Meaning of "go figure" and its origin?

It's an idiom; the equivalent of a shrug in body language.

Saying the phrase "go figure" is the equivalent of saying the word "duh" when something is obviously correct.

"Go figure" is always intended to be cynical. "It figures" can be serious in a sentence, but used alone it is also cynical and has the same meaning, that is, one should not be surprised at an unexpected outcome. "Go" is a command and is used in this phrase to direct the listener (or the person who expressed some surprise at the outcome?), unlike "it figures" which is more of a self deprecating phrase. "Go" in "go figure" is not unlike "go" in " go f___ yourself".

It figures also, that figures:

• It's (or that's) reasonable; it makes sense.

  • *Hanging it upside down sounds like a weird idea, but it figures, or It figures that they won't be coming this year, or So she's complaining again; that figures.

• According to The American Heritage Dictionary of Idiom this expression alludes to reckoning up numbers.(Colloquial; mid-1900s).

Go figure (interjection):

• According The Oxford Dictionary of Idioms its usage is quite recent. Its origin appears to be just a colloquialism derived from (go) try to (figure) it out.

• Try to figure it out :

  • Just try to explain that! They heat the water to make the tea hot, then they put ice in it to make it cold, then they put lemon in it to make it sour, and then they put sugar in it to make it sweet. Go figure.

(McGraw-Hill's Dictionary of American Slang and Colloquial Expressions)

I found an interesting passage from the book, The Dictionary of Cliches: A Word Lover's Guide to 4,000 Overused Phrases on the phrase.

William Safire believes this imperative came from the Yiddish gey rekhn, meaning “go reckon,” or “go figure it out.” More idiomatic English would have it as “go and figure,” but the conjunction was dropped. However, it may also be a version of the American you figure it (with the emphasis on “you”), a phrase Eric Partridge said dates from the 1920s. Whatever the source, the brief phrase expresses a wealth of feeling.

I'd put my money on the Yiddish origin, especially with another source I found which talks in depth of this. The main difference is with the Yiddish word that created the English derivative. The source is this book, Studies in Etymology and Etiology. The author, David L. Gold states that the phrase did not come from "gey rekhn" (like suggested in the first source), but rather "gey farshtey" which means "go understand." They also suggest that "gey rekhn" isn't ever used by Yiddish speakers and is merely "manufactured to account for Go figure"

Dictionary discussions of 'go figure'

John Ayto, Oxford Dictionary of English Idioms, third edition (2009) identifies the phrase go figure as "North American informal":

go figure! work it out for yourself (used to suggest that the conclusion to be drawn about something is obvious). North American informal

Both Leo Rosten, The Joys of Yinglish (1989), and Robert Chapman & Barbara Kipfer, Dictionary of American Slang, third edition (1995), trace the expression to the Yiddish expression "gey vays" meaning, literally, "go know." Here is Rosten's entry:

Go figure A Yinglish variation of the Yiddish Gey vays ("go know"). 1. A expression of surprise that something unexpected happened. [Example:] "Go figure the engine would explode!" 2. A confession of ignorance. [Example:] "Go figure he was a crook!" 3. How could I have anticipated something as crazy as that?! [Example:] "Go figure her brother was a prize-fighter!" 4. Could anyone in the world have been expected to make allowances for such an improbability?! [Example:] "Go figure the whole building would sink right into the bog!"

And here is Chapman & Kipfer's:

go figure v phr To try to understand, esp something contradictory or astonishing: Evidence that drug abuse and street crime derive principally from absence of strong fathers. Go figure—Nation/ Who knows. Go figure people—Scott Turow {fr Yiddish gey vays, "go know"}

Notwithstanding the "contradictory or astonishing" language in Chapman & Kipfer's definition of "Go figure," the example from The Nation seems very much in line with Ayto's observation that the expression is often "used to suggest that the conclusion to be drawn about something is obvious."

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Google Books matches for 'go figure'

The earliest match across the years 1900–1990 that a Google Books search finds is from J. Crow Taylor, "Winning with Building Hobbies," in The National Builder (September 10, 1910), a Chicago periodical:

"I find that a good way to get around a lot of cut throat competition is to get something else to talk about besides prices. Get some features that appeal to the man. See that he gets interested in beautifying the house and getting certain characteristics and then he is not likely to go figure w[i]th somebody else. Not so hard anyway. So, I always have alive two or three special things that I push. Right now this art glass business is one of them, but it is only one. There are several others. ..."

The speaker is identified only as "a progressive builder contractor," and there is no hint of where his use of "go figure" (in the sense, I think, of "compare cost estimates") came from. In any event, it's an isolated occurrence in print, since the next Google Books match for "go figure" is from almost 60 years later. From Chaim Potok, The Promise (1969):

He [Joseph Gordon] gazed across the room where at the couch where Danny and Rachel were sitting alone and talking. "That's quite a young man," he said, smiling faintly around the pipe. "Who would have figured Rachel falling in love with the son of a Hasidic rebbe? Rachel. My crazy, beautiful, sophisticated Rachel...Go figure it," he said. Then he said, "We're meeting his parents next week."

