Actuarial science has always employed theoretical principles in the solution of practical problems and this has often required a substantial amount of numerical work. Most of the calculations involved in conventional actuarial work are not, in concept, particularly difficult; in general, they take the form

Value=Amount payable × probability of payment × discounting factor.

For many years, the major difficulty of those engaged in the development of actuarial science was not the application of the principles behind their calculations, but the practicality of producing numerical answers to any particular problem. Much ingenious work has gone into the development of techniques designed to reduce the computational problems to manageable proportions. The most obvious example is the use of commutation functions, where, once a great deal of basic calculation has been performed, a very powerful tool is available, requiring only simple arithmetic. In an attempt to avoid such onerous numerical work, 'laws of mortality' have been developed. Under these, the decrement table may be described in terms of a mathematical function, which enables analytical techniques to be applied, simplifying the numerical work.