As a secular Jew who abhors mysticism being foisted off on people as an explanation for anything, but finds its history somewhat interesting, I can say a few words on gematria. At its simplest, gematria is just a number system, and we still use it in Hebrew today.

The word gematria is used in Hebrew, too, but it is Greek not Hebrew. Gematria is greek numerals (and a good deal more convenient than roman numerals, but I digress). We just ripped it off the greeks sometime around the 3rd or 2nd century BCE (or BC, if you're DMan). Since the Greeks ripped off the western Semitic alphabet (probably from the Phoenicians), I guess we can't be blamed for liking their mathematics so much.

Each letter has a value; add up the values of all letters in a word and you get the word's value (but see below). Letter values start at 1 for aleph (greek alpha), and count up. But when you reach 10 as yod (greek iota), you start going up by 10 for each letter. So the next letter cav (greek kappa) is 20. When you reach 100 as qof or qov (the letters no longer match greek), you continue by jumping 100s, so reish is 200; the alphabet ends with tav at 400 (there are 22 letters in all).

Normally you'd represent each number by the most "logical" short string summing to it, but there is no reason to do so. For example, my name is spelled aleph-reish-yod-aleph-lamed, so its numeric value is 242 (lamed is 30; it comes after cav). Whether or not you choose to connect this to the U.N. resolution with that very same number is your own business. Since 242 is also "bram" (a slightly archaic word somewhere between "but" and "now"), these 2 words are equivalent.

When larger numbers need to be represented, writing huge strings of the higher letters gets tiresome, so you can take low-order letters and re-start counting, starting with aleph = 1000 (500-900 are left alone); sometimes dots will be placed over such letters, but usually it's just left to context. For instance, the year 2000 is 5760, which is canonically he-tav-shin-samech, which isn't really a Hebrew word (the single letter values here are 5-400-300-60).

In practice, almost any smallish number is some Hebrew word, so you can have some fun. For instance, "wine" is "yayin" (yod-yod-nun = 10+10+50 = 70), and "secret" is "sod" (samech-vav-daleth = 60+6+4), giving new meaning to the Hebrew saying "wine in -- secret out" ("nichnas yayin yatza sod")...

Here are some perhaps amusing examples, not necessarily intended as deep kabbalistic interpretations. Gematria is often used just for simple homiletic purposes, not for the sake of revealing deep mysteries of the universe.

  • OK, one about everyone's favorite, pi: the Bible, in 1 Kings 7, verse 23, talks about a "sea" (a big bath or cauldron, presumably), that is given to be ten cubits across and thirty cubits around. This is obviously an approximation, if you know your geometry: it's really 10*pi cubits, or almost 1-1/2 cubits longer around. Ah, but the word used for "circumference" in the text is "qav," literally "line." And as sometimes happens in the Bible, it is spelled unusually (spelled one way, but the traditional reading is another. It's a Masoretic thing). The word wound up with an extra letter at the end, which we ignore when reading it. But it affects the gematria of course. Without the extra letter, (and without the prefixed conjunction, which we're ignoring entirely), the word "qav" has the value 106. The extra "heh" at the end adds five to that, giving a total of 111. Now, 111/106 times the 30 cubits yields ~31.415 cubits. Not bad! That's approximating pi with 333/106, which is I think the best rational approximation with a denominator less than 113. Bleah, so close! 355/113 is so much better! Coincidence? You decide. Possibly. Not necessarily less interesting because of that.
  • A favorite around the Passover seder table: God is referred to in some prayers as "Hamakom," literally something like "the place"; often translated as "The Omnipresent." Why should "makom/place" refer to God? Well, take God's name, YHWH. Take each of those letters, square them (since a "place" is an area, so squared units), and you get 100+25+36+25=186, which is the same value as "makom/place": 40+100+6+40. Contrived? Yeah. Actually not as much so as some others I've seen that are meant more seriously. You can get anything you want from numbers with enough work.
  • Another old Passover chestnut (my dad in particular likes collecting and inventing these). The Bible says in Genesis 15:13 that God promised Abraham that his children would be enslaved for 400 years. And yet if you do the math and compare years that are given (I have to find sources for this), it was only 210 years that they were enslaved. The difference? Well, God started counting from the birth of Isaac, of whom it is said that he could be called Abraham's "seed" (not Ishmael, though he was older, according to a verse). And so the Passover Haggadah praises God for having "considered the end" when redeeming the slaves. What end? Well, the word they used for "end" (OK, this isn't Biblical) is "qetz", which has the value of 190: God reckoned the 190 years in to reduce the 400 to 210. Earth-shattering? No. But fun.

I've got scads of them, here and there (my dad collects them, I said). I'm not even sure these are the best examples. But you might find them fun.

The two languages to which gematria is most frequently applied are 
Hebrew and Greek.

The letter-values of the Hebrew Alphabet (transliterated in the manner 
of the Hermetic Order of the Golden Dawn):

Aleph (ALP)   A    1
Beth (BITh)   B    2
Gimel (GML)   G    3
Daleth (DLTh) D    4
He (HH)       H    5
Vau (VV)      V    6
Zain (ZIN)    Z    7
Cheth (ChITh) Ch   8
Teth (TITh)   T    9
Yod (IVD)     I   10
Kaph (KP)     K   20 (final value: 500)
Lamed (LMD)   L   30
Mem (MIM)     M   40 (final value: 600)
Nun (NVN)     N   50 (final value: 700)
Samekh (SMK)  S   60
Ayin (OIN)    O   70
Pe (PH)       P   80 (final value: 800)
Tzaddi (TzDI) Tz  90 (final value: 900)
Qoph (QVP)    Q  100
Resh (RISh)   R  200
Shin (ShIN)   Sh 300
Tau (ThV)     Th 400

(Note: "final" values may optionally be used if the letter is at 
the end of a word.)

The letter-values of the Greek Alphabet:

Alpha (ALPhA)       A    1
Beta (BHTA)         B    2
Gamma (GAMMA)       G    3
Delta (DELTA)       D    4
Epsilon (EPsILON)   E    5
Zeta (ZHTA)         Z    7
Eta (HTA)           H    8
Theta (ThHTA)       Th   9
Iota (IWTA)         I   10
Kappa (KAPPA)       K   20
Lambda (LAMBDA)     L   30
Mu (MU)             M   40
Nu (NU)             N   50
Xi (XI)             X   60
Omicron (OMIKRON)   O   70
Pi (PI)             P   80
Rho (RW)            R  100
Sigma (SIGMA)       S  200
Tau (TAU)           T  300
Upsilon (UPsILON)   U  400
Phi (PhI)           Ph 500
Chi (ChI)           Ch 600
Psi (PsI)           Ps 700
Omega (WMEGA)       W  800

(Note: the "missing" values of 6 and 90 are taken, respectively, 
by the obsolete letters Digamma (F) and Koppa (Q).)

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