Judaism, Mathematics, and the Hebrew Calendar (review)

This book is divided into three parts: (1) “Judaism and Mathematics”; (2) “Mathematics and the Hebrew Calendar”; and (3) “Miscellaneous Notes and Proofs and Solutions and Exercises.” In length, these three parts are divided roughly in the ratio 1:2:1.

Since the second and third parts deal in large measure with the technical aspects of the Hebrew calendar, this review will consider mainly the first part on Judaism and mathematics. It should be noted that although the author uses the word “mathematics” throughout, and indeed makes brief—sometimes tangential—references to mathematical giants, Euclid, Cantor, Einstein, Goedel, etc., nothing more than ordinary arithmetic and, possibly, a little elementary algebra in the second section is required to understand the material.

Leaving this aside, the reviewer found the first part on Judaism and mathematics delightful reading and surprisingly interesting. The author has gathered together numerous examples of how numbers, specifically the positive integers, play an important role in—and are intertwined with—many Jewish traditions. Perhaps most readers will recall the Hebrew word “chai” (life) and its associated gematrical (to be explained below) equivalent, the number 18. When giving a gift to a Bar/Bat Mitzvah, it is considered very appropriate to write a check in the amount of $18, $36 or some higher multiple of chai. Similarly, the dues of some Jewish organizations are also based on multiples of chai. Gabai notes that Jerusalem was reunited in 3240 (=180 chai) after the death of Miriam and Aaron; that the state of Israel was founded 3600 years (=200 chai) after the birth of the patriarch Israel. The author argues that these are not exceptions and that there are numerous such numerical references throughout Hebrew learning and tradition. To mention but two examples of the many offered in the book: (1) the closing of the Seder festival is usually marked by those present singing in unison the song “Who Knows One; 1 God, 2 tablets of the commandments, 3 patriarchs, 4 matriarchs, 5 books of the Torah . . .”; (2) the appearance of the number 10 is also very striking: there are 10 commandments, 10 plagues, 10 males required for a minyan, 10 generations from Adam to Noah, 10 curtains of the holy tabernacle, 10 days of repentance, etc. These are by no means the only examples of the appearance of integers in Jewish traditions. As a final striking example, Abraham was born in the year 1948 of the Jewish calendar and the state of Israel was founded in the year 1948 of the Gregorian calendar! Even the skeptic begins to wonder if these are coincidences after all.

The final chapter of this first part deals with “Gematria.” According to Webster’s Unabridged Dictionary Gematria is:

1. 1. a cryptograph in the form of a word whose letters have the numerical values of a word taken as the hidden meaning;

2. 2. the cabalistic method of explaining Hebrew scriptures by means of the cryptographic meaning of the word.

The specific association of numbers to Hebrew letters is as follows. The first ten letters (aleph, beth, . . . yud) are associated with 1, 2, . . ., 10; the next nine letters (kav, lamed, . . ., tzadik) are associated with the integers 20, 30, . . ., 100, and the last three letters (resh, shin, tav) are 200, 300, and 400 respectively. Thus the word “chai,” which is written cheth (8) and yud (10), has, as noted above, the gematria value 18. Also in use is a reverse gematria in which the last letter tav is 1 and the first, aleph, is 400. (There apparently is also a permutation gematria where presumably anything goes!) Very striking is the equivalence of the word “tefila” (prayer) with “Baruch HaShem” (“blessed is the name”) both of which have the gematria and the reverse gematria of 515. The reader can judge for himself where this leads, and Gabai, who gives numerous worked-out examples, cautions the reader to “avoid the type of analysis that may lead to conclusions that are antithetical to the principle and spirit of Judaism.” The reviewer...