Blaise Pascal

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Blaise Pascal

• 1623-1662

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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.

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Pascals greatest achievements

• By age 12, he proved Euclids 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

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1642- Pascals Adding Machine

• Many prototypes were constructed
• Never had a large market, probably because of
  price

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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

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The faith of the man
General distinguishing belief Man cannot do any
act truly pleasing to God without the grace of
God. (regeneration) Gods grace effectively
accomplishes His will.
Writings...
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

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His mathematics applied to faith

• His work with probability produced what has
  become known as Pascals 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 ones
  actions.
• Which way should one act?
• In complete indifference to God or
• In a way compatible with the (Christian) notion
  of God.

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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 Gods 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
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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

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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
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Pascal Beyond

• Unlike the Protestant Reformers, Pascals
  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.
• Pascals independent discovery of Geometrys
  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 others work. - Zimmerman
  Truth and the Transcendent

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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 Bells Men of Mathematics
• These truths conspire together to point to the
  Divine Creator and Sustainer.