GEMATRIA (from Gr. γεωμετρία), one of the aggadic hermeneutical rules for interpreting the Torah (*Baraita of 32 Rules, no. 29). It consists of explaining a word or group of words according to the numerical value of the letters, or of substituting other letters of the alphabet for them in accordance with a set system. Whereas the word is normally employed in this sense of manipulating according to the numerical value, it is sometimes found with the meaning of "calculations" (Avot 3:18). Similarly where the reading in present editions of the Talmud is that Johanan b. Zakkai knew "the heavenly revolutions and gematriot," in a parallel source the reading is "the heavenly revolutions and calculations" (Suk. 28a; bb 134a; Ch. Albeck, Shishah Sidrei Mishnah, 4 (1959), 497).
The use of letters to signify numbers was known to the Babylonians and the Greeks. The first use of gematria occurs in an inscription of Sargon ii (727–707 b.c.e.) which states that the king built the wall of Khorsabad 16,283 cubits long to correspond with the numerical value of his name. The use of gematria (τὸ ὶσόψηφον) was widespread in the literature of the Magi and among interpreters of dreams in the Hellenistic world. The *Gnostics equated the two holy names Abraxas (ʾΑβράξας) and Mithras (Μίθρας) on the basis of the equivalent numerical value of their letters (365, corresponding to the days of the solar year). Its use was apparently introduced in Israel during the time of the Second Temple, even in the Temple itself, Greek letters being used to indicate numbers (Shek. 3:2).
In rabbinic literature numerical gematria first appears in statements by tannaim of the second century. It is used as supporting evidence and as a mnemonic by R. Nathan. He states that the phrase Elleh ha-devarim ("These are the words") occurring in Exodus 35:1 hints at the 39 categories of work forbidden on the Sabbath, since the plural devarim indicates two, the additional article a third, while the numerical equivalent of elleh is 36, making a total of 39 (Shab. 70a). R. Judah inferred from the verse, "From the fowl of the heavens until the beast are fled and gone" (Jer. 9:9), that for 52 years no traveler passed through Judea, since the numerical value of behemah ("beast") is 52. The Baraita of 32 Rules cites as an example of gematria the interpretation that the 318 men referred to in Genesis 14:14 were in fact only Eliezer the servant of Abraham, the numerical value of his name being 318. This interpretation, which occurs elsewhere (Ned. 32a; Gen. R. 43:2) in the name of *Bar Kappara, may also be a reply to the Christian interpretation in the Epistle of Barnabas that wishes to find in the Greek letters τιη, whose numerical value is 318, a reference to the cross and to the first two letters of Jesus' name, through which Abraham achieved his victory; the Jewish homilist used the same method to refute the Christian interpretation. These gematriot are based on the first of four methods of calculating the numeral value of the letters of the Hebrew alpha. Known as Mispar Hekhreḥi, absolute or normative value, each letter is given a specific numerical equivalent. Alef equals 1, bet equals 2, gimmel equals 3, and so on until yod, the tenth letter, which equals 10. The next letter, kaf, equals 20, then lamed, which equals 30, and so on until kuf, which equals 100. The last three letters, resh, shin, taf, equal 200, 300, and 400, respectively. The final forms of the letters, kaf, mem, nun, pei, and ẓadi, used when these letters appear at the very end of a word, are often given the same numerical equivalent as the standard form of the letter. Sometimes, they are given the values 500, 600, 700, 800, and 900, respectively. This brings the numerical equivalencies of the Hebrew alphabet to 1,000, for the alef, the first letter, can also symbolize 1,000. The word alef can also be readas elef, meaning 1,000.
The next two methods of gematria calculation are Mispar Sidduri, ordinal value, where each of the 22 letters of the Hebrew alphabet are given a number between 1 and 22, and Mispar Katan, reduced value, where every letter is equal to a single digit number. This is accomplished by removing the value of 10 or 100. Thus, the alef equals 1, but so do the yod and the kuf, which equal 10 and 100 in the absolute or normative value system. In these last two systems, the five letters that have final forms are usually given the same value as the standard form of the letter. At times, they are assigned special value.
