Pierre de Fermat facts for kids
Quick facts for kids
Pierre de Fermat
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| Born | Between 31 October and 6 December 1607 Beaumont-de-Lomagne, France
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| Died | 12 January 1665 (aged 57) |
| Education | University of Orléans (LL.B., 1626) |
| Known for | Contributions to number theory, analytic geometry, probability theory Folium of Descartes Fermat's principle Fermat's little theorem Fermat's Last Theorem Adequality Fermat's "difference quotient" method (See full list) |
| Scientific career | |
| Fields | Mathematics and law |
| Influences | François Viète, Gerolamo Cardano, Diophantus |
Pierre de Fermat (born between October 31 and December 6, 1607 – died January 12, 1665) was a brilliant French mathematician. He helped create early ideas that led to calculus, a big part of modern math. He found a special way to figure out the highest and lowest points on curved lines. This was similar to differential calculus, which wasn't known yet.
Fermat also did important work in number theory, which is the study of numbers and their properties. He made big contributions to analytic geometry, probability, and optics (the study of light). He is most famous for his Fermat's principle about how light travels. He is also known for his Fermat's Last Theorem in number theory. He wrote this famous idea in the margin of a book by Diophantus called Arithmetica. Besides being a mathematician, Fermat was also a lawyer in Toulouse, France.
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Fermat's Early Life and Education
Pierre de Fermat was born in 1607 in Beaumont-de-Lomagne, France. His family home, a mansion from the late 1400s, is now a museum. His father, Dominique Fermat, was a rich leather merchant. He served as a leader in Beaumont-de-Lomagne for three years. Pierre's mother was Claire de Long. He grew up in his hometown with one brother and two sisters.
Fermat went to the University of Orléans starting in 1623. He earned a degree in civil law in 1626. After that, he moved to Bordeaux. In Bordeaux, he began his first serious math studies. In 1629, he shared his work on Apollonius's De Locis Planis with other mathematicians. He worked on finding maximums and minimums of curves. This work was given to Étienne d'Espagnet, who shared Fermat's interest in math. Fermat was greatly influenced by the work of François Viète during this time.
Fermat's Career and Family
In 1630, Fermat bought a job as a councilor at the Parlement de Toulouse. This was one of France's highest courts. He started this job in May 1631 and kept it for the rest of his life. Because of this job, he was allowed to change his name from Pierre Fermat to Pierre de Fermat. On June 1, 1631, Fermat married Louise de Long. She was a distant cousin of his mother. Pierre and Louise had eight children, and five of them lived to be adults. Their names were Clément-Samuel, Jean, Claire, Catherine, and Louise.
Fermat was very good with languages. He spoke French, Latin, Occitan, classical Greek, Italian, and Spanish. People admired his poems written in different languages. They also asked for his advice on improving Greek texts. He usually shared his math discoveries in letters to friends. Often, he didn't include proofs for his theorems. In some letters, he explored ideas of calculus before Newton or Leibniz did. Fermat was a lawyer by profession, so math was more of a hobby for him. Even so, he made huge contributions to analytic geometry, probability, number theory, and calculus.
At that time, mathematicians often kept their discoveries secret. This led to arguments with other smart people like René Descartes and John Wallis about who discovered what first. According to Anders Hald, Fermat's math was based on old Greek writings. He also used Vieta's new algebra methods.
Fermat's Mathematical Discoveries
Fermat's important work in analytic geometry was shared in handwritten copies in 1636. This was even before Descartes published his famous book La géométrie in 1637. Fermat's work was published after he died in 1679.
In his writings, Fermat developed a method called adequality. This method helped him find maximums, minimums, and tangents (lines that touch a curve at only one point) for different curves. This method was similar to differential calculus. He also used these ideas to find the centers of gravity for shapes. This led to more work on finding the area under curves.
Fermat was the first person known to calculate the integral of general power functions. He used his method to simplify this calculation to adding up geometric series. This formula was very helpful to Newton and Leibniz. They later used it when they developed the fundamental theorem of calculus.
