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 ...

Some mathematical statements feel undeniably true the moment you hear them. Yet proving them can be impossible. This theorem has convinced generations of mathematicians without ever yielding a formal ...

At the beginning of the 20th century, the German mathematician David Hilbert (1862–1943) advocated an ambitious program to formulate a system of axioms and rules of inference that would encompass all ...

Mathematicians explore ideas by proposing conjectures and proving them with theorems. For centuries, they built these proofs line by careful line, and most math researchers still work like that today.