ABSTRACT
Some mathematicians devote themselves to obviously useful activities, employing symbols and abstract ideas to make models of reality and to produce results of practical value in science or engineering. Others regard their subject as a branch of logic, not necessarily connected with tangible creation. A few devote themselves to the apparently trivial, but really quite profound, task of studying the properties of numbers themselves. The theory of probability is firmly based on the mathematical equivalent of common sense, but many people think that they know better. Gamblers, in particular, have an innocent belief in the hoary old fallacy known as the law of averages. If black turns up several times in succession, they say in the casinos, put money on red the next time. The mathematicians have done rather better, to judge from a recent report on an experimental examination designed for the Certificate of Secondary Education.
