Tilde Operator

It means “related to”; the field decides exactly how.

In school geometry, △ABC ∼ △DEF says the triangles are similar: same shape, sides in proportion. In analysis, f(x) ∼ g(x) says the two functions are asymptotically equal, their ratio heading to 1 as x grows. In statistics, X ∼ N(0, 1) reads “X is distributed as a standard normal”. Elsewhere it marks an equivalence relation, a rule saying when two things count as “the same kind”, and some logic books write ∼p for “not p”, alongside ¬p.

Where did the squiggle come from?

From 17th-century notation that evolved, not one inventor.

English mathematician William Oughtred printed a tilde-like mark for the difference between two numbers in 1631. Gottfried Wilhelm Leibniz wrote a sideways S, for Latin similis, “similar”, in his manuscripts; it first reached print in 1710, in a notice attributed to him. Later fields borrowed the squiggle for their own relations.