The ancient Greeks wanted to believe that the universe could be described in its entirety using only whole numbers and the ratios between them — fractions, or what we now call rational numbers. But ...

Say someone sets out to prove, by contradiction, that something is a joke. You would have to assume the opposite of what she’s proving is true. You would follow her thoughts logically until a ...

Many complicated advances in research mathematics are spurred by a desire to understand some of the simplest questions about numbers. How are prime numbers distributed in the integers? Are there ...