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 ...

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 ...

Think too hard about it, and mathematics starts to seem like a mighty queer business. For example, are new mathematical truths discovered or invented? Seems like a simple enough question, but for ...

The starting point for rigorous reasoning in mathematics is a system of axioms. An axiom is a statement that is assumed, without demonstration, to be true. It is usually self-evident, for example, ...