Person: Cohen (2), Jacob Willem
Paul Cohen was an American mathematian who used a technique called _forcing _ to prove the independence in set theory of the axiom of choice and of the generalised continuum hypothesis.
Mathematical Profile (Excerpt):
- After graduating from Stuyvesant High School, Cohen was a student at Brooklyn College from 1950 until 1953 but left without taking a degree having been admitted to graduate studies at the University of Chicago after making a visit to discuss his research options at Chicago.
- The years as a research student were good ones for Cohen and he made many friendships with fellow students, friendships that would last throughout his life.
- In 1957, before the award of his doctorate, Cohen was appointed as an Instructor in Mathematics at the University of Rochester for a year.
- These were years in which Cohen made a number of significant mathematical breakthroughs.
- In On a conjecture of Littlewood and idempotent measures (1960) Cohen made a significant breakthrough in solving the Littlewood Conjecture.
- to Paul saying that if Paul's proof held up, he would have bettered a generation of British analysts who had worked hard on this problem.
- Paul's proof did hold up; in fact, Davenport was the first to improve on Paul's result.
- In 1961 Cohen was appointed to the faculty at Stanford University as an assistant professor of mathematics.
- In August 1962 Cohen participated in the International Congress of Mathematicians in Stockholm.
- On a cruise from Stockholm to Leningrad, following the Congress, Cohen met Christina Karls from Malung, Sweden.
- Cohen used a technique called "forcing" to prove the independence in set theory of the axiom of choice and of the generalised continuum hypothesis.
- Hilbert's famous speech The Problems of Mathematics challenged (and today still challenges) mathematicians to solve these fundamental questions and Cohen has the distinction of solving Problem 1.
- Cohen spoke about his work on the independence of the axiom of choice and the continuum hypothesis from the axioms of Zermelo-Fraenkel set theory in a lecture Independence results in set theory delivered at the international symposium on the 'Theory of Models' at Berkeley on 4 July 1963.
- to this reviewer it seems more than probable that the influence of Cohen's discovery will be at least as deep in metamathematics as in the general philosophy of mathematics (and perhaps not only of mathematics).
- In the same year Cohen was awarded a Fields Medal for his fundamental work on the foundations of set theory.
- Alonzo Church gave an address to the Congress on Paul J Cohen and the continuum problem describing Cohen's remarkable achievements.
- The Fields Medal, however, was not the first award that Cohen received.
- In addition to his work on set theory, Cohen worked on differential equation and harmonic analysis.
- This breadth was highlighted in a conference held at Stanford last September celebrating Cohen's work and his 72nd birthday.
- Cohen was a dynamic and enthusiastic lecturer and teacher.
- From 1969 on Cohen devoted himself to some of the most challenging and unyielding problems, such as the Riemann Hypothesis.
- Cohen was named Marjorie Mhoon Fair Professor in Quantitative Science at Stanford in 1972, being the first holder of this chair.
- As to Cohen's interests outside mathematics, he played both the piano and violin, sang in a Stanford chorus, and was a member of a Swedish folk group.
Born 2 April 1934, Long Branch, New Jersey, USA. Died 23 March 2007, Palo Alto, California, USA.
View full biography at MacTutor
Tags relevant for this person:
Prize Fields Medal, Origin Usa
Thank you to the contributors under CC BY-SA 4.0!
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive