Photo Credit: Mosaica Press

Title: Gematria Refigured
By Rabbi Elie Feder, PhD
Mosaica Press, 2022



I have a love-hate relationship with gematria, the system of assigning numerical values to each letter of the aleph bet and deriving interpretations based upon those values.

I remember being thrilled as a child when I discovered that ba-Torah in numerical value was equal to 613, the number of mitzvot in the Torah. I harbored fantasies of being able to reveal all kinds of secrets through employing the tool of gematria.

But then it was pointed out to me that you could prove just about anything using gematria. The example my father was fond of quoting was that ben (son) in numerical value was equal to kelev (dog). I did not know how to respond to this claim, and did not want to land in the doghouse myself.

As I matured, the counterexamples to the authority of gematria grew more numerous, more amusing, and naughtier. When Donald Trump was running for President in 2016, someone discovered that Donald Trump has the same gematria value as Mashiach ben David. According to the meme making the rounds, someone sent this calculation to Rav Eliyahu (no first name given), who replied, “Don’t get excited – it is also equal to chatzi maneh felafel [half a portion of falafel].” Even more amusing is the number 770, which happens to be the Eastern Parkway address of World Lubavitch Headquarters. Supporters of Chabad can point to the fact that beis Mashiach – the house of the Messiah – is equal to 770. Detractors, unfazed, counter that the same value yields chamor bli da’as (I leave the translation to the reader). And so gematrias are simultaneously beguiling and bedeviling.

The case against the seriousness of gematria is strengthened by numerous other questions, such as:

  • Why is gematria considered valid when off by one, and sometimes even by more, or when counting the word itself or the number of letters in it as part of the sum?
  • How is it possible to actually derive a law using gematria, as the Talmud seems to do in deriving the length of an unspecified period of being a Nazarite as 30 days based upon the value of the word yihiyeh – He shall be (sanctified)?
  • Even if we were to grant the validity of a basic Gematria system, how can we accept subsequent extensions, which take the sum of the names of the letters of a word, even allowing for multiple modes of spelling (Otiyot Miluim)?

It would be easy to simply dismiss gematria, but for three things: First, it has an ancient source. The beraita of Rabbi Eliezer, son of Rabbi Yossi Ha-Gelili, found in the beginning of many editions of Midrash Rabbah, lists gematria as the 29th method of interpretation of scripture. Unlike the 13 rules for deriving law, listed in the beraita of Rabbi Yishmael, these methods are for both law and narrative. The 29th method includes both numerical value of letters (heshbon otiyot) and systems of letter exchange (hiluf otiyot). Second: Not only the Talmud and Midrash, but countless later authors, especially but not limited to the Kabbalistic and Chassidic world, make extensive use of gematria. From the Zohar to the Vilna Gaon and his students, from the Steipler Gaon to Rav Dovid Feinstein, gematria has held a beloved place in the interpretive thought of great minds. Finally, just when one is ready to set aside gematria, one comes across a seemingly perfect one that is impossible to let go. In a chapter of one of his books, autodidact Avraham Korman (1907-1991) spends many pages debunking gematria, only to conclude with a section of examples too good not to share.

Because of the alluring yet slippery nature of gematria, many chart a middle course, suggesting that one may not derive ideas, and certainly not laws from gematria, but that it is a helpful tool with which to derive support for things we already know, thereby deepening our acceptance of such ideas. This position must by necessity dismiss the seeming derivation of 30 days of the Nazarite as an “asmachta,” a hint or mnemonic, rather than a true derivation.

In recent years we have been blessed with two other approaches. In 2012, Rav Moshe Tzuriel of Bnei Brak published Gematria’ot: Hadar Ha-Torah, a collection of the gematria interpretations of Rav Ezra Kinvald, zt”l. He appended an introduction in which he listed ten questions people ask about the legitimacy of gematria and answered each at length. While it is impossible to do justice to his approach in this column, it can be briefly noted that he considers gematria, in the hands of qualified talmidei chachamim, to be the tip of an iceberg, a signpost that alerts the scholar to dig further on the spot and seek connections between the topics that are linked numerically. That is where the real work lies – in excavating the deeper levels of meaning underneath the gematria marker. This immediately relieves us of the problem of each amateur “proving” anything he wishes by means of a superficial numerical connection. To read more, go to

The newest approach is a slim volume entitled Gematria Refigured, written by a rebbi who also trained as a mathematician. Rabbi Dr. Elie Feder delivers shiurim at Yeshiva Bnei Torah in Far Rockaway and teaches mathematics at Kingsborough Community College. One’s first thought when hearing gematria and mathematics in connection with the same individual might be “Of course he’d like gematria – it’s all about adding numbers.” (Indeed, when seeing the complex calculations of some Chassidic Rabbeim, it looks like they were sublimating a mathematical mind.) Not so in Rabbi Feder’s case. He was not drawn by the math of the matter. Nevertheless, in his analyses and mode of presentation, we see the organized mind of a mathematician at work. Reading one of his explanations is like parsing a proof.

