Turing’s diagonalization proof is a version of this game where the questions run through the infinite list of possible algorithms, repeatedly asking, “Can this algorithm solve the problem we’d like …
The original version of this story appeared in Quanta Magazine. In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in …
The original version of this story appeared in Quanta Magazine. So far this year, Quanta has chronicled three major advances in Ramsey theory, the study of how to avoid creating …