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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.

6 votes

Justifying/Explaining math research in a public address

you might be interested in Gowers' one-hour talk on the importance of mathematics. there he justifies/explains mathematical research in a very accessible way.
2 votes

Colloquial catchy statements encoding serious mathematics

Nothing contains everything. or There is no universe. This is how Halmos (pp. 6-7) summarizes the answer of axiomatic set theory to Russell's paradox.