In the last half of the seventeenth century, a revolution in science began, fueled by a radically new type of mathematics. This development occurred entirely in Western Europe, and was communicated mainly through a series of letters exchanged among a small network of highly gifted mathematicians and “natural philosophers.” The impact of the novel ideas that originated during this period extended far beyond scientific thinking to alter our everyday understanding of reality. The Scientific Revolution led by Isaac Newton (1642–1727) and Gottfried Leibniz (1646–1716) would certainly fit this description. It has unquestionably had a profound impact on our basic interpretation of the world around us. But I am referring to a much less celebrated episode in the history of human thought that was also beginning to unfold at this time. The impact of this “quiet revolution” is highly visible today, but took a long and circuitous route before reaching popular awareness.

Beginning in the summer of 1654, an interchange of letters took place between two leading French mathematicians: Blaise Pascal (1623–1662) and Pierre de Fermat (1601–1665). One of the problems that occupied these savants had baffled the greatest mathematical minds for over 200 years. Indeed, it was not even clear that this problem even had a unique solution! Known as the “problem of the points,” this conundrum concerned the fair method of dividing the stakes when a game of chance was interrupted ...

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