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Is numerology an acceptable Jewish practice, and if so how does one differentiate between it and non-Jewish forms?

According to Wikipedia

Numerology is any belief in the divine or mystical relationship between a number and one or more coinciding events. It is also the study of the numerical value of the letters in words, names, and ideas. It is often associated with the paranormal, alongside astrology and similar divinatory arts.

The second sentence sounds like Gematria. However, does Judaism accept any connection between numbers and events or the description in the last sentence?

Is it Jewish to ask someone their birthday and assign characteristics to them using that information? I'm going to assume this type of practice is not condoned.

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Your question spans across numerology and astrology. Both have strong backing in Jewish tradition but rather when using them in a descriptive way (to explain the past) and not to make predictions. To answer your question directly, it is "Jewish" to believe people are influenced by their birthdate although they retain much freedom to influence their fate and that specific dates/months have particular influences on the Jewish people.

More specifically:

Jewish numerology - gematria - works with correspondence between letters and numbers, and have been used heavily in text analysis (e.g., the Baal Haturim on the Torah). In the words of myjewishlearning "If a word’s numerical value equals that of another word, a commentator might draw a connection between these two words and the verses in which they appear and use this to prove larger conceptual conclusions."

Jewish astrology also has strong sources, for instance the belief that certain months have positive (e.g., Adar) or negative (e.g., Av) connotations, see TB Taanit 29b

Rav Pappa said: Therefore, in the case of a Jew who has litigation with a gentile, let him avoid him in the month of Av, when the Jews’ fortune is bad, and he should make himself available in Adar, when his fortune is good.

Another gemara (Shabbat 156a) lists the impact of being born on a certain day or at a certain hour. See there at length. However the gemara concludes that there is no influence of constellations on Israel since it can be counteracted with good deeds.

It is clear that earlier Torah sages were masters in understanding seasons and gematriot (numerology) as well as other esoteric matters (see e.g., Rabban Yoḥanan ben Zakkai in Sukkah 28a).

Nowadays though, one should not use astrology or numerology to predict the future. chabad.org describes it well

The Torah states (Deuteronomy 18:10) “There shall not be found among you one who calculates times.” The Talmud, in the name of Rabbi Akiva, specifically applies this prohibition to one who calculates auspicious times, meaning that one should not make astrology a dominant influence in one’s daily life and predictions through astrology are forbidden. Therefore one should not use horoscopes to determine one’s future actions, though it is permitted to do character analyses through astrology.

Finally, I checked R Yaakov Hillel's Faith and Folly which is a wonderful review of all sorts of occult practices, clearly differentiating between the permitted and the forbidden. Regarding astrology he explains (pp. 55ff) that Jews are beyond the influence of constellations, even more as their perform mitzvot and improve their bonding to God through prayer and Torah study, and quotes the Zohar that a sinner severs his bond with God and his evil deeds block the influences of sanctity, therefore placing him again under the rules of the constellations.

He does not list numerology as a forbidden practice directly, but forbids divining auspicious times, divining by omens and consulting mediums and oracles.

For further reading see also here.

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There's a distinction to be made between finding relationships between words and ideas or maybe describing personal traits and predicting the future.

The former is perfectly fine, as you mentioned, it is well known Gematriot, the later is forbidden under "לא תעוננו" as a branch of idolatry.

Clarification: similarly to astrology, it might be allowed to predict large-scale events, that influence large groups of people (aka General providence) but it is forbidden to make personal predictions (aka Private providence). For example, as in printed in weekly horoscopes - "This week, people of Aries tend to improve their finances" - is OK but "you will seriously profit on Tuesday" is forbidden.

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    Al, there are so many questions that you answer without sources ... who says the last para is correct? Why should we trust you? By now you have noticed that most answerers aim to back their assertions with sources, otherwise how can a reader know whether to trust the answer. You know so very much, but I'm afraid you're not getting the recognition due to you because you don't source enough of your answers – mbloch Feb 11 at 14:24
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    Especially when you could be providing valuable sources and resources in many cases – Dr. Shmuel Feb 11 at 15:05
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    @mbloch In support of your comment to this answer, just consider the contents of Sefer Raziel and Sefer Noach. They both deal with exactly the 'astrological' things that are excluded by the "Clarification". There are multiple categories mentioned in the question of the OP. A proper answer here would be very broad. Truth is, the question needs to be worked on. The language of Rabbi Wikipedia is pretty general. – Yaacov Deane Feb 11 at 16:08
  • I was told to provide a definition for numerology. To be honest, I'm not sure what "numerology" is. Is there such a thing as Jewish numerology. That's what I'm trying to understand. – user27343 Feb 12 at 4:35
  • @mbloch 1. In my view, a true but unsourced answer is better than none. I think -1 should be used when the answer is wrong, as סור מרע but if the answer is true, but not perfect it's just lack of עשה טוב basically. 2. You guys are welcomed to put your effort into answering instead of criticizing others. 3. Some questions need a broad understanding of the topic, instead of bringing narrow sources nobody can truly understand. – Al Berko Feb 12 at 12:58

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