Gematria (/ɡəˈmeɪtriə/; Template:Lang-he-n or Gimatria Template:Hebrew, plural Template:Hebrew or Template:Hebrew, gematriot)^[1] is an alphanumeric code of assigning a numerical value to a name, word or phrase based on its letters. A single word can yield multiple values depending on the cipher used.

Gematria originated as an Assyro-Babylonian-Greek system of alphanumeric code or cipher that was later adopted into Jewish culture.^{[dubious – discuss]} Similar systems have been used in other languages and cultures: earlier, the Greek isopsephy, and later, derived from or inspired by Hebrew gematria, Arabic abjad numerals, and English gematria.

A well-known example of Hebrew gematria is the word chai ("alive"), which is composed of two letters that (using the assignments in the Mispar gadol table shown below) add up to 18. This has made 18 a "lucky number" among the Jewish people. Gifts of money in multiples of 18 are very popular.^[2]

Although the term is Hebrew, it may be derived from the Greek γεωμετρία geōmetriā, "geometry", which was used as a translation of gēmaṭriyā,^[3] though some scholars believe it to derive from Greek γραμματεια grammateia "knowledge of writing". It's likely that both Greek words had an influence on the formation of the Hebrew word.^[4][1] Some also hold it to derive from the order of the Greek alphabet, gamma being the third letter of the Greek alphabet.^[5]

The word has been extant in English since at least the 17th century from translations of works by Giovanni Pico della Mirandola. Although ostensibly derived from Greek isopsephy, it is largely used in Jewish texts, notably in those associated with the Kabbalah. The term does not appear in the Hebrew Bible itself.^[1]

Some identify two forms of gematria: the "revealed" form, which is prevalent in many hermeneutic methods found throughout rabbinic literature, and the "mystical" form, a largely Kabbalistic practice.^[6]

Although gematria is most often used to calculate the values of individual words, psukim (Biblical verses), Talmudical aphorisms, sentences from the standard Jewish prayers, personal, angelic and Godly names, and other religiously significant material, Kabbalists use them often for arbitrary phrases and, occasionally, for various languages: A few instances of gematria in Arabic, Spanish and Greek, spelled with the Hebrew letters, are mentioned in the works of Abraham Abulafia;^[7] some Hasidic Rebbis also used it, although rarely, for Yiddish.^[8] However, the primary language for gematria calculations has always been and remains Hebrew and, to a lesser degree, Aramaic.^{[citation needed]}

A classic Biblical commentary incorporating gematria is Baal ha-Turim by Jacob ben Asher.^[9]

Gematria is often used by the Maharal and Hasidic Torah commentators (such as Sefat Emet by R' Yehudah Aryeh Leib Alter).^{[citation needed]}

Some scholars think it possible that gematria is encoded in the Hebrew Bible. For example, Israel Knohl noted that “it is not out of the question that this technique was already known in the biblical period and was used specifically in religious contexts”,^[10] and has hypothesized “the fact that the representation of the numerical values of letters is not demonstrated in mundane use in ancient Israel before the Hellenistic period may point to the possibility that this method was first a sacred secret knowledge that was kept in closed circles”.^[11] Victor Hurowitz points out “numerological principles in the organization of the book [of Proverbs]” and demonstrates that Gematria has Mesopotamian precedents.^[12] Stephen J. Lieberman writes “we must admit that it is possible such techniques were employed in biblical texts.  The means were available, and if the desire was present, it was certainly possible for hidden messages to be put into the Bible”.^[13]

A Mishnaic textual source makes clear that the word gematria is dated to at least the Tannaic period:

Rabbi Eleazar Chisma^[14] said: the laws of mixed bird offerings and the key to the calculations of menstruation days—these, these are the body of the halakhah. The calculation of the equinoxes and gematriot are the condiments of wisdom.^[15]

Herbert Danby, in his Mishna translation, explains gematriot as follows:

Astronomy and geometry are meant. Of these Eleazar Chisma is reported to have been a diligent student. 'Gematria' later came to mean the device of finding esoteric meanings in words by means of the numerical values of their constituent letters.^[16]

However, Danby also notes a case of the latter kind of gematria already in Mishnah Uktzin 3:12.

