Famous mathematicians and their contributions

¶ … Mathematician

Biography and Works: The Mathematician Blaise Pascal

The Life of Pascal

Blaise Pascal, along with Rene Descartes, is the rare case of a mathematician equally famous for his religious devotion and contributions to theology as he is for his work with numbers. In fact, Pascal would likely prefer to be remembered as a philosopher of religion rather than a mathematician, theorist, and scientist, as he is today. One biographer of famous mathematician tartly observed that Pascal's "mathematical reputation rests more on what he might have done than on what he actually effected, as during a considerable part of his life he deemed it his duty to devote his whole time to religious exercises" (Ball 1908). However, other biographers have seen Pascal's religion and mathematical gifts as complementary.

For example, "Pascal's Wager" is based upon the proposition that a person should believe in God because as a bet, the idea makes sense. There is so much to be gained potentially by believing in God if one is 'correct.' Likewise, there is so much to lose if one is an unbeliever, and one is 'incorrect.' Conversely, there is little to be lost by a person whose belief is in error. A proof of Pascal's Wager might look like this: 1) the probability of God's existence is 50/50. (2) Wagering for God brings infinite reward if God exists (Hajek 2005). If God does not, there is no net loss. Wagering against God brings no gain, and a great loss.

Despite the modernity, even humor, inherent in such moral calculations, Pascal was largely a man of his time, and a devout Christian. Blaise Pascal was born during the 17th century at Clermont on June 19, 1623, and died in Paris on August 19, 1662. Although the Frenchman's early education was confined to modern languages, when his father noted that the boy had unusual mathematical aptitude in geometry (Pascal intuited as a child why the sum of the angles of a triangle is equal to two right angles), his father gave his son a copy of Euclid's Elements. It would not be an understatement to call the young Pascal a prodigy. At the age of fourteen Pascal was admitted to the weekly meetings of French geometricians, at sixteen he wrote an essay on conic sections and at the age of eighteen, he constructed the first arithmetical machine, a kind of prototypical adding machine or calculator (Ball 1908).

However, Pascal suddenly abandoned mathematics in 1647, "after being advised to seek diversions from study and attempted for a time to live in Paris in a deliberately frivolous manner," because of his health ("Blaise Pascal," Island of Freedom, 2008). Pascal's interest in probability theory "has been attributed to his interest in calculating the odds involved in the various gambling games he played during this period" ("Blaise Pascal," Island of Freedom, 2008). However, Pascal's account in his Pensees is different. He says wished to "contemplate the greatness and the misery of man" in a purely religious fashion which was why he abandoned mathematics in his youth (Ball 1908).

Pascal only took up mathematics again in 1653, while administering his father's estate. It was also around this period of his life that he invented the arithmetical triangle, and together with Fermat created the calculus of probabilities. He also experienced a religious conversion. "He was meditating marriage when an accident again turned the current of his thoughts to a religious life. He was driving a four-in-hand on November 23, 1654, when the horses ran away; the two leaders dashed over the parapet of the bridge at Neuilly, and Pascal was saved only by the traces breaking. Always somewhat of a mystic, he considered this a special summons to abandon the world. He wrote an account of the accident on a small piece of parchment, which for the rest of his life he wore next to his heart, to perpetually remind him of his covenant" (Ball 1908).

Pascal was a devout adherent of Jansenism, a highly ascetic Catholic sect that came into conflict with the more worldly Jesuits. The Jansenists were condemned by the pope in 1653 and 1713. 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).