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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.


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.

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    $\begingroup$ If your test is that arithmetic is "scientific" then numerology definitely precedes it since science emerged along with Pythagoreans. But it is more accurate to say that practical and playful/ritualistic uses of numbers developed in parallel, sometimes inseparably, see e.g. I Ching or Babylonian astrology. For prehistoric arithmetical artifacts see hsm.stackexchange.com/questions/3334/… $\endgroup$ – Conifold Jan 24 '17 at 2:35
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    $\begingroup$ Numerology is alive and well still today. There are lot of people trying to discover "deep meaning" into numbers. In ancient civilizations, the first speculations about numbers mixed purported "deep meaning" with "scientific" arithmetical meaning (e.g. the property of being prime) of numbers. $\endgroup$ – Mauro ALLEGRANZA Jan 24 '17 at 9:53
  • $\begingroup$ @Conifold Thanks for the paleolithic ink! Right now I'm working on a combinatorial game, and found this cave etching to be quite compelling, because it's on the floor as opposed to a wall (i.e. raising at least the possibility it could have been a gameboard.) Interesting point is that, in developing a novel set of combinatorial game mechanics, it was the application of metaphors to integers that provided the key insight, not mathematics per se. $\endgroup$ – DukeZhou Jan 24 '17 at 19:53
  • $\begingroup$ @MauroALLEGRANZA I find it interesting that mystical terms are still being applied to mathematical concepts, such as with transcendental numbers. I also know that Cantor's work on infinite sets, for instance, carried philosophical as well as mathematical implications. $\endgroup$ – DukeZhou Jan 24 '17 at 19:54
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    $\begingroup$ I wonder if there is a record of some number-theoretic properties discovered in the course of practicing numerology. On the other hand, Gematria-- a numerological system based on the Hebrew alphabet-- developed some pretty sophisticated techniques using what we would call recursive procedures, permutations, substitutions etc. See en.wikipedia.org/wiki/Gematria So one could argue that numerology is a precursor to combinatorics. $\endgroup$ – Margaret Friedland Jan 25 '17 at 18:12
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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.

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