Samuel 13:1 tells us that Saul was one year old when he began to reign: “ben shana Shaul be-malcho.” If you look at the Soncino, their translation suggests that there is a textual difficulty here and offers: “Saul was __ years old when he began to reign.” But the Daat Mikra suggests: “b-n” was a way of writing “52.” This raises the issue of whether the ancient Israelites thought in terms of numerical equivalents of letters.
There are many references to gematria by Amoraim, and some halachot seem to be derived from them. For example, when a nazir takes a vow for an unspecified period, the period is assumed to be 30 days based on a gematria. See Nazir 5a.
But what about derivations from gematria, or at least the use of numerical equivalents of letters, earlier than the Talmud?
At Avot 3:23 there is a statement that “tekufot ve-gematriot” are only “parperaot” (=peripheral) to wisdom. But the meaning of “gematriot” here may simply be “mathematics.” (“Tekufot” means “astronomy.”)
The last Mishnah in Uktzin uses a gematria and states that God will give each tzaddik 310 worlds, citing a verse that uses the word “yesh” (yod-shin). But this statement is in the name of R. Joshua b. Levi, an Amora.
If we look further, we can find Tannaitic sources that employ gematria. Scattered statements of gematria are made by Tannaim that are found in the Talmud. One example is a statement by a R. Natan at Shabbat 70a. (See Encyclopaedia Judaica 7:369.) He cites a gematria based on a verse to explain the source of the concept of 39 forbidden labors on Shabbat. Another example of a gematria from the Tannaitic period is the baraita at Ber. 8a about the word “totzaot.”
But what about before the Tannaim? Can we find examples of gematria in the B.C.E. period? Even simpler, do we know that Jews understood their letters as having numerical values in the B.C.E. period?
The earliest source for the use by Jews of letters to reflect numerical values are coins issued by King Yannai. Among the coins he issued are ones in which the letters “caf-heh” are used to indicate the 25th year of his reign (=78 B.C.E.). (Some coins perhaps have the date “caf.” There is a dispute as to the actual readings.) (Also relevant in the pre-70 C.E. period is Mishnah Shekalim 3:2.)
But is it possible that we used letters to reflect numerical values even in the First Temple period and earlier? It is possible, but we have no sources for this practice. (The fact that we have no sources here is not surprising. We barely have sources for anything outside the Tanach in the Biblical period.)
Already in the third century B.C.E., and probably earlier, the Greeks used letters to reflect numerical values and they too had a system where equations between words were made based on numerical values. Their system was called “isopsephy.” (It means “equal pebbles.” The early Greeks used pebbles arranged in patterns to learn arithmetic. The word “calculate” derives from the Latin word “calculus”=pebble. There is an interesting article on Wikipedia on “isopsephy.”) The scholar S. Lieberman (“Hellenism in Jewish Palestine,” 1962, p. 73) theorizes that the use of letters as numerals was “a Greek invention that was adopted by the Semites at a much later time.” But no one really knows. (It is interesting that in the Greek system the value for their 11th letter is 20, the value for their 12th letter is 30, etc., etc., just like in our system. This perhaps implies a common origin for the two systems but is not telling us which came first.)
Now let me address a different issue. There is a system that we call today “A-T-B-Sh.” It is a way of writing where you write the last letter, “tav,” to mean “aleph,” “shin” to mean “bet,” etc., etc. The Talmud refers to this system. (It refers to this system as “gematria,” see San. 22a.)
At Jeremiah 51:41, a place name Sheshach is referred to in the same verse as a reference to Bavel (Bet-Bet-Lamed) and seems to be another way of referring to Bavel. Is it possible that Jeremiah is using “A-T-B-Sh” here? In “A-T-B-Sh,” “B-B-L” would be written as “Sh-Sh-C.” Many scholars are willing to accept this approach since we have never found a place named “Sheshach” in or around Babylonia. Also, “A-T-B-Sh” is not dependent on the use of letters to represent numerals. Scholars also observe that letters in antiquity were sometimes written in the following pattern: one line left to right, the next line right to left, the next line left to right, etc. If an ancient Israelite wrote the alphabet in this manner he would regularly see the “A-T-B-Sh” correspondences.
There is other evidence for the use of “A-T-B-Sh” by Jeremiah. At 51:1 he uses the phrase “lev kamai” (=the heart of those who stand against me). L-B-K-M-Y is the equivalent of K-S-D-Y-M in “A-T-B-SH.” The Kasdim are another Biblical term for the Babylonians.
To sum up, a mainstream (but unproven) view is that Jews did not use gematria prior to the Hellenistic period, since we may not have equated letters with numerical values until the Hellenistic period. But “A-T-B-Sh” may have already been in use in the Biblical period. (Its use was not necessarily to conceal, but more likely to amuse.)
Three more points:
1. Scholars who write about the origin of gematria often point out that the Assyrian king Sargon II (eighth cent. B.C.E.) wrote that he made the wall of his newly founded capital 16,283 cubits long in accordance with the numerical value of his name. (Scholars do not yet understand how the length was made equal to his name.) This is the earliest instance of gematria in some form in the ancient near East. But the issue remains whether this has any relevance for ancient Israel.
2. Regarding the etymology of the word “gematria,” the Greek word (“geometry”) originally meant “measuring the earth.” Jastrow and many other scholars observed that the way the Talmud used the word “gematria” did not correspond with this. They suggested that the word “gematria” in the Talmud was a transposition from a Greek word “gramattia” that meant “letters.” But more recent scholarship observes that even in Greek we can find the word “geometry” used as a number that results from a numerological calculation. So there is no reason to posit a transposition and connect it with “grammatia.”
3. Rav Hershel Schachter discusses gematria briefly in his Divrei Soferim. He concludes that gematria is “not the actual source for any matter in Halacha or in Jewish thought.” He is willing to take this position because there are Rishonim who write, in particular instances, that the gematria mentioned in the Talmud is just an allusion to an idea that was derived independently. (He cites Rambam and Ramban, for example.) Rav Schachter concludes that “it would be advisable for the yeshivot that educate young children to de-emphasize these derivations and to greatly decrease the time spent on them.”
(Many of the points I made come from an article by Stephen Lieberman in HUCA, vol. 58, 1987.)
Mitchell First can be reached at [email protected] In his own alternative gematria system, the gematria of his last name is “1.”