The fourth method, Mispar Katan Mispari, integral reduced value, reduces the total value of the word to a single digit number. If the sum exceeds nine, then the integer values of the total are added together again and again until a single digit number is received. For example, the word, ḥesed (lovingkindness) has an absolute or normative value of 72. The ḥet equals 8, the samakh equals 60, and the dalet equals 4. The numbers of the sum of 72 are then added together (7 plus 2) to equal 9. It should be pointed out that the integral reduced value of the ordinal value and the reduced value of ḥesed also add up to 9.
In Kabbalah, an additional system of gematria is used. The absolute or normative value of a word is calculated by treating each letter as a word and then adding up all of the numerical equivalencies of these letter-words. This system is called milu'i or milu'im. Since some letters can be spelled differently as words, different numerical equivalencies can be achieved for a single word. Thus, the Tetragrammaton, yod, hei, vav, and hei, has the values of 72, 63, 45, or 52, each of which has vital significance in Kabbalah.
The form of gematria which consists of changing the letters of the alphabet according to atbash, i.e., the last letter ת is substituted for the first א, the penultimate ש for the second ב, etc., already occurs in Scripture: Sheshach (Jer. 25:26; 51:41) corresponding to Bavel ("Babylon"). The Baraita of 32 Rules draws attention to a second example: lev kamai (Jer. 51:1) being identical, according to this system, with *Kasdim. Another alphabet gematria is formed by the atbaḥ system, i.e., ט is substituted for א, ח for ב, etc., and is called "the alphabet of Ḥiyya" (Suk. 52b). Rav, the pupil of Ḥiyya, explained that Belshazzar and his men could not read the cryptic writing because it was written in gematria, i.e., according to atbaḥ (Sanh. 22a; cf. Shab. 104a).
Gematria has little significance in halakhah. Where it does occur, it is only as a hint or a mnemonic. The rule that when a man takes a nazirite vow for an unspecified period, it is regarded as being for 30 days, is derived from the word yihyeh ("he shall be") in Numbers 6:5, whose numerical value is 30 (Naz. 5a). Even in the aggadah, at least among the early amoraim, gematria is not used as a source of ideas and homilies but merely to express them in the most concise manner. The statements that Noah was delivered not for his own sake but for the sake of Moses (Gen. R. 26:6), that Rebekah was worthy to have given birth to 12 tribes (ibid. 63:6), and that Jacob's ladder symbolizes the revelation at Sinai (ibid. 68:12), do not depend on the gematriot given there. These homilies are derived from other considerations and it is certain that they preceded the gematriot.
Gematriot, however, do occupy an important place in those Midrashim whose chief purpose is the interpretation of letters, such as the Midrash Ḥaserot vi-Yterot, and also in the late aggadic Midrashim (particularly in those whose authors made use of the work of *Moses b. Isaac ha-Darshan), including Numbers Rabbah (in Midrash Aggadah, published by S. Buber, 1894) and Bereshit Rabbati (published by Ḥ. Albeck, 1940; see introduction, 11–20). Rashi also cites gematriot that "were established by Moses ha-Darshan" (Num. 7:18) and some of the gematriot given by him came from this source even if he does not explicitly mention it (Gen. 32:5, e.g., "I have sojourned with Laban" – the gematria value of "I have sojourned" is 613, i.e., "I sojourned with the wicked Laban but observed the 613 precepts," is the interpretation of Moses ha-Darshan, Bereshit Rabbati, 145). Joseph *Bekhor Shor, one of the great French exegetes of the Torah, made extensive use of gematriot, and nearly all the tosafists followed him in this respect in their Torah commentaries (S. Poznański, Mavo al Ḥakhmei Ẓarefat Mefareshei ha-Mikra, 73). A wealth of gematriot occur in Pa'ne'aḥ Raza, the commentary of Isaac b. Judah ha-Levi (end of 13th century), and in the Ba'al ha-Turim, the biblical commentary of *Jacob b. Asher. The Kabbalah of the *Ḥasidei Ashkenaz also caused gematriot to enter the halakhah. In his Ha-Roke'aḥ, *Eleazar of Worms uses gematriot to find many hints and supports for existing laws and customs; with him the gematria at times embraces whole sentences. Thus he establishes by gematria from Exodus 23:15 that work which can be deferred until after the festival may not be performed during the intermediate days (Ha-Roke'aḥ, no 307). Gematriot of the Ḥasidei Ashkenaz occupy a prominent place in their commentaries on the liturgy and on piyyutim. Abraham b. Azriel incorporated the teachings of Judah he-Ḥasid and Eleazar Roke'aḥ in his Arugat ha-Bosem, and followed their lead. These gematriot, which were part of the Kabbalah of the Ḥasidei Ashkenaz, established the definitive text of the prayers, which came to be regarded as sacrosanct. Some authorities forbade it to be changed even when the text did not conform with the rules of grammar. *Naḥmanides, on the other hand, tried to limit the arbitrary use of gematriot and laid down a rule that "no one may calculate a gematria in order to deduce from it something that occurs to him. Our rabbis, the holy sages of the Talmud, had a tradition that definite gematriot were transmitted to Moses to serve as a mnemonic for something that had been handed down orally with the rest of the Oral Law… just as was the case with the gezerah shavah [see *Hermeneutics] of which they said that no man may establish a gezerah shavah of his own accord" (Sefer ha-Ge'ullah ed. by J.M. Aronson (1959), Sha'ar 4; see his commentary to Deut. 4:25).
