The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since deterministic algorithms are used. The paper then discusses the strange behaviour of the quantum world and briefly describes how its properties could be exploited in a quantum computer to produce numbers that are genuinely random. The final section considers how different ways of looking at a problem can yield insights into the concept of randomness. (Contains 2 figures.)