It seems fairly well known that Leray originated the ideas of spectral sequences and sheaves while being held in a prisoner of war camp in Austria from 1940 to 1945. Weil famously proved the Riemann hypothesis for curves in 1940, while in prison for failure to report for army duty. I recently learned that Linnik's famous theorem on primes in arithmetic progressions was published in 1944, just after the siege of Leningrad ended. So now I would like to ask:
What are some other examples of notable mathematics done during World War II?
Best Answer
On the other side of the war, Teichmüller did some of his best work during World War II. According to the MacTutor biography, he volunteered to serve on the Eastern Front in 1943 and got killed. My impression, then, is that his Nazi fanaticism was a crime against his own mathematical career as well as against other mathematicians.