# 6 Amazing Breakthroughs Made by the Ancient Greeks

For more than two millennia, the ideas of the ancient Greeks have spurred some of humanity’s greatest achievements. Philosophy, drama, science, and mathematics sprung from that particular peninsula in the Mediterranean. The work of the Greek scholars propelled Muslim thinkers during the Islamic Golden Age, and the European rediscovery of their ancient texts ignited the Renaissance and sustained the Enlightenment, giving way to new scientific advancements and even new ways of living and governing. These are six amazing breakthroughs from ancient Greece, born from some of history’s greatest minds.

## Pythagoras’ Theorem Formed the Foundation of Geometry

Pythagoras of Samos is arguably the most famous mathematician from ancient Greece (and there were a lot of them), and that’s because nearly every person at some point in their educational journey is taught his eponymous theorem. Expressed as a^{2} + b^{2} = c^{2}, the Pythagorean theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In ancient times, this proved the existence of irrational numbers and formed the cornerstone of what became Euclidean geometry (more on Euclid later), which plays a very real role in construction and navigation today. Some of the world’s smartest minds have set out to provide proofs of the Pythagorean theorem, including Albert Einstein (he was 12 at the time), and new proofs are still being discovered to this day. Simply put, the world would be a very different place without Pythagoras’ triangular insight.