Blaise Pascal was born on the 19th of June 1623, in Clermont and died August 19th, 1662, in Paris. Pascal was French a mathematician and physicist, philosopher, theologian and moralist.
Pascal was precocious as a child, he was educated by his father. The earliest works of Pascal were in the natural and applied sciences. He contributed significantly to the construction of a mechanical calculator (the “Pascaline”) and the study of fluids. He clarified the concepts of pressure and vacuum, adding to the work of Torricelli. Pascal wrote important texts on the scientific method.
Pascal was a Mathematician first, he created two new major research fields: first, he published a treatise on projective geometry during a sixteen year period, then from 1654, with Pierre de Fermat he worked on the theory of probabilities which still strongly influences the modern economic theories and social sciences.
After a mystical experience in late 1654, he left mathematics and physics and decided to dedicate himself to the philosophical and religious reflection. He wrote during this period Provinciales and Thoughts, the latter was published after his death just two months after his 39th birthday. All during his life he was sick he suffered severe migraines in particular.
All his life, Pascal made major contributions to mathematics. From the age of sixteen, he began work on what later became projective geometry. It uses and extends the work of the Draft-project of an attack on the meetings of evenemens cone with a plan Girard Desargues along with Apollonius. One major innovation is the theorem that Pascal said that the hexagram formed by 6 points of a conic opposite sides a concurrent three-point line.
Starting from 1650, Pascal is interested in calculus, and arithmetic, in particular the consequences of whole numbers. He provides for the first time the principle of reasoning by induction.
In 1654, he wrote his Treatise on arithmetic triangles in which he gives a convenient table in the binomial coefficients, the “arithmetical triangle”, now known as the “triangle of Pascal” (a Chinese mathematician in the Qin Dynasty, Yang Hui, had worked for four centuries ago on a concept similar to Pascal’s triangle and Omar Khayyam, six centuries earlier).
The same year, a friend, interested in problems with gambling, asked Pascal to correspond with Fermat. This collaboration of Fermat and Pascal lead to the mathematical theory of probabilities. His friend was the Chevalier de Méré and the problem was the so-called “rule of parties” two players decide to stop playing before the end of the game and wish to share gains in an equitable manner based on the likelihood that everyone had to win at that point. It was the introduction of the concept of “expected value”. Pascal, later in the Pensées use a probabilistic argument, the “Pascal’s wager” to justify his belief in God and a virtuous life. The work done by Pascal and Fermat in the calculation of probabilities is an important piece that would lead to Leibniz infinitesimal calculus.
His latest scientific work was on cycloids. In 1658, he solved some problems that occupied many mathematicians, in particular related to the area and volume created by a cycloid rotation around its axis.
After the mystical experience of 1654, Pascal abandoned almost any work of mathematics. However, after a sleepless night in 1658, he offerd an anonymous award for the resolution of the quadrature of the cycloid. Solutions are proposed by Wallis, Huygens, Wren and others; Pascal, under a pseudonym, then publishes his own solution History of the wheel (in French and Latin) with a suite in the history of the roulette end of the year. In 1659, he sent a letter to Huygens on the dimensions of curved lines as Dettonville.
Had Pascal confined his attention to mathematics he might have enriched the subject with many remarkable discoveries. But after his early youth he devoted most of his small measure of strength to theological questions.
Works Cited:
Connor, James A., Pascal’s Wager HarperCollins, NY, 2006
Hald, Anders A History of Probability and Statistics and Its Applications before 1750, (Wiley Publications, 1990)
The Story of Civilization: Volume 8, “The Age of Louis XIV” by Will & Ariel Durant, chapter II, Subsection 4.4 (pg. 66)
