Can Numerology be said to be the precursor of Number Theory?

Question

My understanding is that alchemy was a precursor to modern chemistry. Some might say that numerology, similarly, was an earlier form of what is now known as number theory, but I feel like it's a more complicated proposition.

At it's heart, numerology is about playing games with and finding relationships between numbers, which seems very similar to number theory. The key distinction may be that number theory is scientific where numerology is mystical, with perhaps some overlap prior to the Enlightenment, Pythagoreanism being an example.

My feeling is that arithmetic is very old indeed, and numerology cannot be said to precede arithmetic because it requires arithmetic.

But I also know there is a distinction between classical arithmetic and modern number theory, so I'd welcome any additional insight, correction, or related information in support or against this idea.

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Note: The impetus for this question came out of a recent question on Stack Mythology regarding the origin of 12 Olympians specifically. In a mythological context such as this, numerological ideas can hold some validity.

Although contemporary numerology is largely concerned with non-scientific prediction and non-scientific attempts to influence reality, I have also read convincing arguments that it may have been used as method of encoding esoteric knowledge, indicating a possible, practical use.

The most satisfactory answer to the question in question was related to the practical aspects of the integer 12.

Answer 1

As the saying goes - yesterday's magic is tomorrow's science. But really, humans progress this way on long timescales relative to a human's lifespan. Myth and superstition generally precede rational understanding, but sometimes the transition is messy. This seems to be a consequence of how humans learn by trial and error of their environment to seek patterns - the better we are at finding and modeling patterns the more we can learn (https://onlinelibrary.wiley.com/doi/pdf/10.1348/000712606X101808).

It is not unfair to classify numerology as a superstition. Sometimes the transition of beliefs from pseudoscience/superstitious to scientific/rational is clear, i.e. alchemy mostly died out by the late 1800's (never mind a few occultist revivalist movements) right when modern chemistry started taking off along with statistical physics (https://en.wikipedia.org/wiki/Alchemy#Late_modern_period). And hardly anyone knows about alchemy these days.

An example of an unclear transition could be from astrology to astronomy. Astrology was made up thousands of years ago and astronomy is relatively modern, and even though astrology is immensely outdated and debunked, still its concepts are more widespread through our population than are the objective facts of astronomy (look in a farmer's almanac and it has more about astrology than astronomy). (https://www.washingtontimes.com/news/2003/aug/17/20030817-105449-9384r/) (https://io9.gizmodo.com/more-than-1-3rd-of-americans-think-that-astrology-is-a-1520598014)

I think this is the case for the numerology to number theory transition, since the origins of numerology and of number theory emerged at around the same time - twas an unclear transition.

My feeling is that arithmetic is very old indeed, and numerology cannot be said to precede arithmetic because it requires arithmetic.

I think this is instead due to the fact that numerology and arithmetic were developed nearly simultaneously. For instance, as far as I understand these things, the Arabic Abjad system did not require the use of arithmetic. Chinese numerology also does not require the use of arithmetic, since it is more linguistic. (https://en.wikipedia.org/wiki/Chinese_numerology)

AS far as we can tell (what records we have), the origin of number theory precede the origin of numerology (assuming it began with Pythagoras), so numerology did not precede number theory. Who knows, maybe a long lost document will be found that shows otherwise.

Answer 2

Reviel Netz's The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History p. 278:

Astrology and number-lore present a different kind of problem. Putting them apart from mathematicians in the ‘Euclidean’ sense would not necessarily reflect ancient views. Mathematicus came to mean in Latin ‘astrologer’.³⁵ As for number-lore, Plato’s lecture had already led directly from the mathematical sciences to the conclusion that the good is unity.³⁶ But I will not count astrologers and numerologists as mathematicians. This is not cultural snobbery. Rather, I am concentrating on the issues which are important for my study, which are cognitive. Astrology and numerology, in themselves, do not impose the same cognitive regime as ‘Euclidean’ mathematical sciences do. A person who has devoted himself to astrology alone, with no element of astronomy, while he may have, say, calculated a great deal, has never proved anything, and he therefore cannot be seen as a mathematician from the perspective adopted in this study.

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<sup>35. s.v. Lewis & Short, 2. ‘post-Aug.’
36. Aristoxenus, El. Harm. II.30.</sup>

Reviewer B. Artmann argues (MR1683176) that "Nicomachus' arithmetic" is "admittedly a book on the border of mathematics and numerology."