Hebrew numerals
Hebrew numerals are an alphabetic numeral system employed in the Hebrew language, where each of the 22 letters of the Hebrew alphabet is assigned a fixed numerical value ranging from 1 to 400, allowing numbers to be represented by combining these letters additively from highest to lowest value, read from right to left.[1] This quasi-decimal system, which lacks a symbol for zero, originated in the late 2nd century BCE as an adaptation of Greek numerals and earlier Aramaic and Phoenician influences dating back to around 800 BCE.[2] Primarily used in Jewish religious and scholarly contexts, such as dating manuscripts, numbering pages in Hebrew books, and indicating chapters or verses in the Torah, the system also forms the basis for gematria, a traditional Jewish practice of interpreting texts through numerical equivalences of words.[3] The core of the Hebrew numeral system lies in the assignment of values to letters, with the first nine letters (aleph to tet) representing units 1 through 9, the next nine (yod to tzadi) denoting tens from 10 to 90, and the final four (kuf to tav) signifying hundreds from 100 to 400.[1] Five letters have special final forms (kaf sofit, mem sofit, nun sofit, pe sofit, tzadi sofit) used at the end of words, which are assigned higher values from 500 to 900 to extend the system's range without introducing new symbols.[1] For example, the number 11 is written as יא (yod + aleph = 10 + 1), while 376 is שסו (shin + samech + vav = 300 + 60 + 6).[3] Numbers above 999 are typically formed by prefixing a multiplier (often aleph for 1,000) followed by the remaining digits, such as ה'תשפ"ד for 5,784 (5 thousands + 400 + 300 + 80 + 4).[1] To distinguish numerals from ordinary text, conventions include placing a geresh (׳) after single letters (e.g., א׳ for 1) and a gershayim (״) before the final letter in multi-letter combinations (e.g., כ״ב for 22).[1] A notable religious sensitivity avoids direct representations of 15 (יה) and 16 (יו), which resemble abbreviations for God's name, substituting them with ט"ו (9 + 6) and ט"ז (9 + 7) instead.[3] While the system is additive and positional in sequence, modern usage often supplements it with Arabic numerals for clarity in secular or international contexts, preserving its traditional role in liturgy and scholarship.[2]History and Origins
Ancient Roots
The Hebrew numeral system traces its origins to the alphabetic scripts of ancient Semitic languages, particularly those derived from Phoenician and Aramaic traditions that developed between the 11th and 8th centuries BCE. The Phoenician script, one of the earliest fully consonantal alphabets, emerged around 1050 BCE and served as the direct precursor to the Paleo-Hebrew alphabet, facilitating the representation of sounds in writing across the Levant. While the script itself enabled textual records, early numeral use in these Semitic contexts relied on non-alphabetic methods, such as cuneiform or hieroglyphic borrowings, before evolving toward more integrated forms in Aramaic by the 8th century BCE, where inscriptions begin to show rudimentary alphabetic associations with numerical concepts.[4] A key example of proto-numeral practices in ancient Hebrew appears in the Siloam Inscription, dated to the late 8th century BCE during the reign of King Hezekiah. This monumental text, carved into the wall of Jerusalem's water tunnel, describes the engineering feat using word-based numerals: it mentions "three cubits" remaining when the voices of the workers calling to each other could be heard, and the tunnel's total length as "one thousand two hundred cubits," with the rock height at "one hundred cubits." These expressions highlight an additive, verbal counting method typical of pre-alphabetic Semitic traditions, where quantities were spelled out rather than symbolized, emphasizing conceptual accumulation over positional notation.[5] Unlike later positional systems such as Babylonian sexagesimal or emerging Indo-Arabic decimal methods, ancient Hebrew counting lacked a native place-value structure, depending instead on additive word forms that summed units without a zero placeholder or multiplier positions. This approach, evident in biblical and epigraphic sources from the Iron Age, reflected broader Semitic numeral conventions where numbers were constructed through juxtaposition or repetition of basic terms, prioritizing linguistic clarity in administrative and narrative contexts.[6] The system's transformation accelerated during the Hellenistic period (c. 200–78 BCE), under Greek cultural dominance following Alexander's conquests, when Hebrew adopted elements of Greek isopsephy—the practice of equating letters to numerical values for mystical and practical purposes. This borrowing created a quasi-decimal alphabetic framework using Hebrew letters, though without zero, marking a shift from purely verbal to symbolic representation while retaining additive principles. The earliest confirmed use of such letter-based numerals in Hebrew artifacts is on coins of Alexander Jannaeus dated to his 25th year (כ"ה), corresponding to 78 BCE, bridging ancient Semitic roots with later adaptations.[2][7]Evolution in Jewish Texts
