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Blaise Pascal, A Math Prodigy Ahead Of His Time

May 9, 2022
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By Ashley Langham

Blaise Pascal was born with a gifted mind especially in the subjects of mathematics, science and theology. Since he was young, he liked to study math and was very good at the application of it. He would become one of the most influential mathematicians in French history despite him living only a very short life. From the age of sixteen, he had already created his own theorem, called Pascal’s theorem, named after him in his honor. This theorem contributed to the works of Euclid’s Elements, the first compilation to the study of geometry. He only used a circle and a ruler. He was so unbelievably gifted he made the likes of Renė Descartes envious of his brilliance. Descartes often stood in dismay that someone so young could have had such a great mind. 

Unfortunately, Pascal suffered with many ailments during his life, both mental and physical. He battled with his religious beliefs and devotion because he was often  having to go between the world of faith and logic. He also believed that the only way to be a true believer was to live a life of utter “perfection” and moral “purity”. He was troubled by the validity in his beliefs, and the stress, with his weakened physical body and immune system, likely caused his passing in 1662. 

An engraving of Blaise Pascal by artist Henry Hoppner Meyer, sometime during the 1830s, via Britannica

Despite living a shortened life, he would go on to develop a new field of math, the theory of probabilities, contributing great strides in the field of geometry, the Pascal triangle, and two powerful theologies in religious studies that were published after his death. Read on to learn more about his work and life!

Blaise Pascal (1623-1662): A Young Gifted Mathematical Mind

Blaise  was born in Clermont, Auvergne, France in 1623 to Etienne Pascal, who was a politician and judge for the Clemont-Ferrant tax court. His mother unfortunately died when he was four years old, right before he was due to go to school. Instead of putting his children through formal education, his father decided to homeschool Blaise and his two sisters, teaching them an array of subjects, including religious studies. His father, not wanting to overwhelm his children with too much information at an early age, forgoed teaching them mathematics. But, he soon realized that was a mistake. Blaise Pascal took a keen interest in math and science since he was a prepubescent. And, at age fourteen, he was admitted and attended weekly meetings with a group that became the French Academy of Science. 

At sixteen, his father got him Euclid’s Elements, a book on geometry to help develop his math skills. Even before he received this gift from his father, he had already worked on and proven thirty one of Euclid’s theorems. He would contribute to the works by discovering his own theorem, named after him in his honor. His theorem was created from using a circle and a ruler. He selected six points on that circle and formed a hexagon from those points, joining them up consecutively. He stated that by avoiding parallels, you would intersect three pairs of the points AB and ED, BC and FE, CD and AF. By marking these points of the intersection, we can find a straight line. René Descartes, the French mathematician and philosopher was blown away by this discovery and, at first, he did not believe it came from Pascal because of his age. But he came around to just how great of a mathematician Pascal was. 

Generic image showing Pascal's theorem on an ellipse, via Wikimedia

At age nineteen, Pascal created an addition and subtraction calculator for his father to help him calculate taxes for the city of Rouen. He continued to improve upon its mechanisms to make it more accessible to the general public. Four versions of his technology are now being displayed in the Museé des Arts et Métiers in Paris. 

Pascal’s Paradoxical Life

He was a great math mind but he struggled a lot with his religious beliefs. By his early twenties, his whole family converted to Roman Catholicism. He was actually a willing participant of this change and became a spiritual advisor for his family. He came to believe that God has no place in the mind, but only the heart. He kept long journals of his beliefs and they were later published, called Les Provinciales (The Provincials) and Les Pensées (Thoughts), originally known as Apologie de la religion chrétienne (Christian Religion Apologetics) . Both these journals discuss his deep “mystical” conversations and visions of his “new life” as a devout believer in God. His sister, Jaquiline, became a nun around this time and entered into PertRoyal, the monastery. 

He became violently ill and probably would have been considered today to have some sort of stress related mental health issues. He suffered from temporary paralysis, during the time of his “spiritual awakening” due to the stress of holding both his beliefs in faith and beliefs rooted in logic. Or, at least trying to hold both of them to be true at the same time.  He also struggled because his family and he were over zealous in the way they thought they had to behave and believe as Catholics. They believed humans were incapable of understanding God if they did not have grace, or were supremely good people. In other words, he believed in order to be a “good Catholic”, you would have to be morally perfect and pristine. He both purported that if we are skeptics of God then those who are skeptics do not benefit if God is not real. But, if God is real, then we can only benefit from believing in God. Essentially, he did not believe necessarily in converting non-believers but he only believed in a finite definition of who that believer could be and how they could behave. These thoughts tormented him throughout his adulthood. 

He also suffered from poor health. He had a weakened immune system since his childhood and suffered from a lot of physical ailments. With the added stress of his convictions, he suffered greatly throughout his life. 

Pascal’s New Field of Math

By 1654, he started a written correspondence with Pierre de Fermat, a French mathematician responsible for the co-development of analytical geometry. They would challenge themselves often with mathematical problems, mainly set on gambling games. 

One of their earlier correspondence was Fermat and Pascal going back and forth on a specific problem. The scenario went as follows:

If there was a game between two players in which each player gained points over the course of the game. Yet, if the game was stopped before the end, how much money should be divided between the two players purely based on the number of points each player won. 

They analyzed these problems as if they were dice games. But, they also questioned the likelihood of certain events using cards and point flips. Their work even caught the attention of gamblers, such as Chevalier de Mére, who was tired of losing his dice games and wanted to understand how he could start winning again. Fermat and Pascal used their correspondence to talk about his dilemma in great detail, in order to help him increase his odds. 

Pascal also was known for developing the Pascal triangle. He is better known for bringing this idea to “modern” times in the West, because other mathematicians from India, Persia, China, Italy, and Germany came up with a similar theorem from the 13th century and prior. Essentially, there are numbers starting at the top with 1s, that are arranged in a triangular shape and cascades down to larger numbers. Those larger numbers are the sum of the top numbers.  

Pascal's triangle to 5 rows, via Wikimedia

Unfortunately, his life was cut short due to his many physical and mental ailments. He died on August 19, 1662 from violent convulsions. Even though he had such a short life, he made a huge impact on the field of mathematics. 

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