Mathematics is distinguished from the sciences by the freedom it enjoys in choosing basic assumptions from which consequences can be deduced by applying the laws of logic. We call the basic ...

Summary We state and prove a surprising incidence theorem that was discovered with the help of a computer graphics program. The theorem involves sixteen points on ten lines and five circles; our proof ...

“You don’t have to believe in God, but you have to believe in The Book,” the Hungarian mathematician Paul Erdős once said. The Book, which only exists in theory, contains the most elegant proofs of ...