Suppose is a collection of mathematical objects (for instance, sets, or functions). Then we say that is rigid if every is uniquely determined by less information about than one would expect.

It should be emphasized that the above “definition” does not define a mathematical object. Instead, it describes in what sense the adjective rigid is typically used in mathematics, by mathematicians.

Let us illustrate this by some examples:

1. Harmonic functions on the unit disk are rigid in the sense that they are uniquely determined by their boundary values.
2. By the fundamental theorem of algebra, polynomials in are rigid in the sense that any polynomial is completely determined by its values on any countably infinite set, say , or the unit disk.
3. Linear maps between vector spaces are rigid in the sense that any is completely determined by its values on any set of basis vectors of .
4. Mostow's rigidity theorem