Blaise Pascal

Most of us know him because of the triangle that was named for him, but Blaise Pascal (1623-1662) did many other things, including creating an early calculating device, which was later named the Pascaline in his honor.  The Pascalines pictured above are all from the 17th and 18th centuries - one is signed by Pascal!  They reside in the Musee des arts et metiers (CNAM) in Paris.  

Pascal invented this calculating machine when he was only 19 years old in order to assist his father, a tax collector, in his exhausting, tedious work of calculating and recalculating what was paid and what was owed.  It was able to carry out addition and subtraction - and also multiplication (as repeated addition) and division (as repeated subtraction).  This may not sound like much to us, with our fancy graphing calculators and our scientific calculators on our smart phones, but it was Pascal and others like him who paved the way for the technology that we enjoy today!

When Pascal was a child his father, who was an avid amateur mathematician himself, came to the strange conclusion that his son should not study mathematics before the age of fifteen.  He therefore removed all mathematics texts from the house.  This ban only raised young Pascal's curiosity about the subject, and he started working on geometry in secret.  When his father saw the results Pascal was achieving he removed the ban and allowed his son to access mathematical texts.

 Above - the man himself.  Below - the triangle named for him.  As so often happens with things, though this object bears his name, he did not invent it.  It was known in China at least as early as the the year 1300, and it was also known to mathematician Omar Khayyam who lived almost 600 years before Pascal, from 1048 to 1131.  But Pascal did do a tremendous amount of study of this triangle.  Among the other patterns you can find inside it (and they are countless - see if you can find some!) are what are known as the "binomial coefficients," and it was Pascal's work on this that paved the way for Sir Isaac Newton to develop the general theorem of binomial coefficients that includes fractional and negative powers.

Because I am a mathematician I often think of Pascal as a mathematician, but he actually focused far more on theology than he did on mathematics. His book Pensees, a collection of fragments on theology and philosophy, is probably his best-known work, and it includes such quotes as:

"Men never do evil so completely and cheerfully as when they do it from religious conviction."

"All of humanity's problems stem from man's inability to sit quietly in a room alone."

"When I consider the brief span of my life absorbed in to the eternity which precedes and will succeed it  .  .  .  .  the small space I occupy and which I seem swallowed up in the infinite immensity of spaces of which I know nothing and which know nothing of me, I take fright and am amazed to see myself here rather than there:  there is no reason for me to be here rather than there, now rather than then.  How put me here?  By whose command and act were this place and time allotted to me?"

It also includes the basis for another item that bears his name: "Pascal's Wager," which begins with the assumption that in deciding whether or not to believe in God all humans are betting their lives and are compelled to do so.  He concludes that a rational person should live as though God exists.  If God does not exist, then this person loses only a finite amount (some pleasures in this brief life).  However, if God does exist then a person who believes in Him receives infinite reward (Heaven) and avoids infinite losses (Hell).

Pascal, along with Pierre de Fermat, laid the foundation for probability theory.  This was prompted when a gambling question was brought up by Antoine Gombaud, Gevalier de Mere.  The question had to do with how to split the pot of money if gamblers had to end a certain game early.  This question had come up before and was treated by earlier mathematicians, but they leaned toward splitting the pot based on the proportion of rounds already won or lost.  Whereas Pascal and Fermat looked at what would happen if the game had continued.  This was a major shift in thinking, as prior to this things that "would happen" were considered to be in God's hands alone and could not be quantified.

Though he loved mathematics and was a brilliant mathematician, he often took long breaks from mathematics.  This was particularly the case when his father became seriously injured and was cared for by brothers of the Jansenist theological movement.  Pascal was greatly influenced by them and came to feel that mathematics was a distraction from concerns about his mortal soul and should thus be avoided.

Eventually he became so overwhelmed by his thoughts of eternal destruction that it was making him ill, and his doctor recommended going back to the activities of a young man, so he took up mathematics again.  He set it aside more than once, and one story of him picking it back up again is that he had a terrible, unbearable toothache - so bad that it was keeping him awake, so he began to do mathematics in order to distract himself and take his mind off the pain.  It worked.

 Pascal lived much of his life in Paris and is buried there.  He had become ill while in his twenties and never fully regained his health.  He lived most of his adult life in great pain and died having only reached the age of 39.  Despite this he continued to engage in life - particularly the life of the mind and soul.  He explored mathematics, philosophy and theology and produced much.  I'm betting he has won his wager!