Paul Cohen, 1934-2007
March 25th, 2007 by WaltAlexandre Borovik is reporting that Paul Cohen has died. Cohen of course proved that the continuum hypothesis is independent of the axioms of set theory, and that the axiom of choice was independent of the other axioms.
Gödel had already established that both the continuum hypothesis and axiom of choice were consistent, in the sense if you could derive a contradiction by adding them as axioms then you could derive a contradiction in set theory without them. Gödel accomplished this by defining a certain minimal model of set theory, the constructible universe, and showing that in this model both axioms hold. Cohen then completed the proof of independence by showing that you can construct a model of set theory in which both axioms are false. To do so, he had to invent a new technique: forcing.
His Wikipedia biography has the oddest snippet:
His twin sons Steven and Eric played the Dancing Twins on the TV show Ally McBeal.
Is that really true?
March 25th, 2007 at 10:50 pm
If it’s true about the Ally McBeal thing, they wouldn’t be the first mathematician’s kids to act. Lee Neuwirth’s daughter was in one of those Law & Order series.
March 27th, 2007 at 8:16 pm
John, I think Bebe Neuwirth was in “Cheers”.
March 27th, 2007 at 8:40 pm
Nothing slips by you, Eric
March 28th, 2007 at 10:00 am
He was a great american-born mathematician. The greatest? Has there ever been an american-born mathematician as great as Paul Cohen? RIP. He will be missed.
March 28th, 2007 at 10:58 am
Brian: Saunders MacLane.
March 28th, 2007 at 1:44 pm
As a graduate of Stuyvesant High School, in the same class as Steven E. Koonin (1968), well after Paul Cohen and
* Joshua Lederberg (Class of 1941) - 1958 Nobel Prize in Physiology or Medicine
* Robert Fogel (Class of 1944) - 1993 Nobel Memorial Prize in economics
* Roald Hoffmann (Class of 1954) - 1981 Nobel Prize in Chemistry
* Richard Axel (Class of 1963) - 2004 Nobel Prize in Physiology or Medicine
but before Brian R. Greene and Lisa Randall (Class of 1980), I can assure you that Paul Cohen was held forth as an exemplar to all aspiring Mathematicians amongs us.
Listing of Notable Alumni in the field of Mathematics.
Bergman, George M.
Graduated: 1960
Cohen, Paul J.
Graduated: 1950
Elkies, Noam D.
Graduated: 1982
Harbater, David
Graduated: 1970
Hochster, Melvin
Graduated: 1960
Khazanov, Aleksandr
Graduated: 1995
Lax, Peter D.
Graduated: 1943
Stein, Elias M.
Graduated: 1949
Weichsel, Paul M.
Graduated: 1949
Zimmer, Robert J.
Graduated: 1964
http://en.wikipedia.org/wiki/Peter_Stuyvesant_High_School
April 17th, 2007 at 12:37 pm
It’s certainly interesting that SHS has produced more leading mathematicians than most universities! The main article at Wikipedia seems to have been edited to remove the internal link to a page which I thoroughly redesigned, http://en.wikipedia.org/wiki/List_of_Stuyvesant_High_School_people which gives math pride of place but also lists some leading physicists, such as Rolf Landauer and Richard H. Price.
April 17th, 2007 at 12:39 pm
Oops, I forgot to point out that Cohen and Elias Stein were on the same Math Team at SHS.
June 18th, 2007 at 4:45 am
The Ally McBeal Season 1 Episode Guide
has repeated entries for The Dancing Twins Eric & Steven Cohen.
Stanford News obituary of Paul Cohen mentions that Cohen is survived by three children, twins Eric and Steven of LA, and Charles of Boston.