Despite *Naḥmanides' attempt to limit its use, gematria found its way into biblical commentary. The Pane'aḥ Raza by Isaac ben Judah ha-Levi (late 13th century) and Ba'al ha-Turim by Jacob ben Asher (c. 1270 to 1340) both make frequent use of gematria. Indeed, gematria became a staple element in kabbalastic literature. For example, the 17th-century work, Megalleh Amukkot, by Nathan Nata ben Solomon Spira, uses gematria extensively. The followers of *Shabbetai Zevi used gematria as proof of his messianism.
Gematria is still used to this very day. Indeed a search on the "Google" internet search engine reveals over 106,000 references to gematria on the World Wide Web, a great number of these sites deal with Christianity, witchcraft, and general (non-Jewish) mysticism. Numerous contemporary Jewish books have been published about gematria as well as assisting the reader to find his own gematria equivalencies. For instance, one such book, Sefer Gematrikon (Jerusalem, 1990) provides gematria equivalents for the numbers 1 to 1,000.
[Encyclopaedia Hebraica /
David Derovan (2nd ed.)]
The use of gematria was developed especially by the Hasidei Ashkenaz and circles close to them in the 12th and 13th centuries. It is possible that traditions of gematriot of Holy Names and angels are from an earlier date, but they were collected and considerably elaborated only in the aforesaid period. Even among the mystics gematria is not generally a system for the discovery of new thoughts: almost always the idea precedes the inventing of the gematria, which serves as "an allusion *asmakhta." An exception is the gematria on the Holy Names, which are in themselves incomprehensible, or that on the names of angels whose meaning and special aspect the German Ḥasidim sought to determine via gematria. Often gematria served as a mnemonic device. The classic works of gematria in this circle are the writings of *Eleazar of Worms, whose gematriot are based – at any rate partially – on the tradition of his teachers. Eleazar discovered through gematria the mystical meditations on prayers which can be evoked during the actual repetition of the words. His commentaries on books of the Bible are based for the most part on this system, including some which connect the midrashic legends with words of the biblical verses via gematria, and some which reveal the mysteries of the world of the *Merkabah ("fiery chariot") and the angels, in this way. In this interpretation the gematria of entire biblical verses or parts of verses occupies a more outstanding place than the gematria based on a count of single words. For example, the numerical value of the sum of the letters of the entire verse "I have gone down into the nut garden" (Songs 6:11), in gematria is equivalent to the verse: "This is the depth of the chariot" (merkavah). Several extensive works of interpretation by means of gematria by the disciples of Eleazar of Worms are preserved in manuscript.
