This essay was written by lower-sixth former Moog Clyde, and shortlisted for the 2020 Fifth Form Transitional Research Project. The following provides a short abstract to the full essay, which can be found at the bottom.
Estimated read time of abstract: 1 minute
Estimated read time of essay: 11 minutes
In 1654, the Chevalier de Mere, a French nobleman, posed the notorious ‘Problem of the Points’ to Blaise Pascal, an esteemed mathematician. The Problem of the Points concerned a game of chance containing two players with equal chances of winning any given round, and posed the question of how to split the stakes if one gambler has to leave the game prematurely. Despite several attempts, finding a definitive solution stumped even the greatest minds of the previous two hundred years, most notably Luca Pacioli (the ‘Father of Accounting’ ) in 1494 and Niccolò Tartaglia (solver of cubic equations and the first to apply maths to the paths of cannonballs, otherwise known as ballistics) in 1556. Even the great Galileo failed to discover a reasonable solution to the problem. Pascal was determined to find a logical and fair solution, and thus reached out to Pierre de Fermat, a brilliant mathematician himself. In their resulting correspondence, the pair developed the first explicit reasoning about what today is known as ‘expected value’ and laid the groundwork of probability, earning them both joint title of ‘the Fathers of Probability.’
Although it is easy to underplay the significance of this breakthrough as merely a clever, tidy solution, to appease opposing gamblers, in reality, it was truly revolutionary. It is difficult to understate how vast and significant the cognitive shift across Europe that occurred following this solution was. The notion that you can hang numbers into the future was alien to mathematicians merely years before this solution was proposed. Soon, others began to see the possibilities that this concept generated.
Within three years Christiaan Huygens adapted Fermat’s theory into a coherent pamphlet entitled ‘De Ratiociniis in ludo aleae,’ which was used as the standard text on probability for the next 50 years. Huygens attributed his developments to “some of the best mathematicians of France” (i.e. Pascal and Fermat). This text spread like wildfire among the academic community as it was evident that the new science of probability had the potential to transform the world. In the next few years, Huygens’ text was ripped out of the context of gambling and thrust into several aspects of life, including law and maths. In particular it was applied to a very different, brand new data set: mortality tables. Almost immediately, by using specific intricate data, insurance shifted from a form of blind gambling, based on hunches and guessing, to a remarkably accurate science.
It now is clear that this rapid chain reaction of discovery underpins all notions of mathematical ‘expected value’ and insurance came not from savvy merchants but from avid gamblers, eager to improve their craft.
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The Unchained Library 