In the Talmud, the term gematria is also used to refer to a different concept: the atbash cipher.^[17]

In the standard version of gematria, each letter is given a numerical value as shown in the following table. In the Mispar gadol (meaning "Big number", see the list of methods below) variation, the five final letters are given their own values, ranging from 500 to 900.

A mathematical formula for finding a letter's corresponding number in Mispar Gadol is: ${\displaystyle f(x)=\left(10^{\lfloor \left(x-1\right)\div 9\rfloor }\right)\times \left(\left(\left(x-1\right)\ \mathrm {mod} \ 9\right)+1\right)}$ where x is the position of the letter in the language letters index (Regular order of letters), and the floor and modulo functions are used.

The value of the Hebrew vowels is not usually counted, but some lesser-known methods include the vowels as well. The most common vowel values are as follows (a less common alternative value, based on digit sum, is given in parentheses):

Sometimes the names of the vowels are spelled out and their gematria is calculated using standard methods.^[18]

There are several methods used to calculate the numerical value for the individual Hebrew/Aramaic words, phrases or whole sentences. More advanced methods are usually used for the most significant Biblical verses, prayers, names of God and angels etc.

• Mispar Hechrachi (absolute value) that uses full numerical value of the 22 letters. Sometimes it is also called Mispar ha-Panim (face number), as opposed to the more complicated Mispar ha-Akhor (back number).
• Mispar Gadol counts the final forms (sofit) of the Hebrew letters as a continuation of the numerical sequence for the alphabet, with the final letters assigned values from 500 to 900.
• The same name, Mispar ha-Gadol, is also used for another method, which spells the name of each letter and adds the standard values of the resulting string.
• Mispar Katan calculates the value of each letter, but truncates all of the zeros. It is also sometimes called Mispar Me'ugal.
• Mispar Siduri (ordinal value) with each of the twenty-two letters given a value from one to twenty-two.
• Mispar Bone'eh (building value, also Revu'a, square^[19]) is calculated by walking over each letter from the beginning to the end, adding the value of all previous letters and the value of the current letter to the running total. Therefore, the value of the word achad (one) is ${\displaystyle 1+(1+8)+(1+8+4)=23}$.
• Mispar Kidmi (triangular value) uses each letter as the sum of all the standard gematria letter values preceding it. Therefore, the value of Aleph is 1, the value of Bet is 1 + 2 = 3, the value of Gimmel is 1+2+3=6, etc. It's also known as Mispar Meshulash (triangular or tripled number).
• Mispar P'rati calculates the value of each letter as the square of its standard gematria value. Therefore, the value of Aleph is 1 × 1 = 1, the value of Bet is 2 × 2 = 4, the value of gimmel is 3 × 3 = 9, etc. It's also known as Mispar ha-Merubah ha-Prati'.
• Mispar ha-Merubah ha-Klali is the square of the standard absolute value of each word.
• Mispar Meshulash calculates the value of each letter as the cube of their standard value. The same term is more often used for Mispar Kidmi.
• Mispar ha-Akhor – The value of each letter is its standard value multiplied by the position of the letter in a word or a phrase in either ascending or descending order. This method is particularly interesting, because the result is sensitive to the order of letters. It is also sometimes called Mispar Meshulash (triangular number).
• Mispar Mispari spells out the standard values of each letter by their Hebrew names ("Achad" (one) is ${\displaystyle 1+8+4=13}$ etc.), and then adds up the standard values of the resulting string.
• Mispar Shemi (also Millui letter "filling"), uses the value of each letter as equal to the value of its name.^[20] For example, the value of the letter Aleph is ${\displaystyle (1+30+80)=111}$, Bet is ${\displaystyle (2+10+400)=412}$, etc. Sometimes the same operation is applied two or more times recursively.
• Mispar Ne'elam (hidden number) spells out the name of each letter without the letter itself (e.g., "Leph" for "Aleph") and adds up the value of the resulting string.
• Mispar Katan Mispari (integral reduced value) is used where the total numerical value of a word is reduced to a single digit. If the sum of the value exceeds 9, the integer values of the total are repeatedly added to produce a single-digit number. The same value will be arrived at regardless of whether it is the absolute values, the ordinal values, or the reduced values that are being counted by methods above.
• Mispar Misafi adds the number of the letters in the word or phrase to their gematria.
• Kolel is the number of words, which is often added to the gematria. In case of one word, the standard value is incremented by one.

