I was recently working on a math problem, which involved some horrifically messy calculations, but which resulted in a surprisingly clean, beautiful, and useful result, and I was wondering what a good expression would be to describe such a thing. My first thought was "diamond in the rough", but that doesn't really convey that it started out as something really ugly, and in any case, the expression reminds me of a song I don't like. Is there a better expression for this? The best I can think of is "ugly duckling", but that expression focuses mainly on the earlier (ugly) phase, rather than the fact that beauty came seemingly out of nowhere.

3 Answers 3


Perhaps gold is a good metaphor for your happy results: "I spun gold from a pile of straw" or "I panned gold nuggets from a pile of mud".

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    Hello, will. Answers lacking research are not usually welcomed on ELU, tending not to reflect actual usage. This answer would be improved if you added the famous allusion you are using (though your second suggestion seems rather D-I-Y). Commented Aug 8, 2017 at 10:30
  • I am grateful for your guidance.
    – will m
    Commented Aug 11, 2017 at 3:50
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    Please add a reference. It's such a good metaphor that I'd like to be able to upvote it. Commented Aug 11, 2017 at 8:14

The butterfly emerged from its chrysalis See YouTube, Monarch Butterfly Emerging from Chrysalis

chrysalis, from Merriam-Webster:

the hardened outer protective layer of a pupa

and a pupa is, according to Merriam-Webster:

an intermediate usually quiescent stage of a metamorphic insect (such as a bee, moth, or beetle) that occurs between the larva and the imago, is usually enclosed in a cocoon or protective covering, and undergoes internal changes by which larval structures are replaced by those typical of the imago

and an imago is, from Merriam-Webster:

an insect in its final, adult, sexually mature, and typically winged state

In this case, the imago is the butterfly.

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    The metamorphosis/butterfly metaphor. Lovely. Too nice to let the mathematicians get hold of;) Commented Aug 8, 2017 at 15:56

You made a silk purse out of a sows ear, that's what you did!!

  • What does this expression mean? see ab2's answer, which adds references. Commented Aug 8, 2017 at 10:29

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