# Pierre de Fermat’s Inventions, Early Life, Education and History

Pierre de Fermat was a French mathematician, lawyer, and scholar who made significant contributions to the fields of number theory, geometry, calculus, and probability. He is best known for his famous statement of Fermat’s Last Theorem, which remained unsolved for over three centuries until it was proved by Andrew Wiles in 1995.

## Early Life and Education

Pierre de Fermat was born on August 17, 1601, in Beaumont-de-Lomagne, France. He was the son of Dominique Fermat, a wealthy leather merchant, and Françoise Cazeneuve, a noblewoman. He had four siblings: Clément, Catherine, Louise, and Antoinette.

He attended the local Franciscan school, where he learned Latin, Greek, and classical literature. He also developed an interest in mathematics and astronomy. He later moved to Bordeaux, where he studied law at the University of Bordeaux. He graduated with a bachelor’s degree in civil law in 1626 and a doctorate in canon law in 1631.

He also continued his self-study of mathematics and became acquainted with other mathematicians like Étienne d’Espagnet, Jean de Beaugrand, and Marin Mersenne. He also corresponded with other prominent mathematicians like René Descartes, Blaise Pascal, John Wallis, and Christiaan Huygens.

## Inventions

Pierre de Fermat made several inventions that advanced the fields of mathematics and science. Some of his inventions are:

- The method of adequality, which is a technique for finding the maxima and minima of functions and solving equations involving fractions.
- The method of infinite descent, which is a technique for proving the impossibility of certain mathematical statements by showing that they would lead to an infinite sequence of smaller and smaller positive integers.
- The principle of least time, which is a principle that states that light travels along the path that takes the least time between two points.
- The principle of Fermat’s point, which is a principle that states that the point that minimizes the sum of the distances from a given set of points is the one that lies on the boundary of the smallest circle that contains them.
- The Fermat numbers, which are numbers of the form $2^{2^n}+1$, where $n$ is a non-negative integer.
- The Fermat primes, which are prime numbers that are also Fermat numbers. Only five Fermat primes are known: 3, 5, 17, 257, and 65537.
- The Fermat’s little theorem, which is a theorem that states that if $p$ is a prime number and $a$ is any integer not divisible by $p$, then $a^{p-1} \equiv 1 \pmod{p}$.
- The Fermat’s Last Theorem, which is a conjecture that states that no three positive integers $a$, $b$, and $c$ can satisfy the equation $a^n + b^n = c^n$ for any integer value of $n$ greater than 2. Fermat claimed to have a proof for this conjecture but never wrote it down. The conjecture was finally proved by Andrew Wiles in 1995.

He also developed several concepts and theories that advanced the understanding of genetics and evolution. Some of them are:

- The genetical theory of natural selection, which is a book that synthesizes Darwin’s theory of evolution with Mendel’s laws of inheritance.
- The fundamental theorem of natural selection, which is a theorem that states that the rate of increase in fitness of any organism is equal to its genetic variance in fitness.
- The Fisher–Wright controversy, which is a debate between Fisher and Sewall Wright over the relative importance of natural selection and genetic drift in evolution.
- The Fisher–Muller hypothesis, which is a hypothesis that states that sexual reproduction enhances the rate of evolution by creating more genetic variation.
- The runaway sexual selection hypothesis, which is a hypothesis that states that female preference for male traits can lead to exaggerated male traits that have no adaptive value.

## History

Pierre de Fermat had a distinguished career as a mathematician, lawyer, and scholar. He worked as a councillor at the Parliament of Toulouse from 1631 to 1653 and as a royal judge at the Chamber of Requests from 1653 to 1660. He also served as an advisor to Cardinal Mazarin during the Fronde civil war.

He published only one mathematical paper during his lifetime: Introduction to Plane and Solid Loci in 1636. Most of his mathematical works were found in his personal notes or letters to other mathematicians. He died on January 12, 1665, in Castres, France. He was buried at the Church of Saint-Dominique in Castres.

He was survived by his wife Louise de Long and their five children Pierre de Fermat was a French mathematician, lawyer, and scholar who made significant contributions to the fields of number theory, geometry, calculus, and probability. He invented several methods and concepts that revolutionized mathematics and science. He also wrote several works that contained his famous statement of Fermat’s Last Theorem, which remained unsolved for over three centuries until it was proved by Andrew Wiles in 1995. He is widely regarded as one of the greatest mathematicians of all time.