Many ancient societies knew important mathematical facts, but only one discovered mathematics—which is not a collection of accurate rules of thumb, but a body of knowledge organized deductively, by ...

Euclid’s Elements, which presented the state of the art in geometry around 300 B.C., has been extraordinarily influential. This massive, 13-volume compendium set the standard for mathematical ...

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 ...

Hyperbolic space is a Pringle-like alternative to flat, Euclidean geometry where the normal rules don’t apply: angles of a triangle add up to less than 180 degrees and Euclid’s parallel postulate, ...