Blaise Pascal

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With 'Pascal's wager' he uses probabilistic and mathematical arguments but his main conclusion is that

...we are compelled to gamble...

His last work was on the cycloid, the curve traced by a point on the circumference of a rolling circle. In 1658 Pascal started to think about mathematical problems again as he lay awake at night unable to sleep for pain. He applied  Cavalieri's calculus of indivisibles to the problem of the area of any segment of the cycloid and the centre of gravity of any segment. He also solved the problems of the volume and surface area of the solid of revolution formed by rotating the cycloid about the x-axis.

Pascal published a challenge offering two prizes for solutions to these problems to  Wren, Laloubère,  Leibniz,  Huygens,  Wallis,  Fermat and several other mathematicians.  Wallis and Laloubère entered the competition but Laloubère's solution was wrong and  Wallis was also not successful.  Sluze,  Ricci,  Huygens,  Wren and  Fermat all communicated their discoveries to Pascal without entering the competition. Wren had been working on Pascal's challenge and he in turn challenged Pascal,  Fermat and  Roberval to find the arc length, the length of the arch, of the cycloid.

Pascal published his own solutions to his challenge problems in the Letters to  Carcavi. After that time on he took little interest in science and spent his last years giving to the poor and going from church to church in Paris attending one religious service after another.

Pascal died at the age of 39 in intense pain after a malignant growth in his stomach spread to the brain. He is described in as:-

... a man of slight build with a loud voice and somewhat overbearing manner. ... he lived most of his adult life in great pain. He had always been in delicate health, suffering even in his youth from migraine ...

His character is described as:-

... precocious, stubbornly persevering, a perfectionist, pugnacious to the point of bullying ruthlessness yet seeking to be meek and humble ...

In the following assessment is given:-

At once a physicist, a mathematician, an eloquent publicist in the Provinciales ... Pascal was embarrassed by the very abundance of his talents. It has been suggested that it was his too concrete turn of mind that prevented his discovering the  infinitesimal calculus, and in some of the Provinciales the mysterious relations of human beings with God are treated as if they were a geometrical problem. But these considerations are far outweighed by the profit that he drew from the multiplicity of his gifts, his religious writings are rigorous because of his scientific training...

J J O'Connor and E F Robertson

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