History of mathematical notation back to any school or period before that of the Ionian Greeks, but the subsequent history may be divided into periods, the distinctions between which are tolerably well marked. Greek mathematics, which originated with the study of geometry, tended from its commencement to be deductive and scientific. Since the fourth century AD, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that in a right-angled triangle the area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of
Pythagorean prime representation can be interpreted geometrically: the Pythagorean primes are exactly the odd prime numbers "p" such that there exists a right triangle, with integer legs, whose hypotenuse has length . They are also exactly the prime numbers "p" such that there exists a right triangle with integer sides whose hypotenuse has length "p". For, if the triangle with legs "x" and "y" has hypotenuse length (with "x" > "y"), then the triangle with legs "x" − "y" and 2"xy" has hypotenuse length "p". Another way to understand this representation as a sum of two squares involves Gaussian integers, the complex