The development of probability

Probability theory was one of the last major areas of mathematics to be developed; its beginnings are usually dated to correspondence between the mathematicians Fermat and Pascal in the 1650's concerning some interesting problems that arose from gambling.

Why Greek, Roman or medieval philosophers and mathematicians hadn't developed probability theory is an area of active debate. Several ideas have been suggested, none of them, however, seem quite satisfactory (Hacking 1975 Hacking1975).

One explanation may have been that in an age where thunder strikes because a god wills it, and where heroes cannot escape their fate no matter how they try, the ideas of uncertainty or risk have a different meaning than they do today. The sociologist Beck, for example, sees this as a reason why risk, and controlling risk, is such a marked feature of modern society but was almost completely absent before (Beck 2007 Beck2007). People no longer see the work of fate or the gods in disasters such as war and famine, but instead view them as risks that through the right actions may be averted or at least managed. Although this may deal with the difference between contemporary and ancient society, around the time probability theory started to develop a mostly deterministic world view was beginning to dominate thinking, so on its own this idea is not convincing.

Another reason may have been the fact that the Roman and Greek notation system for numbers was particularly unsuited for dealing with probability, although the activity that gave the original impetus to the development of probability theory (and which continues to shape it today), gambling, was around in those days.

One of the fundamental developments early on that lead to probability theory was the assumption of equally likely cases (see below on the classical interpretation) and this was possible only once regular dice had replaced the more asymmetrical knuckle-bones used by Roman gamblers. Hacking (1975), however, rejects these convenient explanations and concludes that the scientific study of probability could not have taken place as the very concept itself had not been developed.

So in parallel with the development of the mathematical aspects of probability, mathematicians have had to ask themselves what it actually is that they describe. The question of what precisely is probability, although it is a philosophical question, is not philosophical in the colloquial sense of being of academic interest only. Unlike philosophy in many other areas, this question can have important consequences to the relevant mathematical content, the areas of application, and the very statements about the world that are permissible. In fact, one enduring and still acrimonious split among statisticians, that between the (subjective) Bayesians and the frequentists, has as one of its roots the philosophical interpretation of what we mean by “probability”.