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It is widely accepted that each letter of the Hebrew alphabet has a Gematria (numerical value) attached to it. These numerical values often provide insight when comparing one Gematria to either another Gematria, or a significant number in Judaism. We possibly even learn out Halacha from gematria.

Are there any authorities that reject the existence of this numerical value system, and/or the meaning and insights that they provide? I am looking for Rishonim preferably, or Achronim.

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    Its hard to believe anyone would reject it entirely since Stam nazir is learnt from Gematria in the gemarah – sam Aug 22 '14 at 18:28
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    @sam that could (and probably is) an asmachta, or just a cute remez be'alma – הנער הזה Aug 22 '14 at 18:59
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    @Matt Even if it's an asmachta, you cannot deny the system therefore exists. – Double AA Aug 22 '14 at 19:53
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    @user6618 ibn 3azra commentary on bareisheeth 14 14 – MoriDowidhYa3aqov Aug 22 '14 at 21:11
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    @MoriDoweedhYaa3qob ן׳ עזרא there rejects it as פשט, accepting it as "דרך דרש". – msh210 Aug 24 '14 at 5:47
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Ibn Ezra appears to reject gematria as a means of discovering meaning. In response to Rashi's equating the 318 men with Eliezer (see Genesis 14:14), he writes:

" חניכיו - שחנכם פעמים רבות במלחמה ואם לא נזכר. וחשבון אותיות אליעזר דרך דרש, כי אין הכתוב מדבר בגימטריא, כי יכול יוכל הרוצה להוציא כל שם לטוב ולרע, רק השם כמשמעו."

"and the count of the letters Eliezer is by way of derash, for the Scriptures does not speak in gematria, for anyone who wishes is able to cast any name for good or for bad. Rather the name is as its simple implication."

As I discuss in this post, it seems that he regards this as allegorical, because one can twist gematria any which way one chooses. To emphasize the point, note that when Ibn Ezra says that a midrash is דרך דרש, he does not mean that it is a historical fact which happens to be a midrash. It is obvious that this is a midrash, which comes from a midrashic source and employs midrashic methods. Rather, he is saying that there is a homiletic point, a "drush", which Chazal wish to convey, and they use the midrash as a way of clothing that point. So the midrash is not historical, nor is it a way of extracting any intended meaning from the text.

Also, here is another instance in which Ibn Ezra is silent in the face of gematria. This is interpretable in different ways, but see his comment on Rut 2:

[ב, יז] ויהי כאיפה שעורים. פעם אחת שאלני אדם, מה טעם באיפה שעורים. אמרתי לו, אין טעם לשאלה הזאת, כי הכתוב ספר מה היה. אז נקלותי בעיניו, ויאמר לי כי יש לו טעם, ואני החרשתי ממנו ולא שאלתיו. והנה בא ביום אחד ואמר לי, כי יש לו טעמים הרבה. האחד שראתה רות בדרך נבואה כי עתיד היה אחד מבניה להעמיד עמוד על שם בעלה, וטעם 'איפה' - צ"ו רמונים שהיו על העמוד, וזה בגימטריא 'איפה', ופירוש 'שעורים' כמו 'שיעורים' כמו 'שער בנפשו'. וטעם אחר, 'ויהי' - שתי מלות, ארמית ועברית. והיא כאשר ראתה שיתלה אבשלום שהוא מבניה, והנה כ"ף עם אל"ף רמז לשנות אבשלום במותו. ואחר כך 'איפה שערים' - לשון רבים, בעבור היותו כבד עליו. וטעם אחר, כי תחילת אות כאיפה עם תחילת שעורים הוא בגמטריא 'ישי' שהוא צדיק גמור. אז שמח וישב לבו בקרבו.

  • But then again, see here (to be clearer, objecting to the vague generalization of "appears to reject gematria as a means of discovering meaning" since derash is meaning also) – MTL Aug 26 '14 at 4:08
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    I elaborate in my linked post. I allege that when Ibn Ezra calls a midrash "derech derash", he does not mean it is a midrash. Obviously it is a midrash. It uses midrashic methods and comes from a midrashic source. Rather, he is saying that the midrash is not historical, and that Chazal are expressing their ideas in allegory. In this way, the gematria is not at all the meaning of the text, but just a mechanism and a cloak for the rabbinic authors to express their ideas. – josh waxman Aug 26 '14 at 4:19
  • I hear that. You might want to consider an edit to clarify that point, rather than just linking out for a main point. – MTL Aug 26 '14 at 13:55
  • good idea. now edited. – josh waxman Aug 27 '14 at 0:40
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R. Yehuda Aryeh Modena in his work Ari Nohem (p. 31) criticizes the method of using gematria as any kind of proof, primarily because anything can be "proved" this way.

