Blaise Pascal

Blaise Pascal was a French mathematician, physicist, inventor and Christian thinker who died at 39 after a life of brilliant achievement and chronic illness. As a young man he built one of the first mechanical calculators, proved by experiment that a vacuum can exist and, with Pierre de Fermat, laid the foundations of probability theory. After a religious conversion he turned to the defence of Christianity, and his unfinished Pensées, with its famous wager on God, is one of the classics of French literature and religious philosophy.

Pascal was born on 19 June 1623 in Clermont, now Clermont-Ferrand, in the Auvergne region of the Kingdom of France. His mother died when he was three, and his father, Étienne Pascal, a senior tax official and capable mathematician, educated Blaise and his two sisters, Gilberte and Jacqueline, himself. In 1631 the family moved to Paris, where Étienne joined the scientific circle of the friar Marin Mersenne and took his son along.

Blaise showed exceptional mathematical talent. According to his sister Gilberte, who wrote his first biography, he worked out many of the early propositions of Euclid on his own. At sixteen he wrote a short Essay on Conics, containing a theorem on hexagons inscribed in conic sections that still bears his name. René Descartes was reportedly reluctant to believe that a boy had written it.

In 1640 Étienne was appointed to supervise taxation in Normandy and moved the family to Rouen. To help with his father's endless arithmetic, Pascal designed a mechanical calculator that could add and subtract using geared wheels. He built around fifty versions over the following decade, and in 1649 received a royal privilege for it. The Pascaline was too expensive to sell widely, but several examples survive and it is one of the ancestors of modern computing machines.

Pascal next took up the question of the vacuum. Following the Italian Evangelista Torricelli, he repeated experiments with tubes of mercury and argued, against the long tradition descending from Aristotle, that nature does not abhor a vacuum and that the column of mercury is held up by the weight of the air. In 1648, at his request, his brother-in-law Florin Périer carried a barometer up the Puy de Dôme near Clermont and found the mercury fell as he climbed, as Pascal had predicted. His work on fluids led to what is known as Pascal's principle, that pressure applied to an enclosed fluid is transmitted equally in all directions, the basis of the hydraulic press. The modern unit of pressure, the pascal, is named after him.

In 1654, prompted by a gambler's question about how to divide the stakes of an interrupted game, Pascal exchanged letters with Pierre de Fermat. Together they worked out methods for calculating expected outcomes, which became the beginnings of probability theory. In the same year he wrote a treatise on the arithmetical triangle, the arrangement of numbers now called Pascal's triangle, although it was known much earlier in Persia, India and China.

The family had come into contact with Jansenism in 1646. This was a strict Catholic movement, centred on the abbey of Port-Royal near Paris, which stressed human sinfulness and dependence on God's grace, following Augustine of Hippo. Jacqueline became a nun at Port-Royal in 1652. On the night of 23 November 1654 Pascal had an intense religious experience, which he recorded on a sheet of parchment he sewed into his coat; it begins with the word "Fire" and was found only after his death. From then on he devoted himself mainly to religion, though he continued to do some mathematics, including work on the cycloid curve in 1658.

In 1656 and 1657 Pascal published eighteen anonymous letters, the Provincial Letters, defending the Jansenist theologian Antoine Arnauld, who was being condemned by the Sorbonne. They mocked the Jesuits for what Pascal saw as their lax moral teaching, especially casuistry, the reasoning by which serious sins could be excused in particular cases. Written in clear, witty and lively French, they were a sensation, and they are often seen as a model of modern French prose. The Church put them on its Index of forbidden books, and they did not save Port-Royal, which was eventually suppressed.

In his last years Pascal planned a great defence of Christianity addressed to sceptics and indifferent people of the world. He never finished it. The notes he left, from short sentences to long passages, were published in 1670 as the Pensées, or Thoughts. They describe the human condition as a mixture of greatness and wretchedness: human beings are fragile, a mere "thinking reed", lost between the infinitely large and the infinitely small, yet their capacity for thought gives them dignity. He argued that people distract themselves with amusements to avoid thinking about death, and that "the heart has its reasons, which reason does not know".

The best-known passage is the wager. Pascal argued that reason cannot prove or disprove God's existence, yet everyone must in effect bet one way or the other. If one bets on God and God exists, the gain is infinite; if God does not exist, little is lost. A rational person should therefore choose to live as a believer. Critics have objected, among other things, that the argument could equally support many different gods and that belief cannot be chosen at will, but it remains a pioneering use of decision theory.

Pascal suffered from poor health most of his adult life, with severe headaches and digestive pain. In his last year he helped launch a public transport service of horse-drawn coaches in Paris, one of the first of its kind, giving much of the profit to the poor. He died in Paris on 19 August 1662, aged 39, possibly of stomach cancer or tuberculosis; the cause is uncertain.

His mathematics shaped probability theory and influenced Gottfried Wilhelm Leibniz, who took ideas from his work on curves towards the calculus and studied his calculator when designing his own. As a writer, he was admired and argued with by Voltaire, who attacked his gloomy view of humanity, and later by Kierkegaard and the existentialists. He stands apart from the confident rationalism of much early modern philosophy and remains a central figure in the history of France.