Within the wider topic of Gematria are included the various alphabet transformations where one letter is substituted by another based on a logical scheme:

• Atbash exchanges each letter in a word or a phrase by opposite letters. Opposite letters are determined by substituting the first letter of the Hebrew alphabet (Aleph) with the last letter (Tav), the second letter (Bet) with the next to last (Shin), etc. The result can be interpreted as a secret message or calculated by the standard gematria methods. A few instances of Atbash are found already in the Hebrew Bible. For example, see Jeremiah 25:26, and 51:41, with Targum and Rashi, in which the name ששך ("Sheshek") is thought to represent בבל (Babylon).^[1]
• Albam – the alphabet is divided in half, eleven letters in each section. The first letter of the first series is exchanged for the first letter of the second series, the second letter of the first series for the second letter of the second series and so forth.
• Achbi divides the alphabet into two equal groups of eleven letters. Within each group, the first letter is replaced by the last, the second by the tenth, etc.
• Ayak Bakar replaces each letter by another one that has a 10-times-greater value. The final letters usually signify the numbers from 500 to 900. Thousands is reduced to ones (1000 becomes 1, 2000 becomes 2 etc.)
• Ofanim replaces each letter by the last letter of its name (e.g. "Fe" for "Aleph").
• Akhas Beta divides the alphabet into three groups of 7, 7 and 8 letters. Each letter is replaced cyclically by the corresponding letter of the next group. The letter Tav remains the same.
• Avgad replaces each letter by the next one. Tav becomes Aleph. The opposite operation is also used.

Most of the above-mentioned methods and ciphers are listed by Rabbi Moshe Cordevero.^[21]

Some authors provide lists of as many as 231 various replacement ciphers, related to the 231 mystical Gates of the Sefer Yetzirah.^[22]

Dozens of other far more advanced methods are used in Kabbalistic literature, without any particular names. In Ms. Oxford 1,822, one article lists 75 different forms of gematria.^[23] Some known methods are recursive in nature and are reminiscent of the graph theory or use heavily combinatorics. Rabbi Elazar Rokeach often used multiplication, instead of addition, for the above-mentioned methods. For example, spelling out the letters of a word and then multiplying the squares of each letter value in the resulting string produces very large numbers, in orders of trillions. The spelling process can be applied recursively, until a certain pattern (e.g., all the letters of the word "Talmud") is found; the gematria of the resulting string is then calculated. The same author also used sums of all possible unique letter combinations, which add up to the value of a given letter. For example, the letter Hei, which has the standard value of 5, can be produced by combining ${\displaystyle 1+1+1+1+1}$, ${\displaystyle 2+1+1+1}$, ${\displaystyle 3+1+1}$, ${\displaystyle 4+2}$, ${\displaystyle 2+2+1}$, or ${\displaystyle 2+3}$, which adds up to ${\displaystyle 30}$. Sometimes combinations of repeating letters are not allowed (e.g., ${\displaystyle 2+3}$ is valid, but ${\displaystyle 3+1+1}$ is not). The original letter itself can also be viewed as a valid combination.^[22]

Variant spellings of some letters can be used to produce sets of different numbers, which can be added up or analyzed separately. Many various complex formal systems and recursive algorithms, based on graph-like structural analysis of the letter names and their relations to each other, modular arithmetic, pattern search and other highly advanced techniques, are found in the "Sefer ha-Malchuth" by Rabbi David ha-Levi of Draa Valley, a Spanish-Moroccan Kabbalist of the 15–16th century.^[18] Rabbi David ha-Levi's methods take into consideration the numerical values and other properties of the vowels as well.

Kabbalistic astrology uses some specific methods to determine the astrological influences on a particular person. According to one method, the gematria of the person's name is added to the gematria of his or her mother's name; the result is then divided by 7 and 12. The remainders signify a particular planet and Zodiac sign.^[24]

The most common form of Hebrew gematria is used in the Talmud and Midrash, and elaborately by many post-Talmudic commentators. It involves reading words and sentences as numbers, assigning numerical instead of phonetic value to each letter of the Hebrew alphabet. When read as numbers, they can be compared and contrasted with other words or phrases – cf. the Hebrew proverb נכנס יין יצא סוד (nichnas yayin yatza sod, lit. "wine entered, secret went out", i.e. "in vino veritas"). The gematric value of יין ("wine") is 70 (י=10; י=10; ן=50) and this is also the gematric value of סוד ("secret", ס=60; ו=6; ד=4)‎.^[25]

