Mathematics

Blaise Pascal

1623 to 1662, Clermont-Ferrand, France

From the geometry of chance to the wager on God: a mathematician who weighed the vacuum, the odds, and the limits of reason itself.

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Lessons

The Birth of Probability

How a gambler’s puzzle - the ‘problem of points’ - drew Pascal and Fermat into the 1654 correspondence that founded probability theory, and gave the world its first rigorous grip on chance through the…

The Arithmetical Triangle and Proof by Induction

Pascal’s Treatise on the Arithmetical Triangle : how one simple table of numbers unifies the binomial coefficients, combinations, and figurate numbers - and how, to prove one of its properties for infinitely many…

The Machine and the Weight of the Void

Pascal the physicist and engineer: the Pascaline calculating machine; the great Puy-de-Dôme experiment proving that the air has weight and that the vacuum can exist, against the ancient dogma that ‘nature ab…

The Provincial Letters and the Wager

Pascal turns reason on the probability of belief : the Provincial Letters demolish the lax ‘probabilism’ of the casuists, and the Wager of the Pensées applies the mathematics of expectation - which Pa…

The Two Infinites and the Limits of Reason

The Pensées on the human condition: the being suspended between the infinitely large and the infinitely small; the ‘thinking reed,’ feeble yet aware; the heart that knows what reason cannot prove; and…

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