I think that modern physics has definitely decided in favor of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.

"[986a] [1] they assumed the elements of numbers to be the elements of everything, and the whole universe to be a proportion1 or number. Whatever analogues to the processes and parts of the heavens and to the whole order of the universe they could exhibit in numbers and proportions, these they collected and correlated;and if there was any deficiency anywhere, they made haste to supply it, in order to make their system a connected whole. For example, since the decad is considered to be a complete thing and to comprise the whole essential nature of the numerical system, they assert that the bodies which revolve in the heavens are ten; and there being only nine2 that are visible, they make the "antichthon"3 the tenth.We have treated this subject in greater detail elsewhere4; but the object of our present review is to discover from these thinkers too what causes they assume and how these coincide with our list of causes.Well, it is obvious that these thinkers too consider number to be a first principle, both as the material5 of things and as constituting their properties and states.6 The elements of number, according to them, are the Even and the Odd. Of these the former is limited and the latter unlimited; Unity consists of both [20] (since it is both odd and even)7; number is derived from Unity; and numbers, as we have said, compose the whole sensible universe.Others8 of this same school hold that there are ten principles, which they enunciate in a series of corresponding pairs: (1.) Limit and the Unlimited; (2.) Odd and Even; (3.) Unity and Plurality; (4.) Right and Left; (5.) Male and Female; (6.) Rest and Motion; (7.) Straight and Crooked; (8.) Light and Darkness; (9.) Good and Evil; (10.) Square and Oblong."

In the philosophy of Democritus the atoms are eternal and indestructible units of matter, they can never be transformed into each other. With regard to this question modern physics takes a definite stand against the materialism of Democritus and for Plato and the Pythagoreans. The elementary particles are certainly not eternal and indestructible units of matter, they can actually be transformed into each other. As a matter of fact, if two such particles, moving through space with a very high kinetic energy, collide, then many new elementary particles may be created from the available energy and the old particles may have disappeared in the collision. Such events have been frequently observed and offer the best proof that all particles are made of the same substance: energy.

Pythagoras says that number is the origin of all things, and certainly the law of number is the key that unlocks the secrets of the universe. But the law of number possesses an immanent order, which is at first sight mystifying, but on a more intimate acquaintance we easily understand it to be intrinsically necessary; and this law of number explains the wondrous consistency of the laws of nature.

Since the science of nature is conversant with magnitudes, motion, and time, each of which must necessarily be either infinite or finite...[we] should speculate the infinite, and consider whether it is or not; and if it is what it is. ...[A]ll those who appear to have touched on a philosophy of this kind... consider it as a certain principle of beings. Some, indeed, as the Pythagoreans and Plato, consider it, per se, not as being an accident to any thing else, but as having an essential subsistence... the Pythagoreans... consider the infinite as subsisting in sensibles; for they do not make number to be separate; and they assert that what is beyond the heavens is infinite; but Plato says that beyond the heavens there is not any body, nor ideas, because these are no where: he affirms, however, that the infinite is both in sensibles, and in ideas. ...Plato establishes two infinities, viz. the great and the small.

Fragment 2. All things, at least those we know, contain number; for it is evident that nothing whatever can either be thought or known, without number. Number has two distinct kinds: the odd, and the even, and a third, derived from a mingling of the other two kinds, the even-odd. Each of its subspecies is susceptible of many very numerous varieties; which each manifests individually.

Despite the vociferous claims of the Platonists and Neoplatonists, Plato was not a mathematician. To Plato and his followers mathematics was largely a means to an end... they viewed the technical aspects of mathematics as a mere device for sharpening one's wits, or at most a course of training peparatory to handling the larger issues of philosophy. This is reflected in the very name "mathematics,"... a course of studies or... a curriculum. ...in the Dialogues... such topics as harmony, triangular numbers, figurate numbers... which we view today as more or less irrelevant, if not trivial, were taken up at length. ...the guiding motive behind the... Pythagoreans and Platonists was... metaphysical ...which for the nonprofessional have all the earmarks of the occult. ...We also discover in the Pythagorean speculations more than a mere germ of... the scientific attitude.

Thales thought that water was the primordial substance of all things. Heraclitus of Ephesus... thought that it was fire. Democritus and his follower Epicurus thought that it was the atoms, termed by our writers "bodies that cannot be cut up" or, by some "indivisibles." The school of the Pythagoreans added air and the earthy to the water and fire. Hence, although Democritus did not in a strict sense name them, but spoke only of indivisible bodies, yet he seems to have meant these same elements, because when taken by themselves they cannot be harmed, nor are they susceptible of dissolution, nor can they be cut up into parts, but throughout time eternal they forever retain an infinite solidity.

Some key physical entities such as empty space, elementary particles and the wavefunction appear to be purely mathematical int he sense that their only intrinsic properties are mathematical properties.

"However, it has been found that even the "elementary particles" can be created, annihilated and transformed, and this indicates that not even these can be ultimate substances but, rather, that they too are relatively constant forms, abstracted from some deeper level of movement."

What seems certain is that Pythagoras developed the idea of mathematical logic... He realized that numbers exist independently of the tangible world and therefore their study was untainted by inaccuracies of perception. This meant he could discover truths which were independent of opinion of prejudice and which were more absolute then any previous knowledge.

The Pythagoreans were fascinated by the regular solids, symmetrical three-dimensional objects all of whose sides are the same regular polygon. The cube is the simplest example, having six squares as sides. There are an infinite number of regular polygons, but only five regular solids. (The proof of this statement, a famous example of mathematical reasoning, is given in Appendix 2.) For some reason, knowledge of a solid called the dodecahedron having twelve pentagons as sides seemed to them dangerous. It was mystically associated with the Cosmos. The other four regular solids were identified, somehow, with the four “elements” then imagined to constitute the world; earth, fire, air and water. The fifth regular solid must then, they thought, correspond to some fifth element that could only be the substance of the heavenly bodies. (This notion of a fifth essence is the origin of our word quintessence.) Ordinary people were to be kept ignorant of the dodecahedron.

Although a poem be not made by counting of syllables upon the fingers, yet "numbers" is the most poetical synonym we have for verse, and "measure" the most significant equivalent for beauty, for goodness, and perhaps even for truth. Those early and profound philosophers, the followers of Pythagoras, saw the essence of all things in number, and it was by weight, measure, and number, as we read in the Bible, that the Creator first brought Nature out of the void.

The first clear expression of the idea of an element occurs in the teachings of the Greek philosophers. ...Aristotle ...who summarized the theories of earlier thinkers, developed the view that all substances were made of a primary matter... On this, different forms could be impressed... so the idea of the transmutation of the elements arose. Aristotle's elements are really fundamental properties of matter... hotness, coldness, moistness, and dryness. By combining these in pairs, he obtained what are called the four elements, fire, air, earth and water... a fifth, immaterial, one was added, which appears in later writings as the quintessence. This corresponds with the ether. The elements were supposed to settle out naturally into the earth (below), water (the oceans), air (the atmosphere), fire and ether (the sky and heavenly bodies).