The alphabetic numeral system for Hebrew, adapted during the late Second Temple period under Hellenistic influences, supplementing earlier word-based expressions in rabbinic literature, with alphabetic numerals appearing in the Gemara and later texts for dates and numerical counts by the Talmudic era (3rd–5th centuries CE).[8] In these rabbinic compilations, letters like aleph for 1 and bet for 2 facilitated precise enumeration in legal and chronological contexts, marking an early textual integration that reflected the system's growing utility amid diverse counting practices.[9] By the medieval period, particularly in the 12th century, scholars like Maimonides advanced the standardization of this system in their writings, such as his commentary on the Mishnah, where he explicitly explained the alphabetic numerals and established consistent values up to 400, ensuring uniformity in Jewish legal and philosophical works.[6] This codification helped solidify the system's role in scholarly discourse, transitioning it from sporadic use to a reliable framework for complex calculations in texts like the Mishneh Torah. The evolution also involved a notable shift from predominantly word-based representations—such as spelling out "twenty" (esrim)—to the fully alphabetic method by the Middle Ages, as letter combinations became the norm for efficiency in manuscripts and inscriptions.[2] This change, evident in post-Talmudic literature, allowed for more compact notation while preserving the phonetic integrity of the Hebrew alphabet. In the 9th–10th century Masoretic texts, which meticulously preserved biblical vocalization and orthography, specific conventions emerged to avoid religiously sensitive letter combinations in numerals, such as rendering 15 as טו (tet-vav, 9+6) and 16 as טז (tet-zayin, 9+7) instead of forms resembling divine names like יה and יו.[2] These adjustments, rooted in reverence for sacred terminology, were integrated into scribal practices to maintain textual sanctity across Jewish scriptural traditions.[10]Basic Components
Letter Value Assignments
The Hebrew numeral system, also known as gematria in its interpretive form, assigns fixed numerical values to the 22 letters of the Hebrew alphabet, enabling the representation of positive integers up to 400 through individual letters alone. This alphabetic numeral approach lacks symbols for zero or negative numbers, distinguishing it from modern positional systems.[11] The standard assignments, termed mispar hechrachi, have been consistent since at least the medieval period, when they were systematically applied in Jewish mystical and exegetical traditions.[12] These values progress sequentially: the initial letters correspond to units from 1 to 9, followed by 10, then tens from 20 to 90, and hundreds from 100 to 400. Notably, certain letters like Vav (ו, value 6) and Yod (י, value 10) function primarily as matres lectionis for vowel sounds in unpointed Hebrew text, yet retain their numerical assignments without phonetic alteration.[13] For numbers exceeding 400, the system relies on combinations of letters or multipliers, as no additional letters beyond Tav (ת) are assigned values.[11] The five letters with final forms—Kaf, Mem, Nun, Pe, and Tzadi—typically share the same numerical values as their standard forms in basic assignments.[13] The following table summarizes the standard numerical values for all 22 Hebrew letters:| Hebrew Letter | Name | Numerical Value |
|---|---|---|
| א | Aleph | 1 |
| ב | Bet | 2 |
| ג | Gimel | 3 |
| ד | Dalet | 4 |
| ה | He | 5 |
| ו | Vav | 6 |
| ז | Zayin | 7 |
| ח | Het | 8 |
| ט | Tet | 9 |
| י | Yod | 10 |
| כ | Kaf | 20 |
| ל | Lamed | 30 |
| מ | Mem | 40 |
| נ | Nun | 50 |
| ס | Samekh | 60 |
| ע | Ayin | 70 |
| פ | Pe | 80 |
| צ | Tzadi | 90 |
| ק | Kuf | 100 |
| ר | Resh | 200 |
| ש | Shin | 300 |
| ת | Tav | 400 |