I did not say anything.

"Go figure it," he said again in a tone of wonder and walked away, shaking his head.

An interesting discussion of the phrase "go figure" as a truncation of "go figure it out" appears in Lillian Feinsilver, "The Yiddish Is Showing" in The Taste of Yiddish (1970), reprinted in Perspectives on American English (1980):

'Go figure it out!' (I'll be darned; can you match that?) This is a frequent heading for oddities presented in the Jewish Digest. It has appeared in other places, sometimes cut to 'Go figure', as in the conclusion of a recent New York Times article on culture in Indianapolis: 'It might be added that the new Clowes Hall is...one of the best sounding halls in the United States. Its acoustic properties, with clouds and everything, were designed by the same Bolt, Beranek & Newman who were responsible for Philharmonic Hall [in New York City]. Go figure.' (As music lovers know, the acoustics of Philharmonic Hall were for some time less than ideal.)

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A brief look at 'it figures'

The wording "it figures" in the sense of "it stands to reason" goes back much farther than "go figure" does. One early instance appears in a footnote in The Æneid, book 3, in The Works of Virgil (1790):

636. Solum sub fronte. Those who would see the rise of this fiction, may consult Banier's Mythology, vol. IV. P. 290, &c. of the English. Some allegorize this Circumstance of their having but one Eye; Eustathius particularly says, it figures that in Aпger, or any other violent Passion, Men see but one single Object, as that Passion directs, or see but with one Eye; and that Passion transforms us into a Kind of Savages, and makes us brutal and sanguinary like this Polypheme; And he that by Reason extinguishes such a Passion, may, like Ulysses, be said to put out that Eye.

Here, "it figures" has very nearly the same meaning that the stand-alone expression "It figures" does, though without the laconic tone: "It makes sense." The first stand-alone instance of "It figures" that a Google Books search finds appears in Raymond Chandler, Farewell, My Lovely (1940):

Hemingway kicked the car away from the curb and a solid grin settled on his face. "Lets go collect," he said. "It figures. It figures swell. Sonderborg was hiding hot boys. If they had dough, that is. His set-up was perfect for it. Good money, too."

Late as that occurrence is, it's still well ahead of even the first long-form version of "Go figure" to show up in Google Books searches—and it has numerous run-in antecedents in the Google Books database that provide a foundation for its appearance as a stand-alone phrase.

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Conclusions

Aside from an anomalous occurrence of "go figure" in 1910 in an unrelated sense (and in a context where it is by no means a stand-alone expression), the earliest Google Books occurrences of "go figure" in the sense of "what a surprise!" are from 1969 and 1970, and in distinctly Jewish contexts. Although Chaim Potok's novel (from 1969) is slightly earlier than Lillian Feinsilver's article (from 1970), the latter mentions "Go figure it out" as a recurring headline—"a frequent heading for oddities"—in the Jewish Digest, which presumably takes the occurrence of that expression in English, but in a Jewish context, to the 1960s at least. These points (in my view) provide strong circumstantial evidence in favor of the theory that "go figure" has its roots in an earlier Yiddish expression, rather than in some mathematical or logical idiom that originated in English.

"It figures" offers a sharp contrast to "go figure": It dates at least to 1790 in contexts where it has much the same sense of "it stands to reason" that the stand-alone expression "it figures" has today. Its presence in English for so many more years than "go figure" convinces me that this phrase is essentially unrelated to "go figure" beyond having the word figure[s] as its second component.

As others have indicated, it means pretty much the same as "Go figure it out", "Go compute it", or "Do the math". This comes directly from the literal, math meaning of the verb "figure" as "calculate". That's the origin.

Sometimes it is used sarcastically, to indicate that there is really nothing difficult to figure out, that is, that the thing in question is obvious. In this use it means about the same thing as "Duh!", as @alexisclayton indicate.

Just spitballing here, but could 'it figures' in the sense of to draw a conclusion or "stands to reason" or "figure out" be related to the sense of "figure" in a categorical syllogism. Once you determine the figure and the mood of a syllogism you can understand it's form and can determine if it is a valid form or not.

So in this analyst part of determining whether the form of a syllogism is valid or not you have to "figure it" out.

see: https://www.oed.com/view/Entry/70079?rskey=5bn5Xv&result=1#eid

Etymology: < French figure (= Provencal, Spanish, Italian figura ), < Latin figūra , < *fig- short stem of fingĕre : see feign v. The Latin word was the ordinary rendering of Greek σχῆμα (see scheme n.1) in its many technical uses; several of the senses below are traceable, wholly or in part, to Greek philosophy.