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Blaise Pascal (1623-1662)

Blaise Pascal is known as one of the co-founders of present day probability theory.  He is known by many titles such as geometer, philosopher, mathematician, probabilist, physicist, and inventor.  On June 19, 1623, he was born in Clermont, France to Ètienne, a mathematician and civil servant, and his

     Pascal had gained an abundant amount of knowledge in the field of mathematics by the age of sixteen.  He learned much of this mathematics material by attending and listening to group discussions, such as the Académie Parisienne, between various scientists and mathematicians with his father.  In 1640, he wrote a pamphlet titled, Essai sur les coniques, which discussed the foundations of what is known as projective geometry.  Writing a treatise to clarify one of Gérard Desargues’ works, he further analyzed the work and produced his own theorem which dealt with about 400 propositions and corollaries. 

     In 1641, Pascal’s health began to decline.  He continued to work at home and developed a calculator to help his father with his tax work.  This became the first manufactured calculator.  It used cogged wheels to perform the operations of addition and subtraction.  Around 1646, Pascal began work in physics, concentrating on vacuums, atmospheric and barometric pressure.  In relation to this, he developed a principle (now called Pascal’s principle) which says "that pressure will be transmitted equally throughout a confined fluid at rest, regardless of where the pressure is applied" (Young, 1998, p. 386). 

     Later in his life, Pascal and Fermat started corresponding via letters concerning probability.  Their solutions of probability problems lead to the development of the probability theory we know today (see Brief History of Probability).  Although their early correspondence concerned probability concepts, Pascal and Fermat began to lay the foundations of  calculus when Pascal used what we know as Pascal’s triangle to solve problems involving mathematical concepts, such as the curve cycloid.  These results were published in a 1658 work, Lettre circulaire relative a la cycloïde (Young, 1998).  This work established foundations of both differential and integral calculus.

     In 1658 Pascal’s health continued to decline.  He died on August 19, 1662 before his last project, the development of a public transportation system of carriages in Paris, was put into use (Young, 1998).  

Additional Links:
MacTutor - Pascal
Existentialism and Blaise Pascal by Katharena Eiermann
An Essay on Blaise Pascal by Iain Proctor
Mathematicians of the Seventeenth and Eighteenth Centuries - Pascal
All You Ever Wanted to Know About Pascal's Triangle and more

Activity #7:

Use Pascal’s triangle to determine the probability that a family with five children has (a) five girls, (b) four girls and one boy, (c) three girls and two boys, (d) two girls and three boys, (e) one girl and four boys, or (f) five boys.

Link to solution.

Picture reproduced from MacTutor History of Mathematics archive with permission.