A major pre-Socratic philosopher, Thales held that water as the unifying principle or system by which the universe operated. Thus, he believed that all parts of life came from water. This principle extended to his cosmological belief that the Earth itself floated on water.

Leucippus is widely credited with the development of the pre-Socratic theory of atomism. Atomism was a materialist philosophy whose first principle was that the world was composed of tiny indivisible parts, called atoms. 

Diogenes Laertius was a historiographer and biographer of philosophers who actually disputed the historical existence of Leucippus. Epicurus is a later philosopher, and rather obviously, is more associated with Epicurean philosophy rather than atomism.

Pythagoreanism is the set of beliefs outlined by later philosophers, like Plato and Aristotle, ascribed to followers of Pythagorus of Samos, widely credited as the discoverer of the Pythagorean theorem. Knowing this, one might be tempted into the answer stating that "all of life was strictly dependent on mathematics." Pythagoreanism, however, emphasized math as an example of the kind of harmony people should seek in all aspects of life. The school of thought, while heavily invested in mathematics as a guiding philosophical principle, was not exclusive in its emphasis on mathematical harmony.

In the ancient Greek religion there was an extensive pantheon of Gods. Each God or Goddess was associated with certain areas of life, occupations, and ideals. All of these Gods are correctly paired with the areas of life they were said to watch over, except Poseidon. Poseidon was the God of sailors, horses and the sea.

The philosophical tradition of atomism, or the belief that all things are composed of atoms, was first developed by the ancient Greek Democritus. Democritus and Leucippus developed the original atomic theory of the universe. They argued that everything was composed of atoms, which were indivisible and indestructible.

Although ancient Greek philosophy is usually associated with Athens more than any other city-state, it actually first emerged among the Ionian Greeks (living in modern-day Turkey). The Ionians were the center of Greek culture and wealth in the seventh century BCE. It was here that Pre-Socratic philosophy, as it is generally referred to, was first developed.

In the ancient Greek pantheon, Hephaestus was the God of blacksmiths and craftsmen. Hephaestus is generally presented as physically handicapped and is often mistreated by the other Gods as a result.

Anaximander, Thales of Miletus, and Anaximenes are the three main figures in the so-called “Ionian Awakening.” They were the first three major philosophers in ancient Greek history and were all part of the Milesian school of thinkers. Parmenides, on the other hand, lived in southern Italy and founded the Eleatic school of philosophy.

Of these ancient Greek Gods only Mars is incorrect. Mars was the Roman name for the ancient Greek God of war, Ares. The Romans adopted the same pantheon of Gods as the ancient Greeks, although all their Gods had different names. 

In Greek mythology, as told by Hesiod in The Theogony, Zeus comes to power by overthrowing his father, Kronos. Kronos himself came to power by overthrowing the God Sky. In Greek mythology, the Gods experience a very-human existence, full of power struggles, violence, love, and betrayal.