In the beginnings of Sephardi Kabbalah gematria occupied a very limited place. The disciples of *Abraham b. Isaac of Narbonne and the kabbalists of Gerona hardly used it and its impact was not considerable on the greater part of the Zohar and on the Hebrew writings of *Moses b. Shem Tov de Leon. Only those currents influenced by the tradition of the Hasidei Ashkenaz brought the gematria into the kabbalistic literature of the second half of the 13th century, mainly in the work of *Jacob b. Jacob ha-Kohen and Abraham *Abulafia and their disciples. The works of Abulafia are based on the extensive and extreme use of gematria. His books require deciphering before all the associations of the gematriot in them can be understood. He recommended the system of developing power of association in gematria to discover new truths, and these methods were developed by those who succeeded him. A summary of his system is found in Sullam ha-Aliyyah by Judah *Albotini, who lived a generation after the Spanish expulsion (Kirjath Sefer, 22 (1945–46), 161–71). A disciple of Abulafia, Joseph *Gikatilla, used gematria extensively as one of the foundations of the Kabbalah in Ginnat Egoz (Hanau, 1615; the letters gimmel, nun, tav of Ginnat are the initials of gematria notarikon, and temurah – the interchange of letters according to certain systematic rules). This work influenced considerably the later Zohar literature, Ra'aya Meheimna and Tikkunei Zohar.
Two schools emerged as the Kabbalah developed: one of those who favored gematria, and another of those who used it less frequently. In general, it may be stated that new ideas always developed outside the realm of gematria; however, there were always scholars who found proofs and wide-ranging connections through gematria, and undoubtedly attributed to their findings a positive value higher than that of a mere allusion. Moses *Cordovero presented his entire system without recourse to gematria, and explained matters of gematria only toward the end of his basic work on Kabbalah (Pardes Rimmonim). A revival of the use of gematria is found in the Lurianic Kabbalah, but it is more widespread in the kabbalistic works of Israel *Sarug and his disciples (mainly Menahem Azariah of *Fano and Naphtali *Bacharach, author of Emek ha-Melekh) than in the works of Isaac *Luria and Ḥayyim *Vital. The classic work using gematria as a means of thought and a development of commentative ideas in the Kabbalah in the 17th century is Megalleh Amukkot by Nathan Nata b. Solomon Spira, which served as the model for an entire literature, especially in Poland. At first only the part on Deut. 3:23ff. was published (Cracow, 1637) which explains these passages in 252 different ways. His commentary on the whole Torah (also called Megalleh Amukkot) was published in Lemberg in 1795. Apparently Nathan possessed a highly developed sense for numbers, which found its expression in complex structures of gematria. In later kabbalistic literature (in the 18th and 19th centuries) the importance of the methods of commentary via gematria is well-known and many works were written whose major content is gematria, e.g., Tiferet Yisrael by Israel Ḥarif of Satanov (Lemberg, 1865), Berit Kehunnat Olam by Isaac Eisik ha-Kohen (Lemberg, 1796; complete edition with commentary of gematria, 1950), and all the works of Abraham b. Jehiel Michal ha-Kohen of Lask (late 18th century).
In the Shabbatean movement, gematriot occupied a place of considerable prominence as proofs of the messianism of *Shabbetai Ẓevi. Abraham *Yakhini wrote a great work of Shabbatean gematriot on one single verse of the Torah (Vaveiha-Ammudim, Ms. Oxford), and the major work of the Shabbatean prophet Heshel *Zoref of Vilna and Cracow, Sefer ha-Ẓoref, is based entirely on an elaboration of gematriot surrounding the verse Shema Yisrael ("Hear O Israel"; Deut. 6:4). In ḥasidic literature gematria appeared at first only as a byproduct, but later there were several ḥasidic rabbis, the bulk of whose works are gematria, e.g., Igra de-Khallah by Ẓevi Elimelekh Shapira of *Dynow (1868), Magen Avraham by Abraham the Maggid of Turisk (1886), and Sefer Imrei No'am by Meir Horowitz of Dzikow (1877).
The systems of gematria became complicated in the course of time. In addition to the numerical value of a word, different methods of gematria were used. In Ms. Oxford 1,822, one article lists 75 different forms of gematriot. Moses Cordovero (Pardes Rimmonim, part 30, ch. 8) lists nine different types of gematriot. The important ones are the following:
(1) The numerical value of one word (equaling the sum of the numerical value of all its letters) is equal to that of another word (e.g., גבורה (gevurah) = 216 = אריה (aryeh)).
(2) A small or round number which does not take into account tens or hundreds (4 = ת; 2 = כ).
