Werner Heisenberg quote: “The elementary particles in Plato's Timaeus are finally not substance but mathematical forms. "All things are numbers" …”

“In modern quantum theory there can be no doubt that the elementary particles will finally also be mathematical forms”

Werner Heisenberg (1901–1976) German theoretical physicist

Physics and Philosophy (1958)
Context: But the resemblance of the modern views to those of Plato and the Pythagoreans can be carried somewhat further. The elementary particles in Plato's Timaeus are finally not substance but mathematical forms. "All things are numbers" is a sentence attributed to Pythagoras. The only mathematical forms available at that time were such geometric forms as the regular solids or the triangles which form their surface. In modern quantum theory there can be no doubt that the elementary particles will finally also be mathematical forms but of a much more complicated nature.

“Therefore, the mathematical forms that represent the elementary particles will be solutions of some eternal law of motion for matter.”

Werner Heisenberg (1901–1976) German theoretical physicist

Physics and Philosophy (1958)
Context: The equation of motion holds at all times, it is in this sense eternal, whereas the geometrical forms, like the orbits, are changing. Therefore, the mathematical forms that represent the elementary particles will be solutions of some eternal law of motion for matter. Actually this is a problem which has not yet been solved.<!-- p. 72

“[T]he atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts.”

Werner Heisenberg (1901–1976) German theoretical physicist

“Now it is one great object of this work, to shew the importance and advantage of ascertaining the relative weights of the ultimate particles, both of simple and compound bodies, the number of simple elementary particles which constitute one compound particle, and the number of less compound particles which enter into the formation of one more compound particle.”

John Dalton book A New System of Chemical Philosophy

Source: A New System of Chemical Philosophy (1808), Ch. III. On Chemical Synthesis

“What is still more wonderful with respect to this principle of combination, all the elementary substances observe certain mathematical proportions in their unions. It is hence supposed that matter is composed of”

Robert Chambers (publisher, born 1802) book Vestiges of the Natural History of Creation

Source: Vestiges of the Natural History of Creation (1844), p. 35
Context: It is remarkable of the simple substances that they are generally in some compound form. Thus oxygen and nitrogen, though in union they form the aerial envelope of the globe, are never found separate in nature. Carbon is pure only in the diamond. And the metallic bases of the earths, though the chemist can disengage them, may well be supposed unlikely to remain long uncombined, seeing that contact with moisture makes them burn. Combination and re-combination are principles largely pervading nature. There are few rocks, for example, that are not composed of at least two varieties of matter, each of which is again a compound of elementary substances. What is still more wonderful with respect to this principle of combination, all the elementary substances observe certain mathematical proportions in their unions. It is hence supposed that matter is composed of infinitely minute particles or atoms, each of which belonging to any one substance, can only (through the operation of some as yet hidden law) associate with a certain number of the atoms of any other.

“About 70 years ago, only a small number of “elementary particles”, thought to be the basic building blocks of matter, were known: the proton, the electron, and the photon as the quantum of radiation. All these particles are stable (the neutron is stable only in nuclear matter, the free neutron decays by beta decay: n→p+e−+\overline{\nu}). Owing to the availability of large accelerators, this picture of a few elementary particles has profoundly changed: today, the standard reference Review of Particle Properties lists more than 100 particles. The number is still growing as the energies and luminosities of accelerators are increased.”

Walter Greiner (1935–2016) German physicist

Source: Quantum Chromatodynamics (3rd ed., 2007), Ch. 1 : The Introduction of Quarks

“There is no kind of material, no body, and no thing that can be produced or conceived of, which is not made up of elementary particles;”

Vitruvius book De architectura

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book II, Chapter I, Sec. 9
Context: There is no kind of material, no body, and no thing that can be produced or conceived of, which is not made up of elementary particles; and nature does not admit of a truthful exploration in accordance with the doctrines of the physicists without an accurate demonstration of the primary causes of things, showing how and why they are as they are.