He did arguably explicitly predict that basic mathematical/geometric forms underlie the structure of the universe. E.g., that atoms would be composed of pyramids, cubes, dodecahedrons and that the behaviour of atoms would be based upon the different geometric properties of basic forms.
That idea is only partially correct, however. Atoms are based on the basic mathematical forms -- but on the spherical harmonics of electron clouds, not point geometries. Whoops! Otherwise, the idea is commensurable with modern atomic understanding.
Earth, water, air and fire correspond not to elements (ice can melt, obviously) but to phases of matter. (Solid, liquid, gas, plasma).
There is a reason Classical Greek philosophy underlies western civilization. They were not dummies and there is still a lot we can learn from them. It's not like all their ideas were examined in the 1800s and we took all the good ones, leaving the classics as a sort of intellectual skin worth shedding. Instead, it is the core we build on. It's worth understanding the core -- and giving them the benefit of the doubt to identify interesting ideas.
Like that the universe begins with "the one" :)
That's accurate, though. If I told you a statement and backed it up with the claim that "at some point in history, a human said it" then you really haven't learned very much. Likewise, if a statement is tagged with "and by the way, an ancient philosopher believed it," you may have learned something about history, but the statement itself hasn't gotten any more believable.
However, new sentences are made every day, new words made very often. Nobody cares about the technical sense of the words "no information". If your argument was extended from 'ancient philosophy' to 'anything ever said by humans', then anything ever said by humans would fill the sentence space fairly uniformly, so finding out that anyone has said anything doesn't help.
A single human has not considered and thought about every sentence possible. They have their own beliefs and knowledges, and by reading ancient philosophy, they can expand that knowledge base, change those beliefs. Ancient philosophy is not inconsequential, and it certainly contains "information".