<P> In ancient Greek philosophy, arche (ἀρχή) is the beginning or the first principle of the world . Thales of Miletus claimed that the first principle of all things is water . His theory was supported by the observation of moisture throughout the world and coincided with his theory that the earth floated on water . </P> <P> Thales's theory was refuted by his pupil and successor, Anaximander . Anaximander noted that water could not be the arche because it could not give rise to its opposite, fire . Anaximander claimed that none of the elements (earth, fire, air, water) could be arche for the same reason . Instead, he proposed the existence of the apeiron, an indefinite substance from which all things are born and to which all things will return . </P> <P> Anaximenes, Anaximander's pupil, advanced yet another theory . He returns to the elemental theory, but this time posits air, rather than water, as the arche . Anaximenes suggests that all is made from air through either rarefication or condensation (thinning or thickening). Rarefied, air becomes fire; condensed, it becomes first wind, then cloud, water, earth, and stone in order . </P> <P> Pythagoras of Samos, a mathematician, mystic, and scientist, taught that number, rather than matter, constitutes the true nature of things . He seems to have influenced Socrates' ideal form . </P>

Who speculated about the composition of matter by saying fire is the essence of all things