Excerpt from The Development of Insurance Mathematics: Two Lectures Delivered Before the Students in the School of Commerce of the University of Wisconsin, the Fall Term of 1901
It is most interesting to study the growth and evolution of any branch of science and to observe how it sprang from some other branch of science, and what things had to be known as a preparation for the dawning of the new learning. It is a far cry, perhaps, from actuarial science to the decimal system of notation, and yet, had it not been for the invention of that system it may well be doubted whether arithmetic would ever have reached the stage which renders mathematical problems that would otherwise be difficult of operation, simple and easy. Addition, which is now so simple, albeit so laborious a matter, was exceedingly difficult under the old systems of notation. A student may readily form some conception of the difficulties if he will range a number of Roman numerals side by side, or one under the other - one arrangement is about as convenient as the other - and proceed to add. Multiplication, which is continued addition, was even harder. It follows that operations which must be performed upon a very large scale, in order that actuaries may do their tasks, were then almost impossible upon anything but a limited scale.
Almost equally absurd it may at first seem to declare that the new science could not have come into existence until after algebra was discovered; but it will be seen to be perfectly reasonable to say this when it is taken into account that actuarial science is merely a department of algebra, and that all its operations are algebraic. The form which all its formulas take is that of equations, and they are evolved from other equations by purely algebraic processes.
Algebra and decimal notation were both introduced into Europe by the Arabs through the Moorish schools of Spain and Africa, in the thirteenth century.
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