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What are some of your favorite colloquial sounding names for mathematical objects, proofs, and so on? For example, manifolds are often described using an atlas and a neighborhood describes a small set surrounding a point.

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I especially like the agricultural theme very consistently upheld in sheaf theory (stalks, germs, ...).

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  • $\begingroup$ That's a great example! $\endgroup$ – 114 May 17 '14 at 15:56
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There's the arboreal theme in graph theory (forests, trees, leaves, roots, ...).

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I can't believe no one has yet mentioned the following. These were quite common, at least at one time (1970s).

abstract nonsense -- refers to (Eilenberg/MacLane) category theory

invariant under change of notation -- refers to differential geometry, especially when tensors are involved

proof by diagram chasing -- refers to a proof involving commutative diagrams, especially when the proof is essentially solving a path puzzle or hedge maze puzzle

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