] Proc. Tarski Symp., internat. Symp. Honor Afred Tarski, Berkeley
>1971, Proc. Symp. Pure
>Math. 25, 325-330 (1974).).
>
>Paul E. Cohen only worked on logic and set theory.
>
>Note that I might have missed entries if the author is abbreviated.
>
>Since I only once had a three-afternoons-course on forcing, I cannot say
>which Paul Cohen invented it.

Math Reviews has _four_ Paul Cohens. In addition to Paul F. (one logic paper in
1975) and Paul R. (3 computer science papers in the 1980s), there is
a Paul E. Cohen, with 11 papers in logic, including forcing, in the second
half of the 1970s (extending to some work in point-set topology). This must
have been a real trip, sharing a name, a decade, and a discipline with a 
Field's medalist! 

But the correct reference in this thread is to Paul Joseph Cohen, born 1934.
His Ph.D. (1958, Chicago) was with Zygmund -- clearly analysis. Indeed, he
won the Bocher prize for some work in measure theory. Shortly thereafter he
published quite a few papers in set theory; it was for this work that he was
awarded the Field's medal in 1966. He continued this line of inquiry but also
continued to publish a few papers in analysis. The MacTutor entry ends 
   In addition to his work on set theory, Cohen has worked on
   differential equations and harmonic analysis.

With this sterling recognition of his work it is perhaps surprising that
Cohen has no more than 20 publications altogether, and none since the
early 1970s. Fame, I imagine, takes its toll.

The listing of PJC's work above misses the spectacular earlier papers.
Perhaps Puchta was limited to the guest search feature of Zentralblatt
(3 article limit, usually the most recent ones). A better reference might be
"A minimal model for set theory", Bull. Amer. Math. Soc. 69 (1963) 537--540.

By the way, others I speak with have heard the same tale of Cohen's brash
undertaking of this problem outside his original field. Might be true.
But truth, in the legend business, is irrelevant ;-)

dave