How Greek Mathematicians Influenced Modern Mathematics

Math as we know it today has been influenced by so many people but one of the biggest contributors were the Greek mathematicians. The Greeks have heavily influenced modern mathematics in a variety of ways many being in geometry but I am only going to focus on one of their contributions which I would arguably say was their greatest contribution. In my opinion the biggest way Greek mathematicians influenced modern mathematics was with the idea of proofs. Mathematical proofs have now become a common occurrence in math, anyone studying math has had to learn how to write mathematical proofs. The reason why I believe that the Greek mathematician's greatest influence was the idea of the proof because proofs changed the way people thought about mathematics. They were now looking at math in a more abstract way and focused more on finding patterns that could be applied to multiple cases and less on solving individual problems. The ancient Greeks used proofs to show that math wasn't just about performing calculations but math could actually be used to understand the world around us. Instead of focusing on literal values they generalized things so they could find universal patterns in mathematics. They went about this with proofs which were convincing arguments that showed that something was true. The early Greek math proofs were mainly all geometric demonstrations, such as Pythagoras's proof of the Pythagorean Theorem. In this proof Pythagoras showed that the area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the remaining squares. In mathematics today geometric demonstrations are not a very popular form of proof. It was the Greek Mathematician Euclid who changed how things were proved by establishing definitions and postulates which he used to proof his propositions. The proofs and definitions Euclid established formed the basis of mathematics. His style of proving things is being used and taught today to prove new conjectures in math. Greek Mathematicians didn't just influence modern math but they influenced the way we understand, view, and verify our new discoveries in math.