(3) The squared number in which the letters of the word are calculated according to their numerical value squared. The Tetragrammaton, יהו״ה = 102 + 52 + 62 + 52 = 186 = מקום ("Place"), another name for God.
(4) The adding up of the value of all of the preceding letters in an arithmetical series (ד (dalet) = 1 + 2 + 3 + 4 = 10). This type of calculation is important in complicated gematria that reaches into the thousands.
(5) The "filling" (Heb. millui); the numerical value of each letter itself is not calculated but the numerical values of all the letters that make up the names of the letter are calculated (בי״ת = 412; דל״ת = 434; יו״ד = 20). The letters ה and ו have different "fillings" – הא ,הה ,הו and ויו ,ואו ,וו; millui dealefin (alef "filling"), millui de-he'in (he "filling"), or millui deyudin (yod "filling"), respectively. These are important in Kabbalah with regard to the numerical value of the Name of God (יהו״ה), the Tetragrammaton, which varies according to the four different "fillings" יוד, הא, ואו, הא (= 45, in gematria אָדָם (Adam), symbolizing the 45-letter Name of God); יוד, הה, וו, הה (= 52, in gematria ב״ן, representing the Holy Name of 52 letters); יוד, הי, ואו, הי (= 63, in gematria ג״ס, the 63-letter Name); יוד, הי, ויו, הי (= 72, in gematria ע״ב, representing the Holy Name of 72 letters).
Other calculations in gematria involve a "filling" of the "filling," or a second "filling." The gematria of the word itself is called ikkar or shoresh, while the rest of the word (the "fillings") is called the ne'elam ("hidden part"). The ne'elam of the letter י is וד = 10; the ne'elam of שד״י is לת ,ין and וד = 500.
(6) There is also a "great number" that counts the final letters of the alphabet as a continuation of the alphabet (500 = ם; 600 = ן; 700 = ץ; 800 = ף; 900 = ך). However, there is a calculation according to the usual order of the alphabet whereby the numerical values of the final letters are as follows: ך = 500, ם = 600, ן = 700, etc.
(7) The addition of the number of letters in the word to the numerical value of the word itself, or the addition of the number "one" to the total numerical value of the word.
Criticism of the use of gematria as a justified means of commentary was first voiced by Abraham *Ibn Ezra (in his commentary on Gen. 14:14) and later by the opponents of the Kabbalah (in Ari Nohem, ch. 10). But even several kabbalists (e.g., *Naḥmanides) warned against exaggerated use of gematria. Joseph Solomon *Delmedigo speaks of false gematriot in order to abolish the value of that system. When the believers in Shabbetai Ẓevi began to widely apply gematriot to his name (shaddai (God) and its "filling" = 814), those who denied him used mock gematriot (ru'aḥ sheker = ("false spirit") = 814). In spite of this, the use of gematria was widespread in many circles and among preachers not only in Poland but also among the Sephardim. To this day the homiletical and allegorical literature according to the method of *Pardes (the four levels of meaning of a text), especially of the North African rabbis, is full of gematria.
According to the findings of Stephen Lieberman, a variety of techniques similar to gematria are found already in Mesopotamia. Among the *Ḥasidei Ashkenaz books devoted to the gematria'ot found in the Bible are known, as is the case with R. *Judah he-Ḥasid, and his descendant R. *Eleazar ha-Darshan (Ms. Munchen 221). An interesting example of wide-ranging gematria in most of its varieties is found in the manuscript writings of a contemporary of Eleazar of Worms, R. Nehemiah ben Solomon the Prophet, which reflect the centrality of this technique outside the circle of Kalonymide esotericism in Worms. One of the most famous gematriot, Elohim = teva = 86, presumably had an influence on Spinoza's philosophy.
[Moshe Idel (2nd ed.)]
