Who had direct inside knowledge of the canon through the alleged secret oral tradition? Some possible examples that have been alluded to include Pythagoras, Plato, Euclid, Copernicus, Galileo, Kepler, Leibniz and Newton. Grattan-Guinness mentions the oral tradition in The Norton History of the Mathematical Sciences but he gives no sources. Partial introduction to what is recorded in written history by Conifold Did geometric patterns in nature suggest the early notions of proportion and ratios?
Proportion is the key concept that underlies most of mathematics. In its modern guise, it's described as the straight line or linearity.
Now consider that the epitome of motion in Newtons theory is straight line motion. Further consider that Einstein then described motion in GR as straight lines on a curved surface. More, consider that calculus is simply the linearisation of a nonlinear function - in none variable, in many variables, in curved surfaces, in curved manifolds and in curved higher dimensional manifolds.
Even more, consider that quantum mechanics - mathematically speaking, is a linear theory.
Once one has understood the many different ways mathematicians have leveraged the concept of linearity, and hence proportionality into many areas and fields of mathematics, one might think that mathematics is simply the unfoldingness of one very simple idea: that of proportion.
This is an idea that every child can easily understand. It's not occult, nor is it a secret. It's one that every mathematician knows. Perhaps it's a secret to the average man in the street who is impressed by the occult looking symbols. This is the same impulse undoubtably that has driven numerology and astrology. Rest easy, there is only one single idea here - if one can only see it.
The Canon: An Exposition of the Pagan Mystery Perpetuated in the Cabala As the Rule of All Arts by William Stirling (architect)
The Canon is the numerical interpretation of the Cosmic law and, since man is a microcosm of the universe, it is also the law of human nature. The history of all civilizations is the history of their interpretation of the Canon. Codified by ancient philosophers and guarded by priests in the temples, the Canon sanctified the society that possessed it, regulating its institutions in accordance with the laws of nature. Plato, writing in "The Laws of the Egyptian Canon, " claimed that by its use the high civilization of ancient Egypt had been preserved from deterioration for 10,000 years.
The Canon was instituted by the ancient theocracies as a standard in music, architecture and all other arts. Even after the decline of the old world order and of the canonical standard, knowledge of the Canon was preserved in the mystery schools of Greece and Alexandria, and in the tradition of masonic and other craft guilds.
One of the most revolutionary books of the late 19th century, The Canon owes its high reputation to the august literary style of its author, as well as to its remarkable contents.
The old Masonic writers declare that the true system of the universe, and the foundation of all geometrical proportion is to be found in the forty-seventh proposition of Euclid, as expounded by Pythagoras, and communicated in writing by Plato, .... [p.56].
Guénon, René. The Reign of Quantity & The Signs of the Times. Sophia Perennis, 2001. "Critique of modern Western civilization from the point of view of traditional metaphysics."