Pierre Fermat French mathematician, one of the creators of analytical geometry and number theory (Fermat's theorem) Date of Birth: 17.08.1601 Country: France

1. Biography of Pierre de Fermat
2. Early Life and Education
3. Personal Life and Legacy
4. Contributions to Mathematics
5. Fermat's Last Theorem
6. Other Contributions

Biography of Pierre de Fermat

Pierre de Fermat was a French mathematician who was one of the creators of analytic geometry and number theory (Fermat's theorem). Although mathematics was only a hobby for Fermat, he laid the foundations for many of its areas: analytic geometry, calculus of infinitesimals, and probability theory. Fermat did not leave behind any completed works, and most of his sketches were not published during his lifetime.

Early Life and Education

Pierre Fermat was born in the town of Beaumont-de-Lomagne in the south of France, where his father, Dominique Fermat, held the position of "second consul," a kind of assistant to the mayor. His baptismal record from August 20, 1601, states: "Pierre, son of Dominique Fermat, bourgeois and second consul of the city of Beaumont."

In college, Pierre acquired a good knowledge of languages: Latin, Greek, Spanish, and Italian. Fermat was renowned for his expertise in antiquity, and he was consulted on difficult passages in Greek classics. However, Fermat directed all the power of his genius towards mathematical research. Nevertheless, mathematics did not become his profession. Fermat chose to study law, and he was awarded a bachelor's degree in Orléans. In 1630, Fermat moved to Toulouse, where he obtained a position as a counselor in the Parliament (i.e., the court).

Personal Life and Legacy

In 1631, Fermat married his distant relative on his mother's side, Louise de Long. Pierre and Louise had five children, the eldest of whom, Samuel, became a poet and scholar. Samuel was responsible for publishing the first collection of Pierre Fermat's works, which was released in 1679. None of Fermat's works were published during his lifetime. However, he gave a complete form to several treatises, and they became known in manuscript form to most of his contemporary scientists.

Contributions to Mathematics

Fermat's major contribution to science is usually seen in his introduction of infinitesimals into analytic geometry, similar to what Kepler did with the geometry of the ancients. He made this important step in his works on greatest and least quantities dating back to 1629. These works opened up a series of investigations by Fermat that became one of the most significant links in the history of the development of not only higher analysis in general but also calculus of infinitesimals in particular.

Fermat was one of the first to tackle the problem of rectifying curves, that is, calculating the length of their arcs. He managed to reduce this problem to the calculation of certain areas. The further success of the methods for determining "areas," on the one hand, and "methods of tangents and extrema," on the other hand, consisted in establishing the mutual connection between these methods.

Fermat's Last Theorem

On October 18, 1640, Fermat made the following statement: if the number a is not divisible by the prime number p, then there exists an exponent k such that a-1 is divisible by p, and k is a divisor of p-1. This statement became known as Fermat's little theorem and is fundamental in elementary number theory.

In the problem of the second book of his "Arithmetica," Diophantus posed the problem of representing a given square as the sum of two rational squares. In the margins against this problem, Fermat wrote: "On the contrary, it is impossible to decompose either a cube into two cubes, or a biquadrate into two biquadrates, or in general any power greater than a square into two powers with the same exponent. I have discovered a truly marvelous proof of this, but these margins are too narrow to contain it." This is the famous Fermat's Last Theorem.

Fermat's Last Theorem holds the record for the number of incorrect proofs given for it. Fermat himself left the proof of the theorem for fourth powers.

In the last century, while working on Fermat's Last Theorem, Kummer developed arithmetic for certain types of algebraic integers. This allowed him to prove the theorem for a certain class of prime exponents n. Currently, the truth of Fermat's Last Theorem has been verified for all exponents n less than 5500.

Other Contributions

Fermat was the first to come up with the idea of coordinates and created analytic geometry. He also worked on problems in probability theory. Fermat is credited with discovering the law of light propagation in media. Using his method of maxima and minima, he found the path of light and established, among other things, the law of refraction.

Pierre de Fermat passed away on January 12, 1665, during one of his business trips.