Randomness refers to the lack of definite patterns or predictability in information, where individual events are unpredictable but outcomes follow known probability distributions over repeated trials. The concept is formalized in mathematics, statistics, and probability theory, and has applications across science, politics, gaming, medicine, and other fields. Despite common misconceptions, true randomness is theoretically impossible for large structures, and degrees of randomness can be studied and measured using various methods and tests.

• •Pure randomness is impossible for large structures according to Ramsey theory, though degrees of randomness exist in an infinite hierarchy
• •Random selection is used to ensure fairness and reduce bias in various applications including juries, lotteries, clinical trials, and democratic processes
• •Common misconceptions about randomness include the gambler's fallacy (that numbers are 'due'), the belief that past outcomes affect future independent events, and misunderstanding how probabilities change with new information
• •Three mechanisms generate apparent random behavior: environmental randomness, sensitivity to initial conditions studied in chaos theory, and pseudorandomness from algorithmic systems
• •In quantum mechanics, microscopic phenomena are objectively random, while evolutionary biology attributes life's diversity to random genetic mutations followed by natural selection

Theodore Motzkin, Cristian S. Calude, John Venn, Andrey Kolmogorov, Per Martin-Löf, Ray Solomonoff, Gregory Chaitin, Yongge Wang, Paul Erdős, Alfréd Rényi, Ancient Athens, Pompei