The history of discoveries about the inner structure of matter is the history of quantum physics. The history of quantum physics is the story of the rediscovery of harmony handed down by Pythagoras and the Pythagoreans (History of Harmonyics). What has apparently been redone has never been formulated explicitly. You could summarize it like this:
“What is the Wisest? Number”
Hearing spells of Pythagoras
That matter is composed of the smallest elements shows the word “atomos”, the indivisible one. The Greek origin of this word indicates a notion thought to come from Greece: “In Greek philosophy, the idea of the atom was first handed down to Leukipp in the 5th century BC His student Democritus systematized them and introduced the term átomos, which means something like” the unbreakable “, that is, an object that cannot be further divided.” Wikipedia / Atom / Philosophy
However, one knows from earlier mentions:
“An early mention of the atomic concept in philosophy is known from India, and the Nyaya and Vaisheshika schools developed elaborate theories of how atoms combine into more complex entities (first in pairs, then three pairs each).”
Wikipedia / Atom / Philosophy
What happened to the discovery of the quantum of action by Max Planck in 1900, neither Planck nor the world understood so well. It was the beginning of a new era that shook the world view of the 19th century and is still misunderstood today. But for the Pythagorean tradition it was also the factual confirmation of its philosophy of numbers. Heisenberg wrote:
“… such demands have been called quantum conditions since the famous work of Planck in 1900. And these conditions brought just that peculiar element of numerical mysticism into atomic physics, which we have already mentioned. Certain variables to be calculated from the orbit were integer multiples Such rules recalled the observations of the ancient Pythagoreans, according to which two vibrating strings harmoniously clash when their lengths are in an integer relationship at the same tension.”
Werner Heisenberg, The Part and the Whole, p. 47
John Borrow writes in The Nature of Nature:
“The quantization of energy levels also causes the uniformity of nature.” If the orbits of the electrons around the central nucleus were described by classical Newtonian mechanics, the electron could orbit the nucleus on a path of arbitrary radius if it only had the proper velocity. An electron could have a different velocity and a different orbit radius almost every time it is bound on a lane around a proton, so each time there would be a different configuration and every hydrogen atom would be different. ” Barrow, John D .; The nature of nature; Rohwolt, Hamburg, 1996; P.234.
The structure of the electron shell was largely unraveled in the 20th century, especially by Niels Bohr, Wolfgang Pauli, Werner Heisenberg and Erwin Schrödinger.
These results are not only of a general nature, they confirm Pythagorean philosophy quite concretely.
See: Harmonic Reflections on the Modern Ideas of the Atom (in German)