meaning - What does the expression “rabbit-out-of-a-hat” mean?



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.




Answer



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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