A part of the first chapter of the book The spirit and the uses of the mathematical sciences talks about the beauty of mathematics. The author quotes from a lecture of Hasse and introduces the notion of a mousetrap proof. I feel that the author gives a lucid exposition on what talked about, but regretfully without an example of a proof of such type.
Seeking after is at least one example of a proof of such type.
If answering this question necessitates more information, please feel free to state that.
The original paragraph is in the following formulation, the chapter having which is entitled The characteristic features of mathematical thought and written by PROF. DR. RER. NAT. J. WEISSINGER:
Criteria of beauty at the second level, according to Hasse, are purposefulness and elegance. Purposefulness means that at every point of a proof we should know where we stand and should have the goal in view. The opposite of this is the so-called mousetrap proof, in which we are nudged forward conclusion by conclusion until suddenly the door snaps shut. We feel ambushed, extraordinarily stupid, and irritated by the esoteric ingenuity of the author, yet when we try to gnaw at the bars of the logical conclusions, we are compelled to admit that the proof is solid and without flaws.
Beauteous, is not it? Here the boldfaced words are those quotation-marked in the original text.