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I read this phrase on a guide for texts about mathematical logic, it says that this proof is “rabbit-out-of-a-hat”.

What does this mean? Is it a slang expression? The exact sentence is:

A little unfortunately, the proof of that is rather too rabbit-out-of-a-hat for my liking.

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    Magicians pulls rabbits out of hats. In this case I'm assuming that the proof was arrived at my guesswork/intuition/magic -- which is actually quite common in math.
    – dcaswell
    Commented Aug 29, 2013 at 23:25
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    It is an idiom that can mean to solve a problem in an unexpected way or simply to produce something from nothing, as if by magic. See english.stackexchange.com/questions/26879/… .
    – choster
    Commented Aug 29, 2013 at 23:28
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    Probably the opposite. The proof required something magical or out of the ordinary, to be completed.
    – dcaswell
    Commented Aug 29, 2013 at 23:31
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    It is this.
    – terdon
    Commented Aug 30, 2013 at 0:55
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    @bib Perhaps, but not half so much as it is like a lepus ex petaso. :)
    – tchrist ♦
    Commented Aug 30, 2013 at 2:06

2 Answers 2

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Referring to proof steps as “rabbit-out-of-a-hat” or as like pulling a rabbit out of a hat is not slang, but rather a popular metaphor in mathematical writing (1,2,3,4,5,6). Generally, it refers to use of unmotivated, non-intuitive, “out of left field”, “out of the blue”, or “off the wall” techniques, that at first may seem completely unrelated to what is being proved and that may seem mysterious or magical. Rabbit-from-hat steps are denigrated when they do not illustrate a method that can be used in proving other theorems, or when the train of thought that prompted the step gets tidied away out of sight.

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It's an analogy to a popular magic trick. The magician shows the audience an empty top hat. They then place the hat upside-down on a table and pull a live rabbit out of it.

The implication of "rabbit-out-of-a-hat" is that the person has unexpectedly produced a desired result, with no indication of how they achieved it.

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