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 flourished about 50 years after Aristotle and was certainly familiar with Aristotle's Logic. Euclid's organisation of the work of earlier geometers was truly innovative. His results depended ...

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 ...

The work of mathematicians from centuries or even millennia ago speaks to their living peers in ways that practitioners of other disciplines must find baffling. Euclid’s proof that the list of prime ...

The ancient Greek geometer Euclid presented a list of five axioms he held to be self-evidently true. They are (or are equivalent to): You can draw a line between any two points. You can extend lines ...