The first attested use of gematria occurs in an inscription of Assyrian ruler Sargon II (727–705 BCE) stating that the king built the wall of Khorsabad 16,283 cubits long to correspond with the numerical value of his name.^{[26][dubious – discuss]}

Gematria or isopsephy was borrowed from the Greek probably soon after their adoption of the Semitic writing system.^{[27][dubious – discuss]}

The extant examples of use in Greek come primarily from the Christian literature and, unlike rabbinic sources, is always explicitly stated as being used.^[27]

It has been asserted^[where?] that Plato (c. 427-347 BC) offers a discussion of gematria "in its simplest forms" in the Cratylus, where he is said to have claimed that "the 'essential force' of a thing's name is to be found in its numerical value, and that words and phrases of the same numerical value may be substituted in context without loss in meaning". A direct review of the Cratylus, however, shows that Plato made no such claim and that gematria is not discussed in it either explicitly or implicitly.^{[citation needed]} What can be more accurately stated is that Plato's discussion in the Cratylus involves a view of words and names as referring (more or less accurately) to the "essential nature" of a person or object, and that this view may have influenced – and is central to – Greek gematria.^[28][29]

The Latin-script languages exhibit borrowing of gematria methods dating from the early Middle Ages after the use lapsed following the collapse of the Roman Empire in the 5th century. Many researchers connect the "Number of the Beast", referred to in the Book of Revelation of the New Testament, with Hebrew gematria as used by the early Christians. According to such interpretations, the number in question, six hundred sixty-six (666; see Revelation 13:18Template:Bibleverse with invalid book) was originally derived from the Latin name of the Roman emperor at the time, Nero Caesar, via the Greek, 'Neron Kaisar', and transliterated into Hebrew gematria. The result of this operation is six hundred sixty-six (${\displaystyle 50+200+6+50+100+60+200=666}$. (נרון קסר Neron Qesar).^[30]

• Klein, Ernest, Dr., A comprehensive etymological dictionary of the English language: Dealing with the origin of words and their sense development thus illustrating the history and civilization of culture, Elsevier, Oxford, 7th ed., 2000
• Davies, William David & Allison, Dale C., A Critical and Exegetical Commentary on the Gospel According to Saint Matthew, Continuum International Publishing Group, 2004
• Acres, Kevin, Data integrity patterns of the Torah: A tale of prime, perfect and transcendental numbers, Research Systems, Melbourne, 2004 [2]
• Clawson, Calvin C., Mathematical Mysteries: The Beauty and Magic of Numbers, Perseus Books, 1999
• Davis, John J. Biblical Numerology. Grand Rapids, MI: Baker Books, 1968.
• Hughes, J. P., Suggestive Gematria, Holmes, 2008
• Genesis Rabbah 95:3. Land of Israel, 5th Century. Reprinted in, e.g., Midrash Rabbah: Genesis. Translated by H. Freedman and Maurice Simon. Volume II, London: The Soncino Press, 1983. ISBN 0-900689-38-2.
• Deuteronomy Rabbah 1:25. Land of Israel, 5th Century. Reprinted in, e.g., Midrash Rabbah: Leviticus. Translated by H. Freedman and Maurice Simon. Volume VII, London: The Soncino Press, 1983. ISBN 0-900689-38-2.
• Lawrence, Shirley Blackwell, The Secret Science of Numerology – The Hidden Meaning of Numbers and Letters, New Page Books, 2001
• Menninger, Karl. Number Words and Number Symbols: A Cultural History of Numbers. Cambridge: MIT Press, 1969.
• Ratzan, Lee, Understanding Information Systems: What They Do and why We Need Them, ALA Editions, 2004
• Rawn, Jonathan D. Discovering Gematria: Foundational Exegesis and Primary Dictionary. 1,968 pp. Gematria Publishing, 2008.
• Sefer hamilim. Qonqordantzia hakhadash (lekol haTanakh). Lebovits-Kest Memorial, B'nei-Torah Compact Library, Printed in Israel
• Zeitler, William. Musical Gematria. Musica Arcana, 2013, ISBN 978-1-940630-02-1

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