Thales, Pythagoras, and Heraclitus formed part of one of the earliest group of ancient Greek Philosophers. They were revolutionaries in that they explored the functioning of the world using their rational minds. As such, even though they disagreed on some basic principles it is not a stretch to call these three legends the fathers of rational thought.
Thales was a member of the Milesian school. They believed that "the complex world has a simple, permanent underpinning in the reality of a single kind of stuff from which all else emerges" (Traylor). Thales believed that all things came from water, and was legendary for his mathematical abilities which most famously included being able to predict a solar eclipse. His most important contribution to the world was his theorem that a triangle inscribed inside a semi-circle has a right angle. This theorem is the root of all deductive science, "the process of deriving suppositions and mathematical statements from observation by means of logic" (Knierim).
Pythagoras was perhaps the greatest of the ancient greek deductive scientists. Pythagoras built on Thales' mathematics to create his eponymous theorem: a¦+b¦=c¦. His meditations on the world led him to conclude that "all things are numbers" (Knierim). Pythagoras has certainly stood the test of time as a mathematician; but he was also one of the first Western proponents of reincarnation. He believed that "the soul 'transmigrates' into other living bodies at death, with animals and plants participating along with human beings in a grand cycle of reincarnation" (Traylor).
While Pythagoras believed in the ideal of harmony as peaceful coexistence, Heraclitus emphatically rejected this point of view. Heraclitus believed that the natural world was characterized by perpetual struggle and strife. His most famous summation of his philosophy is that "All is flux;" noting that "Upon those who step into the same river, dif...