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John Tabak, "Probability And Statistics: The Science Of Uncertainty (History of Mathematics)"

Some types of mathematics are as old as the written word. Geometry is probably older. We have written records from cultures that arose early in world history in which we can find geometry problems and solutions. Ancient scholars were working on geometry even as they were developing a system of writing to express their geometric insights. We can also point to cultures that never developed their own written language but did develop their own arithmetic. At least in some cultures, ’rithmetic is the oldest of the three Rs.

Arithmetic and geometry are branches of knowledge that concern aspects of our perception—number and shape—that are both abstract and concrete. For example, three birds and three books are both concrete manifestations of the abstract idea of the number 3. Similarly, we all recognize that soccer balls and bubbles have something in common: Both are concrete manifestations of the abstract idea of a sphere. These “simple” observations have been made by many people living in many different cultures at many different times in our history. Our ancestors may have begun to think about geometry and arithmetic almost as soon as they began to think at all.

Probability is different. Unlike geometry and arithmetic, whose origins lie in prehistoric times, the theory of probability is a comparatively recent discovery. We know when probability, as a branch of mathematics, was discovered. The theory of probability has its origins in the Renaissance with the work of Girolamo Cardano and later Galileo Galilei, but their work had little impact on those who lived later. The investigation of probability begins in earnest with an exchange of letters conducted by two French mathematicians, Pierre de Fermat and Blaise Pascal. Mathematicians have been studying probability ever since.

One might think that the discovery of a new branch of mathematics means the solution of a new and difficult equation or the discovery of a new and exotic geometric shape. For probability, however, this is false. Many of the solutions to important problems early in the history of probability involved little more than simple arithmetic. This is not to say that just anyone could have solved these problems. These “simple” problems challenged some of the

best minds of the day, because despite the elementary arithmetic involved in their solution, the concepts on which the solutions were based were new and challenging.

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