Pierre de Fermat | Biography and Facts

Pierre de Fermat was a notable French mathematician, and Pierre de Fermat contributions to mathematics are prominent. His contributions have accounted for many new formulae and rules that evolved in the field of Mathematics. It was also because of him that early development was possible in infinitesimal calculus. Pierre is particularly popular for his contribution to differential calculus and number theory. He invented the method of finding the biggest and smallest points of curved lines, which resulted in the discovery of differential calculus. Fermat was the mathematician of the 17th century who was the contemporary of Rene Descartes. Along with Blaise Pascal, Fermat co-founded the theory of probability.

Early Life 

Fermat was born in 1607 in France and died on 12th January 1665. However, there is uncertainty regarding the date of his birth. The mansion where Fermat was born has been elevated to a museum. Dominique Fermat, his father, traded in leather, and his mother’s name was Claire de Long. He had three siblings. He was born and grew up in Gascony.

Fermat received a degree in Civil law from the University of Orleans in 1626 and left for Bordeaux. Pierre owned an office as a councillor in 1630 at the Parliament of Toulouse. He owned the office until his last breath. Fermat was skilled in another field as well. He knew six languages: French, Latin, Occitan, Classical Greek, Italian and Spanish. The verses written by Fermat were popular in many languages. 

Fermat married his mother’s cousin Claire de Fermat. They had eight children, but only five of these children survived to adulthood. Their children are Clement-Samuel, Jean, Claire, Catherine and Louis.

Pierre de Fermat Contributions to Mathematics

He began his mathematical research in Bordeaux, and in 1929, he restored De Locis Plans of Apollonius, also known as Apollonius of Perga. During his stay in Bordeaux, Pierre de Fermat discoveries included maxima and minima. During that time, Fermat was inspired by other mathematicians, including Etienne d’Espagnet and Francois Viete. Pierre de Fermat contributions to mathematics also include 

• Analytic geometry

• Determination of maxima and minima

• Differential Calculus

• Quadrature

His contribution to analytic geometry circulated in the form of a manuscript in 1636, which was published in 1679. Fermat also successfully obtained the centre of gravity, which led to quadrature. 

Number Theory of Fermat

Pierre de Fermat number theory includes perfect numbers and friendly integers, later known as Fermat numbers. Fermat discovered the ‘little theorem’ while working on perfect numbers. The Factorisation method discovered by Fermat is known as Fermat’s Factorisation method. Pierre de Fermat number theory also includes the two-square theorem and polygonal number theorem. 

For the first time, Fermat developed the integral of General power functions leading to the sum geometric series. Later, Newton and Leibniz developed the fundamental theorem of calculus with the help of Fermat’s formula. 

Despite Fermat’s claim that he could prove all arithmetic theorems, only a few proofs were found. Since only limited mathematical methods of Fermat were available, many mathematicians, including Gauss, doubted his claims due to the difficulty of the problems. 

Theorems of Fermat

The theorems of Fermat are known as Fermat’s little theorem and Fermat’s Primary Test. Through his theorems, the first statement he gave was that the prime number and integers do not divide each as they are relatively prime. But P divides ap − a.

Many of Fermat’s theorems no longer exist as very few proofs were found to support them. The proof of this theorem was known to be done by a Swiss Mathematician for the first time in 1736. The name of that Mathematician was Leonhard Euler. 

Although there was insufficient proof, Pierre de Fermat’s contributions to Mathematics are significant. With the association of Blaise Pascal, Fermat was able to find the theory of probability. Due to their successful collaboration, both of them were able to discover probability theory. Fermat got the credit for carrying out the first rigorous probability calculation.

Fermat also refined and verified the variational principles in Physics. The principles were first articulated by Euclid. According to Euclid, when the path of light reflects from a mirror, the angle of incidents becomes equal to the angle of reflection. Later the Greek Mathematician, Hero of Alexandria, stated that the path gave the shortest length and the least time. Later Fermat generalised it by saying, “light travels between two given points along the path of shortest time,” which is known as the principle of least time. Due to this major refinement, Fermat is considered an important person in developing the principles of least action.

Conclusion

Pierre de Fermat’s contributions to mathematics cannot be described in a few words. Due to his major research and development, the field of mathematics has found many major theories. With the help of his theories, many other mathematicians were able to develop further in the field. His number theory made him more popular. His other contributions, including the analysis of curves, are also prominent. Besides his contribution to mathematics, Fermat also significantly contributed to Physics. Without his contribution to both fields, many theories and principles would not have evolved.