2. 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.
3. 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
4. 1642- Pascal’s Adding Machine
•Many prototypes were constructed
•Never had a large market, probably because of price
5. 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
6. 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.
7. 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.
8. 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
9. 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
10. 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
11. 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
12. Pascal & Beyond
Many 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
