What is the problem of "the one and the many that presented itself to early greek philosophers?
LOL. Being stuck on this for an hour is pretty typical. Some philosophers get stuck on this question for decades. Even then, some never get it. The reason is, I think, is that it really can't be comprehended by logical analysis, because the better tool is poetry. Emerson wrote a good poem called "Brahma."
Looks like this was an early ancient Greek formulation of the problem of SETS^. And the problem what set contains each-and-every-common-type set except its own unique or uniquely defined one. Hence the ONE & the MANY.
Parmenides and Heraclitus are often contrasted. In basic terms, Parmenides considered the One to be a permanence of perfection. Heraclitus thought that the one was a kind of permanent fiery energy change. Both were combined by Plato, in his theory of Forms, which was more permanent patterns of perfection, and copies of the forms, which were changeable. Thus one may see in a seashell or a sunset, a pearl or a smile, the pattern of beauty and perfection these embody and reflect. Pythagoras understood mathematical forms and formulas to be the universal truth, expressing the One harmony or music of the spheres. These four represent an early interest in "why is there something?", and "how does it unfold?", both of which are interests of mankind in all cultures, all climes. The ancient Greeks and others, as we understand by reading their dramas, poems, and histories, were quite modern--another way to say this is that people's characters haven't changed much, if at all, in the 2,500 years following Buddha, Confucius, Socrates, and others, in Hinduism and in Judaism (e.g., Ezekiel and Isaiah). Another, more materialistic "oneness" was that of Democritus, who intuited that there were invisible, indivisible particles (hence non-cuttable, a-tom), perhaps by noticing that aroma of freshly baking bread or scent of flowers wafted across thin air. Democritus thus had various shapes and kinds of a-toms, including a psi atom for the soul, which he believed, like Aristotle, was the finest aspect of man. There was in this general ancient tradition a "Valley Guy" or "well, it's truth for you" thinker, named Protagoras. Like Heraclitus, this "one" was relative or changey, but Protagoras went a step further, saying that if one grew up near Pythagoras, the one truth was in numbers and harmony, if one grew up near Plato, the One was Form and Ideas, etc.--a kind of "ethos" or "when in Rome, do as the Romans" kind of cultural relativism. Even while today's physics has no fundamental understanding of "Energy," although having many measures of it in action, etc., scientific experiment has given indications of which early Greek thinking is most accurate. Pythagoras tops the list, as "bit = it;" Heraclitus' notion of fiery flux ~ = "Energy," and Parmenides, Plato, and Democritus are also accurate in Forms and bits of geometrized Energy. No one in philosophy or science has answered or even given falsifiable hypotheses about where Energy "comes from." Related: https://www.businessinsider.com.au/watch-universe-evolution-big-bang-animation-2016-5 https://en.wikipedia.org/wiki/Standard_model