Pythagoras was a thinker from the 5^{th}century. He is well known for a theorem that he is credited with, called the Pythagorean theorem, but in actuality he did much more than that. He created an entire school, or religious cult as many people called it, that influenced the way we think for generations to come. The group he made was called the Pythagorean brotherhood, and they were very secretive about the framework of the group. Their most common teaching associated with the Pythagorean brotherhood is metempsychosis. This term is the notion that every soul is immortal, and that upon death that soul enters a new body. This method of thinking motivated individuals in the brotherhood, because it made them believe that their work, research, and thinking were a part of some larger plan that they can’t devise at the moment. Their knowledge never stops growing, even after their mortal body dies. The 5^{th}and 6^{th}century are known for being politically unstable, so this method of thinking is a way to motivate the students that there are some aspects of life that are more stable than previously shown. This is one example of Pythagoras’ thinking, and teaching that were effected by the state of the world at this time.

As for the Pythagorean Theorem that he discovered, there has always been speculation about whether he truly was the first person to write out a^{2}+b^{2}=c^{2}. Some credit Pythagoras with being the first person to introduce the theorem to the Greeks, because the Babylonians, and Indians used the Pythagorean theorem centuries before. Although his impact on the Pythagorean theorem is questionable, it is certain that Pythagoras changed the world with his discoveries. His most widely used discovery was the connection between music, astronomy, and mathematics. He studied music by testing the sounds that different sized hammers made when they struck a solid surface. This relation is false, but his initial pairing of ideal sounds together was a large step forward in the relation of math and music. As for astronomy, he is credited as one of the first people to claim that the earth is spherical. This claim isn’t exactly mathematical, but it is monumental in changing the way that we view the world. Pythagoras also was responsible for sectioning the globe into five different climate zones. All of these claims at the time seem small, but proved monumental in influencing the later thinking of philosophers such as Plato and Aristotle.