Image of computer code

Paul J. Cohen

  • National Medal of Science
  • Mathematics And Computer Science

For epoch-making results in mathematical logic which have enlivened and broadened investigations in the foundation of mathematics.

The youngest of four children, Paul J. Cohen was nine years old when his sister Sylvia ventured to the library to borrow a book about calculus for him. The librarians – arguing that calculus isn’t for children – didn’t want to give her the book.

But Cohen, the son of Jewish immigrants from Poland, made do with what he had, eventually rising through the ranks as one of Stanford’s finest logicians. In the 1960s, Cohen studied a question proposed in the 1870s by mathematician Georg Cantor. The question, known as the continuum hypothesis, involved quantifying the possible sizes of infinite sets of numbers – a query many deemed hopeless. “Indeed,” Cohen said. “They thought you had to be slightly crazy to even think about the problem.”

In 1963, Cohen proved that the problem was not solvable using the axioms of set theory – a conclusion that sparked discussion among mathematicians and philosophers across the globe.