When I tell someone I am a mathematician, one of the most curious common reactions is: “I really liked math class because everything was either right or wrong. There is no ambiguity or doubt.” I ...

Kurt Gödel's incompleteness theorem demonstrates that mathematics contains true statements that cannot be proved. His proof achieves this by constructing paradoxical mathematical statements. To see ...

Computers are extremely good with numbers, but they haven’t gotten many human mathematicians fired. Until recently, they could barely hold their own in high school-level math competitions. But now ...

Randomness would seem to make a mathematical statement harder to prove. In fact, it often does the opposite. Of all the tools available to the mathematician, randomness would seem to offer little ...