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 ...

Have you ever wondered who is behind geometry's most fundamental truths? You guessed it: it is Euclid of Greece.

The first proof that many people ever learn, early in high school, is the ancient Greek mathematician Euclid’s proof that there are infinitely many prime numbers. It takes just a few lines and uses no ...

Do you recall your high school geometry? Given isosceles triangle ABC, where side AB is equal to side BC, then angle A is also equal to angle C. That’s not something your math teacher invented—it’s a ...

There is no satisfactory theory of three-dimensional non-Euclidean geometry, from an intuitional point of view, unless it gives us a clear three-dimensional image in our ordinary space, assuming, of ...