דבשלמא אם אחר הנחה אמתית ומקובלת וברורה מן התורה נמצא איזה ראשי תיבות או סופי תיבות או גימטריאות להיות לנו כמן זכרון מקומי הוא יפה אף נעים אך להוכיח דבר בלתי נודע ובלי ראיה אחרת וכ"ש מסודות התורה למעלה מן השכל והסברא מכח אחד מאלה הבל הבלים יחשב לכל משכיל כי מי לא ידע שכל אדם פקח וחריף יוכיח ההפך וכל דבר ודבר באותו דרך בעצמו וכן אני אומר לשומדים ברצונם להוכיח איזה עיקר גדול נגדנו על פי ראשי תיבות וגימטריאות והופך להם הדרך ההוא בעצמו נגד פניהם ולכן אמרו חכמינו ז"ל תקופות וגמטריאות פרפראות לחכמה כפרפרת ללפת את הפת ר"ל יופי וסיוע לחכמה אבל לא חכמה

If following a premise that is true, accepted, and clear from the Torah, we find acronyms or last-letter-acronyms or numerical equivalencies to be a memory aide, it is fine and even nice. But to prove something hitherto unknown, and without any other proof, especially about the secrets of the Torah which are above the intellect, using one of these methods, would be considered utter folly by any intellectual. For who does not know that any astute and sharp man can prove the opposite or anything else using the very same method? And so I tell missionaries when they try to prove some major idea against us via acronyms and numerical equivalencies, and reverse their very methods to their faces. And therefore the Sages stated that calculations and numerical equivalencies are seasoning for wisdom like seasoning for bread, meaning to say that they are beautifiers and facilitators for wisdom but they are not actually wisdom.

Later on (p. 49) he mentions this again.

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The most telling piece in the puzzle is the mishna in Avos which reffers to gematarios as being a appetizer for wisdom and none of the major mipharshim explain it to mean the letters equal numbers idea. The exception is the pirush attributed (incorrectly) to Rashi. But even according to him the point of the mishna is to juxtapose gemataria against halacha.

Another point is that gemataria is not on any list of drashos that the Torah is nidrash with. Not on the list of thirteenth or thirty two.

Once while desperately looking for someone who discusses the subject I did find a Ramban who seemed to say halachicaly a gemataria is an asmachta or along those lines. I will try to find that maareh makom again bl'n.

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If you may allow me to answer from a broader perspective the question "is gematria acceptable by all?", if defined rigorously, yes. After all, gematria is but an alphanumeric system.

For instance, the Method of Gematria that allows association can be precisely defined as follows: Let V_1 and V_2 be two verses in the Bible. Let N_1 be the total gematria of a set of words in V_1. Let N_2 be the total gematria of a set of words in V_2. It is possible that V_1 and V_2 are contextually or thematically linked if and only if N_1=N_2.

Once we have a precise definition, it is possible to invoke existing mathematical axioms to create other useful definitions. For instance, we can use prime numbers to find associations in biblical texts. Let V_1 and V_2 be two verses in the Bible. Let N_1 be the gematria of a set of words in V_1. Let N_2 be the gematria of a set of words in V_2. It is possible that V_1 and V_2 are contextually or thematically linked if and only if Prime(N_1 )=N_2. In this way, we are using gematria within existing mathematical axioms.

Once we have such definitions, we can prove theorems using gematria, For example, it is simple to prove the following theorem based on the above definition using prime numbers. THEOREM: Let N be a quantity, with N being a natural number. Then Prime(N) can be the total gematria of a set of verses in the Bible. Conversely, let Prime(N) be the total gematria of a set of verses in the Bible. Then N can be the total gematria of a set of verses in the Bible.

In addition, if used within a biblical framework, it is just as valid as any tool for biblical interpretation. For example, if we insist (which we can always do) that the outcome of any gematria-based analysis satisfies Deuteronomy 29:29, then divination by the application of gematria or numerology has no foothold.

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