Paul Cohen

He is noted for inventing a technique called forcing which he used to show that neither the continuum hypothesis nor the axiom of choice can be proved from the standard Zermelo-Fraenkel axioms of set theory. In conjunction with the earlier work of Gödel, this showed that both these statements are independent of the Zermelo-Fraenkel axioms: they can be neither proved nor disproved from these axioms. For his efforts he won the Fields Medal.

This result is possibly the most famous non-trivial example illustrating Gödel's incompleteness theorem.

External link:

• O'Connor and Robertson: MacTutor biography of Paul Cohen: http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Cohen