Editing Paul Cohen (section)

==Early life and education==
Cohen was born in [[Long Branch, New Jersey]] in 1934, into a [[Jews|Jewish]] family that had immigrated to the United States from what is now [[Poland]]; he grew up in [[Brooklyn]].<ref>Macintyre, A.J. [http://old.lms.ac.uk/newsletter/360/360_09.html "Paul Joseph Cohen"] {{webarchive|url=https://web.archive.org/web/20101225053150/http://old.lms.ac.uk/newsletter/360/360_09.html |date=2010-12-25 }}, [[London Mathematical Society]]. Accessed March 3, 2011. "Cohen's origins were humble. He was born in Long Branch, New Jersey on 2 April 1934, into a Polish immigrant family."</ref><ref name="mmp">{{citation|contribution=Paul Cohen|title=More Mathematical People|editor1-first=Donald J.|editor1-last=Albers|editor2-first=Gerald L.|editor2-last=Alexanderson|editor2-link=Gerald L. Alexanderson|editor3-first=Constance|editor3-last=Reid|editor3-link=Constance Reid|publisher=Harcourt Brace Jovanovich|year=1990|pages=42–58}}.</ref> He graduated in 1950, at age 16, from [[Stuyvesant High School]] in [[New York City]].<ref name="Stanford_obit"/><ref name="mmp"/>

Cohen next studied at the [[Brooklyn College]] from 1950 to 1953, but he left without earning his [[bachelor's degree]] when he learned that he could start his graduate studies at the [[University of Chicago]] with just two years of college. At [[Chicago]], Cohen completed his master's degree in mathematics in 1954 and his [[Doctor of Philosophy]] degree in 1958, under supervision of [[Antoni Zygmund]]. The title of his doctoral thesis was ''Topics in the Theory of Uniqueness of Trigonometrical Series''.{{sfn|Cohen|1958}}<ref name="pro">{{cite web |url=https://www.proquest.com/openview/710f92e193e41d7b2bc082f6df8f09a8/1?pq-origsite=gscholar&cbl=18750&diss=y |title=Topics in the Theory of Uniqueness of Trigonometrical Series |website=ProQuest |access-date=2024-11-02}}</ref>

In 1957, before the award of his doctorate, Cohen was appointed as an Instructor in Mathematics at the [[University of Rochester]] for a year. He then spent the academic year 1958–59 at the [[Massachusetts Institute of Technology]] before spending 1959–61 as a fellow at the [[Institute for Advanced Study]] at Princeton. These were years in which Cohen made a number of significant mathematical breakthroughs. In ''Factorization in group algebras'' (1959) he showed that any integrable function on a locally compact group is the convolution of two such functions, solving a problem posed by [[Walter Rudin]]. In {{harvtxt|Cohen|1960}} he made a significant breakthrough in solving the Littlewood conjecture.<ref>{{MacTutor Biography|id=Cohen|title=Paul Joseph Cohen}}</ref>

Cohen was a member of the [[American Academy of Arts and Sciences]],<ref>{{Cite web |title=Paul Joseph Cohen |url=https://www.amacad.org/person/paul-joseph-cohen |access-date=2022-08-22 |website=American Academy of Arts & Sciences |language=en}}</ref> the United States [[National Academy of Sciences]],<ref>{{Cite web |title=Paul J. Cohen |url=http://www.nasonline.org/member-directory/deceased-members/56837.html |access-date=2022-08-22 |website=www.nasonline.org}}</ref> and the [[American Philosophical Society]].<ref>{{Cite web |title=APS Member History |url=https://search.amphilsoc.org/memhist/search?creator=Paul+Cohen&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced |access-date=2022-08-22 |website=search.amphilsoc.org}}</ref> On June 2, 1995, Cohen received an [[Honorary degree|honorary doctorate]] from the Faculty of Science and Technology at [[Uppsala University]], [[Sweden]].<ref>{{cite web|url=http://www.uu.se/en/about-uu/traditions/prizes/honorary-doctorates/|title=Honorary doctorates - Uppsala University, Sweden|website=www.uu.se|access-date=21 March 2018}}</ref>