Characteristic beliefs of the school included "the idea of the total sinfulness of humanity, predestination, and the need for Christians to rely upon a faith in God which cannot be validated through human reason. Jansenism often, but it continued to have a strong following among those who tended to reject papal authority, but not strong moral beliefs" ("Jansenism," About.com, 2008). After his final conversion, Pascal moved to the Jansenist monastery in Port Royal. He had already convinced his younger sister to move to the nunnery in the same location. It was there he penned the work that would contain his famous wager, the famous Pensees. He continued to live at the monastery until his death in 1662, worn out, it was said, "from study and overwork," although later historians think that tuberculosis stomach cancer was the likely culprit (Ball 1908; "Blaise Pascal, Island of Freedom, 2008).

Major Discovery

Pascal made many notable discoveries in geometry. "Pascal's Theorem" states that if a hexagon be inscribed in a conic section, the points of intersection of the opposite sides will lie in a straight line. Pascal's arithmetical triangle is constructed so that each horizontal line is formed by the one above it "by making every number in it equal to the sum of those above and to the left of it in the row immediately above it" (Ball 1908).

Pascal is most famous for his theory of probabilities (hence, the formation of his famed theological principle as a 'wager'). He entered into a correspondence with the mathematician Fermat (of the only recently 'cracked' Fermat's theorem) in 1654.

Pascal proposed: "Two players of equal skill want to leave the table before finishing their game. Their scores and the number of points which constitute the game being given, it is desired to find in what proportion they should divide the stakes" (Ball 1908). He solved this problem using his arithmetical triangle. The last mathematical work of Pascal was on the cycloid in 1658. The cycloid is the curve traced out by a point on the circumference of a circular hoop which rolls along a straight line (Ball 1908).

How Pascal's discoveries are used today

Although he only lived until age 39, Pascal's work in probability formed the...

Game theory deals with predicting the results of a series of choices and determines the likely outcomes when dealing with incomplete information. Pascal's scientific work, repeating Torricelli's experiments with a barometer was revolutionary in demonstrating that a genuine vacuum could and did exist above the mercury in the barometer. In defending these conclusions at a public debate, Pascal is said to have given one of the clearest statements of scientific method in the seventeenth century ("Blaise Pascal," Oregon State University, 2008). Of course, Pascal's 'adding machine,' the prototype of the modern digital, scientific calculator is in daily use today, in situations to numerous to calculate ("Pascal," the World Great Mathematicians, 2008).
Pascal's studies in geometry, hydrodynamics, and hydrostatic and atmospheric pressure led him to invent the syringe and hydraulic press and to discover what became known as "Pascal's law of pressure." His work on conic sections and produced important theorems in projective, or non-Euclidian, geometry that are important to creating perspective when drawing. They explain how two parallel lines seem to strive to meet into infinity when viewed from a distance. Thus, even without his famous wager, the name of Blaise Pascal would be remembered today.

Works Cited

Ball, Rouse. "Blaise Pascal (1623-1662)." From a Short Account of the History of Mathematics. 4th edition, 1908. Excerpt available on 7 Apr 2008 at http://www.maths.tcd.ie/pub/HistMath/People/Pascal/RouseBall/RB_Pascal.html

Blaise Pascal." Island of Freedom. 7 Apr 008. http://www.island-of-freedom.com/PASCAL.htm

Blaise Pascal." Oregon State University. 7 Apr 008. http://oregonstate.edu/instruct/phl302/philosophers/pascal.html

Hajek, Alan. "Pascal's Wager." The Stanford Internet Encyclopedia of Philosophy. First Published Sat May 2, 1998; substantive revision Tue Feb 17, 2004. 8 Apr 2008. http://plato.stanford.edu/entries/pascal-wager/#4

Jansenism." About.com. 7 Apr 2008. http://atheism.about.com/library/glossary/western/bldef_jansenism.htm

Pascal." The World Great Mathematicians. 8 Apr 2008. http://www.sci.hkbu.edu.hk/scilab/math/pascal.html