Informally, the property of a numeric sequence of containing no recognizable patterns or regularities; exemplified in the results of an ideal die roll, or the digits of π (as far as we can tell).

Informally, the property of a string being not longer than any computer program that can produce that string; that is, the property of a string being incompressible.

Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets is a book by Nassim Nicholas

A randomness test (or test for randomness), in data evaluation, is a test used to analyze the distribution of a set of data to see whether it can be described as random (patternless).

A randomness extractor, often simply called an "extractor", is a function, which being applied to output from a weak entropy source, together with a short, uniformly random seed, generates a highly random output that appears independent from the source and uniformly distributed.

Randomness has many uses in science, art, statistics, cryptography, gaming, gambling, and other fields.

The seven states of randomness in probability theory, fractals and risk analysis are extensions of the concept of randomness as modeled by the normal distribution.