Pythagoras from Samos is often portrayed as the first ”real” mathematician. We do not know much about his achievements because the students of the philosophical - religious school he founded, attributed all his discoveries to him. Since they used only oral communication in their work, there are no preserved writings of Pythagoras or his followers. All we know today about them is what others wrote. Most of their achievements are described around 300 BC in Euclid’s Elements. In general, their most significant breakthroughs are in arithmetic, geometry, music and astronomy. Mathematics was big part of the Pythagorean life. They studied various types of natural numbers, laying the foundation for the theory of numbers. They investigated the properties of even and odd numbers. They dealt with prime and complex numbers as well as perfect and amicable numbers and various types of figurate numbers. They also knew the arithmetic, geometric and harmonic mean of numbers. What we remember most about Pythagoras today is Pythagoras’ theorem. Although this theorem was also known to some earlier civilizations, it bears Pythagoras’ name since he was the first to prove it. Also, the Pythagoreans were aware of the reversal of this theorem. It’s application is very important in mathematics but also in other sciences. In addition to the Pythagorean theorem, Pythagorean triples were also studied. They were first to prove that the sum of the angles in a triangle is 180° and they generalized this claim. Studying the commensurability of sizes, the Pythagoreans discovered the existence of irrational numbers that contradicted their beliefs, so they kept this discovery in secret. Other important discoveries in geometry include results in geometric algebra and regular polyhedra.