Why did Paul Cohen win the Fields Medal?

American mathematician Paul Cohen was awarded the Fields Medal for his groundbreaking proofs regarding set theory. Specifically, he demonstrated that both the continuum hypothesis and the axiom of choice are independent from Zermelo-Fraenkel set theory. The Fields Medal itself is a prestigious international prize awarded every four years to researchers under the age of 40.

What we know

• Paul Cohen was awarded a Fields Medal for proving that the continuum hypothesis and the axiom of choice are independent from Zermelo-Fraenkel set theory. [2]
• The Fields Medal is awarded to two, three, or four mathematicians under 40 years of age at the International Congress of Mathematicians. [3]
• Paul Cohen lived from April 2, 1934, to March 23, 2007. [2]

Where to go next

• how it workedWhat is the continuum hypothesis?
• the bigger pictureWhat is the axiom of choice?
• a case in pointWho else has won the Fields Medal?
• how we knowWhat is Zermelo-Fraenkel set theory?
• compared withHow does the Fields Medal compare to the Abel Prize?
• an unexpected connectionHow do physics PhD holders connect to the Fields Medal?Although the Fields Medal is strictly for mathematics, two people holding PhDs in physics have managed to win it.

Sources

• [1]Paul Cohen (Wikidata Q216809) · CC0 1.0
• [2]Paul Cohen · CC BY-SA 4.0
• [3]Fields Medal · CC BY-SA 4.0
• [4]Paul Cohen (disambiguation) · CC BY-SA 4.0
• [5]Chicago school (mathematical analysis) · CC BY-SA 4.0