Blaise Pascal

1623-1662

The Beginning

• Born in Clermont-Ferrand, France, June 19, 1623

• His father, Etienne, was a royal tax officer

• Probably grew up in wealthy circumstances

• He was taught by his father with an unorthodox approach– First learned methods of reason and judgment -

discovering the why behind facts.

– At age 12, Pascal was allowed to learn Latin, but not mathematics.

Pascal’s greatest achievements…

• By age 12, he proved Euclid’s theorems (The Elements) on his own!

• By 16, Had published a book on conic sections

• Invented projective geometry

• Proved that vacuums could be created

• Invented the syringe and hydraulic lift

• Unified and proved much in fluid mechanics

• Came up with the basis for much of modern insurance and probability work, together with Pierre de Fermat

• Cleared up many question concerning cycloids

1642- Pascal’s Adding Machine

•Many prototypes were constructed

•Never had a large market, probably because of price

The faith of the man…

• Christ was the center of his theology

– “In [Jesus] is all our virtue and all our happiness. Apart from Him there is only vice, misery, error, darkness, death, despair.”

• He converted to Jansenism, a branch of Catholicism, in 1646– They rediscovered Augustine and opposed

semi-Pelagianism

– Major beliefs sound quite similar to Reformers

– Stressed moral purity

The faith of the man…

Provincial Letters

-These were Jansenist letters that were written in opposition to the Jesuits

Pensées (“Thoughts”) - chapters include discussion on

• mathematics & reason

• fundamentals of Christianity

• proofs for Jesus Christ

Writings...

General distinguishing belief:

Man cannot do any act truly pleasing to God without the grace of God. (regeneration)

God’s grace effectively accomplishes His will.

His mathematics applied to faith…

His work with probability produced what has become known as Pascal’s wager

• It demonstrates a method of coming to a “reasonable” decision.

– Either God is or God is not. One has no choice but to “wager” on which of these statements is true, where the wager is in terms of one’s actions.

– Which way should one act?• In complete indifference to God or

• In a way compatible with the (Christian) notion of God.

His mathematics applied to faith… (cont.)• Which way should one act?

– If God is not, it does not matter much.

– If God is, • wagering that there is no God will bring damnation while

• wagering that God exists will bring salvation.

– Because the outcome of the latter is infinitely more desirable than the former, the outcome of this “decision-problem” is clear, even if one believes that the probability of God’s existence is small:

• The reasonable person will act as if God exists.

"If God does not exist, one will lose nothing by believing in Him, while if He does exist, one will lose everything by not believing." -Pascal

Development of Calculus

• From 1653-1654 he wrote – Traité du triangle arithnétique– Traité des ordres numériques (published in 1665)

– Traité de la sommation des puissances numériques

• Here Pascal laid down the principles of differential and integral calculus

Pascal,

a man who lived and worked in light of the existence of a Sovereign, Personal God who revealed Himself in the person of the Lord Jesus Christ,

grew gravely ill in 1659 and died in August 1962

Pascal & Beyond

• Unlike the Protestant Reformers, Pascal’s religious order saw an unscriptural dichotomy between secular and ecclesiastical activities. Instead of doing all to the glory of God, Pascal felt an unnecessary tension between his mathematical studies and his faith.

• Pascal’s independent discovery of Geometry’s postulates testifies that mathematics is a discovery of the works of God and not merely an invention of man.– “One could believe that calculus was a work of art produced by the free will of

man if one could believe the possibility of a symphony arising from the scores of a number of composers who supposed they were writing only tone poems for solos or chamber groups. This symphony comes together without changing even the key, though the artists wrote during hundreds of years in different corners of the globe without the knowledge of each other’s work.” - Zimmerman Truth and the Transcendent

Pascal & BeyondMany discoveries even occurred simultaneously in the history of mathematics despite great distances and slow communication– Law of Inverse Squares by Newton and Halley

– Logarithms by Burgi and Napier/Briggs

– Calculus by Newton on the island and Leibniz on the continent

– Two geometries of Russian Lobachevski and Hungarian Bolyai

– Modern vector calculus by both Hamilton and Grassman

– Contradiction Hypothesis by H.A. Lorentz and Fitzgerald

– The double Theta functions by Gopel and Rosehain

– The rectification of the semi-cubal parabola by Van Heauraet, Neil, and Fermat

– Geometric law of duality by Oncelet and Gergone

– Principle of Least Squares by Gauss and Legendre

“It seems to be my fate to concur in nearly all my theoretical works with Legendre” - Gauss quoted in Bell’s Men of Mathematics

These truths conspire together to point to the Divine Creator and Sustainer.