Rabbi Feder maps out his territory from the outset, limiting himself to gematrias that originate in the Talmud or Midrash and which are quoted by Rashi. Each chapter of his book deals with a different variety of gematria. Some examples of the 11 types:

  • A straightforward gematria in which one word is substituted for another of equal value. The Torah states that G-d blessed Abraham ba-kol – with everything, and Rashi cites the Midrash that ba-kol equals ben, a son.
  • A gematria in which the value of a word proves significant to understanding the text. Lot, Abraham’s nephew, pleads with the angels destroying Sodom to spare the city of Tzo’ar as a refuge. Please (“na”) may I flee there. Rashi says that Tzo’ar had not grown sufficiently evil because it was only 51 years old, the numerical value of “na,” while the other cities were 52.
  • Letters of a word are reordered to yield a significant number. Yaakov tells Esav that he dwelt – garti – with Lavan. Rashi, rearranging the letters of garti, adds: But I observed all taryag (613) mitzvot.
  • Exaggerated numbers result from gematria. Haman tells his assembled cronies of his great wealth and many sons – rov banav. The Midrash says that Haman had 208 sons, the numerical value of rov.

In each chapter, Rabbi Feder tackles the question of why this particular interpretation had to be expressed by the Midrash through the medium of gematria, rather than another means of drasha. His governing principle is that gematria interpretations are all based on some message related to quantity. But in order to properly understand that message, it is necessary to correctly comprehend the lesson of the particular Midrash. Once he has reached an interpretation that satisfies him, Feder shows how that interpretation is related in some way to the concept of quantity.

Because each chapter involves the development outlined above, it becomes very difficult to summarize even one properly, but a reviewer must try. In the gematria that interprets G-d’s blessing to Avraham of ba-kol as the blessing of a son (ben), the message is that for Avraham, “everything” can be quantified in one item – a son. Most people wish for wealth and can never be satisfied. Avraham’s goal, however, was to spread the knowledge of the one G-d. To do that as a mortal of limited lifespan, he needed one thing alone – a son. And now the application to quantity: For Avraham and Avraham alone, the concept of “everything,” normally infinite, becomes a finite quantity, embodied in a son to continue his mission. (If you would like to read an expanded version of this explanation, and have access to Facebook, you can access the November 13th post in the group Judaism Reclaimed, in which Rabbi Feder posted much of his chapter on this topic.)

Rabbi Feder’s book is very accessible. Because of his conversational tone and organized presentation, the reader is drawn into the discussion and knows what stages to expect in each chapter. The reader identifies with the author, who shares his own original doubts about the gematria system and traces his journey towards amassing the material contained within this work. If there is a potential weak spot it is in whether the reader accepts the explanation Feder arrives at for each Midrash. Some are straightforward; others are complex. But even if you are not sold on the entire explanation, you are likely to find gems of interpretation in the course of the discussion, which themselves are worth the price of admission.

Will you be sold on Rabbi Feder’s method? The answer is subjective. I did not think that a book like this could succeed, but then I saw the glowing words of Rabbis Asher Weiss, Yitzchok Berkowitz, and Yitzchok Breitowitz, from the book’s cover and publicity, and had to see for myself. I may not agree with everything, but I was not disappointed.

Who would have thought that our day would produce such new and robust defenses of gematria?

Go refigure.


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Rabbi Moshe Rosenberg is the spiritual leader of Congregation Etz Chaim of Kew Gardens Hills, N.Y., and a Judaic Studies educator at SAR Academy in Riverdale, N.Y. He is most well known for his "Unofficial Hogwarts Haggadah and Superhero Haggadah," but his writings on religion, ethics, and Jewish law have also appeared in Tablet Magazine, The Forward, The Jewish Week, and The Journal of Halakha and Contemporary Society, among other national publications. He lives in Queens with his wife, Dina, and their seven children. Additional writings can be found in Ketoret, a semi-regular newsletter which looks at the world through the combined lenses of Torah, literary fiction, technology, game design, and anything else that can help. Subscribe to Ketoret at