The Ancient Greeks emphasized the importance of temperance, but they were extreme in everything, in pure thought, in war, and in sin. Their Prototype was Prometheus who brought fire from heaven, and was rewarded with eternal torment.
Pythagoras
The nature of mathematical truths is different than those from other sciences, which were derived from false ideas about the world. Astronomy came from Astrology, chemistry from alchemy. But mathematics was derived straight from the real world.
Mathematical truths were obtained from mere thinking. Through mathematics, it was thought that thinking was superior to sense, intuition to observation.
Heraclitus
The one is from the many, and the many is from the one. Conflict and tension creates new forms, they create unity. For instance, a couple is both a unit, and made up of two people who are diverse in all matters.
There is no such thing as good and bad in an objective sense. God is everything, thus everything is good. What man considers good or bad is only so from his warped perspective. War and peace are both good, and so is up and down. Each thing contributes to the creation, each thing is necessary.
Everything is in a state of flux. You cannot step twice into the same river. Thus, nothing ever is, everything is in a state of becoming. This painful realization goes against the natural impulse of the philosopher and the scientist, to find out things that are not subject to changes. Russel thinks that this need for wholeness comes from man’s desire for refuge and for home. That is why the need for philosophy is most pronounced in those who have to contend with perpetual tragedy.