Great Mathematics Geniuses - Blaise Pascal and Pierre de Fermat

Fermat was born near Toulousse in 1601. He died in Castres in 1665. He was the son of a leather merchant and received his early education at home.

As he was a lawyer, he spent most of his spare time doing mathematics. He published little during his life. Some call him the greatest mathematician of the seventeenth century.

Five years after his death, his son published an edition of his Arithmetica. There were many errors in this edition.

Fermat is most famous for his Last Theorem:
There do not exist positive integers x,y,z,n such that xⁿ+yⁿ=zⁿ, for n>2

It was stated in the margin of a book, and Fermat said he could not include the proof, though he had one, as the margin was too narrow. Many mathematicians have attempted a proof. This proof has had the most number of incorrect proofs published for it and finally accepted as solved after great investigations on the proposed solution of British mathematician Andrew Wiles.

Blaise Pascal was born at Clermont (now Clermont-Ferrand), Auvergne, France on June 19, 1623. His father was Clermont's local judge. In 1631, Pascal's father moved him and his son to Paris. Pascal was required to stay at home to study because his father was afraid of Pascal being overworked at school. His education at first was confined to the study of languages, while the study of mathematics was excluded because it was too tedious. Naturally, it generated a lot of interest from the boy about math. In 1635, when Pascal was twelve years of age, he asked his tutor what geometry was. His tutor answered that it was the science of constructing figures and determining proportions between the different parts of the figures. Interested, Pascal gave up his leisure time to study math. In several weeks, he discovered many properties of figures. In particular, he proposed that the sum of the angles of a triangle is equal to two right angles. Impressed, Pascal's father gave him a copy of Euclid's Elements. Pascal read it with enthusiasm and quickly mastered the concepts presented in the Elements.

When Pascal was fourteen, he attended weekly meetings with many French geometricians like Roberval, Mersenne, Mydorge, and others. Two years later, he wrote an essay on conic sections. In 1641 he constructed the first arithmetical machine. He further improved this machine eight years later. As a result of his correspondence with Fermat, Pascal was starting to focus on analytical geometry and physics. From the early age of 17 or 18, he was also suffering from insomnia and acute dyspepsia because of his intense study.

In 1650, Pascal very suddenly abandoned his mathematical research to study religion. Three years later, he had to administer to his father's estate and began his research again. Around this time, he invented the arithmetical triangle, and with Fermat created the theories of probabilities. In addition, Pascal was considering marriage when an accident happened to him that made him turn his thoughts back to a religious life. He was driving a carriage with four horses on November 23, 1654 when the horses ran away. The two leading horses ran off the bridge at Neuilly, and Pascal was saved only by the reins breaking. After this accident, Pascal considered this a special summons from God to abandon the world. He wrote about this accident on a small piece of paper and kept this parchment near his heart for the rest of his life. He thus moved to Port Royal where he lived until his death in the year of 1662.

Pascal's most famous work in philosophy is Pensées, a collection of personal thoughts on human suffering and faith in God. He began this work in late 1656 and did not complete it until 1658. This work contains 'Pascal's wager' which claims to prove that belief in God is rational with the following argument:

"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."

With this 'wager,' Pascal uses probabilistic and mathematical arguments to prove that God exists. Today's many philosophers criticize him because of his eye-to-eye prize versus punishment approach to God subject.

Pascal contributed to mathematics in many fields. These include:

• conic geometry
• theory of probabilities
• cycloids
• invented the first arithmetical machine called the Pascaline
• experiments on atmospheric pressure

Pascal died in Paris, France on Aug. 19, 1662.