W. Bacher, Exegetische Terminologie…, 1 (1899), 125–8; 2 (1905), 124; F. Dornseiff, Das Alphabet in Mystik und Magie (19252), 91–118; A. Berliner, Ketavim Nivḥarim, 1 (1945), 34–37; S. Lieberman, Hellenism in Jewish Palestine (1950), 69–74; H. Waton, Key to the Bible (1952); T. Wechsler, Ẓefunot be-Masoret Yisrael (1968); Scholem, Mysticism, index; S.A. Horodetzky, in: ej, 7 (1931), 170–9. add. bibliography: H. Gabai, Judaism, Mathematics and the Hebrew Calendar (2002); Y. Ginsburgh, The Hebrew Letters: Channels of Creative Consciousness (1990); Sefer Gematrikon (1990); M. Munk, The Wisdom of the Hebrew Alphabet: The Sacred Letters as a Guide to Jewish Deed and Thought (1983); M. Zuriel, Or ha-Torah: Bi'ur le-Darkhei ha-Gematriot be-Toratenu (1983); S. Sambursky, in: Journalof Jewish Studies, 29:1 (1978), 35–38; G. Locks, The Spice of Torah – Gematria (1985). kabbalah: D. Abrams, "From Germany to Spain: Numerology as a Mystical Technique," in: jjs, vol. 47 (1996), 85–101; J. Dan, "The Ashkenazi Hasidic Gates of Wisdom," in: G. Nahon and Ch. Touati (eds,), Hommages à Georges Vajda (1980); I.R. Gruenwald, "Uses and Abuses of Gematria," in: M. Bar Asher (ed.), Rabbi Mordechai Breuer Festschrift 2 (1992), 823–32 (Heb.); M. Idel, Absorbing Perfections: Kabbalah and Interpretation (2002); idem, Language, Torah and Hermeneutics in Abraham Abulafia (1989); idem, "Deus sive natura" – the Metamorphosis of a Dictum from Maimonides to Spinoza, in: R. Cohen and H. Levinw (eds.), in: Maimonides and the Sciences (2000), 87–110; D. Abrams and I. Ta-Shma (eds.), Sefer Gematriot of R. Yehudah the Pious (1998); S. Lieberman, "A Mesopotamian Background for the So-Called Aggadic 'Measures' of Biblical Hermeneutics?," in: huca vol. 58 (1987), 157–225; D. Segal, Sefer Sodei Razei Simmukhim (2001); A. Wasserstein, in: Tarbiz, vol. 43 (1974), 53–55 (Heb.). websites: www.inner.org/gematria/gematria.htm; www.jhom.com/topics/envy/letters/gematria.html.
A form of numerology. In Jewish mysticism gematria was the study of Hebrew letters in association with numbers. The method was used to discover hidden meanings in Hebrew words. Prominent words could be systematically converted into numbers and linked to other words with the same numerical value, which were then regarded as comments upon the original words. This kind of numerology was also used with the Greek alphabet.
A related system of gematria is Notarikon, in which letters taken from phrases form mystical acronyms, or words are developed into mystical phrases. A more complicated procedure is temurah, in which letters of words are transposed or replaced according to complex rules. Some modern occultists have applied gematria to the tarot cards, associating the 22 trump cards with the Hebrew letters, a practice suggested by Éliphas Lévi, author of The History of Magic (1913).
Gematria became an integral part of modern ceremonial magic as practiced in the Hermetic Order of the Golden Dawn and by Aleister Crowley. Crowley and William Westcott of the Golden Dawn wrote several books on the subject, and Crowley published a key word guide to numerological meanings of words titled 777.
Bond, Bligh, and Thomas Simcox Lea. Gematria: A Preliminary Investigation of the Cabala. London: Research into Lost Knowledge Organization, 1977.
Crowley, Aleister. 777. London: Walter Scott Publishing, 1909. Revised as 777 Revised. London: Neptune Press, 1952.
Ginsburg, Christian D. The Kabbalah (with The Essenes ). London: Routledge, 1863. Reprint, New York: Samuel Weiser, 1970.
Kozminsky, Isidore. Numbers—Their Meaning and Magic. New York: Samuel Weiser, n.d.
Westcott, William W. An Introduction to the Study of the Kabalah. New York: Allied Publications, n.d.
——. Numbers: Their Occult Power and Mystic Virtues. New York: Allied Publications, n.d.
In Islam, the equivalent techniques are known as ʿilm ul-ḥurūf, based on abjad (the numerical values of the letters). Thus Adam and Eve are specially related to God because their names = the Divine Name (of Allāh).