Number Theory Contributions
In number theory, Fermat studied many interesting topics. These included Pell's equation, perfect numbers, and amicable numbers. He also studied what are now called Fermat numbers. While looking into perfect numbers, he discovered Fermat's little theorem. He also invented a way to factor numbers, called Fermat's factorization method. He made the proof method called infinite descent popular. He used it to prove Fermat's right triangle theorem. This theorem includes a special case of Fermat's Last Theorem for n = 4.
Fermat also developed the two-square theorem. This theorem says that some numbers can be written as the sum of two perfect squares. He also created the polygonal number theorem. This theorem states that any number can be written as a sum of three triangular numbers, or four square numbers, or five pentagonal numbers, and so on.
Fermat said he had proofs for all his number theory ideas. However, very few of his proofs have survived. Many mathematicians, like Gauss, doubted some of his claims. This was because the problems were very hard, and Fermat had limited math tools available. His most famous idea, Fermat's Last Theorem, was found by his son in the margin of his father's copy of a book by Diophantus. Fermat wrote that the margin was too small to write the proof. This theorem was finally proven in 1994 by Sir Andrew Wiles. Wiles used advanced math techniques that Fermat didn't have.
Probability and Optics
In 1654, Fermat and Blaise Pascal wrote letters to each other. Their discussions helped create the foundation for probability theory. They are now seen as the co-founders of this field. Fermat is known for doing the first careful probability calculation. A professional gambler asked him a question. The gambler won if he bet on rolling at least one six in four throws of a die. But he lost if he bet on rolling at least one double-six in 24 throws of two dice. Fermat used math to show why this happened.
The first idea about how light behaves in physics came from Euclid. He said that when light reflects off a mirror, the angle of incidence (the angle at which light hits the mirror) equals the angle of reflection (the angle at which it bounces off). Later, Hero of Alexandria showed that this path was the shortest and took the least time. Fermat made this idea better and more general. He said that "light travels between two points along the path of shortest time." This is now known as the principle of least time. Because of this, Fermat is a key figure in the history of the important principle of least action in physics. Fermat's principle and Fermat functional are named after him.
Fermat's Death and Legacy
Pierre de Fermat died on January 12, 1665, in Castres, France. The oldest and most respected high school in Toulouse is named after him: the Lycée Pierre-de-Fermat. A French sculptor named Théophile Barrau made a marble statue called Hommage à Pierre Fermat. This statue honors Fermat and is now in the Capitole de Toulouse.
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Place of burial of Pierre de Fermat in Place Jean Jaurés, Castres. Translation of the plaque: in this place was buried on January 13, 1665, Pierre de Fermat, councillor at the Chambre de l'Édit (a court established by the Edict of Nantes) and mathematician of great renown, celebrated for his theorem,
an + bn ≠ cn for n>2 -
Monument to Fermat in Beaumont-de-Lomagne in Tarn-et-Garonne, southern France
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Bust in the Salle Henri-Martin in the Capitole de Toulouse
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Holographic will handwritten by Fermat on 4 March 1660, now kept at the Departmental Archives of Haute-Garonne, in Toulouse
How Fermat's Work Changed Math
Pierre de Fermat was one of the two most important mathematicians of the early 1600s, along with René Descartes. According to Peter L. Bernstein, Fermat was a "mathematician of rare power." He independently invented analytic geometry. He also helped develop early calculus. He researched the weight of the earth and worked on how light bends and optics. His letters with Blaise Pascal were a big step in the theory of probability. But Fermat's greatest achievement was in number theory.
Isaac Newton said that his own early ideas about calculus came directly from "Fermat's way of drawing tangents." This shows how important Fermat's work was.
The 20th-century mathematician André Weil wrote about Fermat's number theory work. He said that Fermat's methods for dealing with certain curves are still the basis for modern theory. Fermat's special method, called "descent," was very new and important. With his talent for understanding number relationships and proving his ideas, Fermat basically created the modern theory of numbers.
See also
In Spanish: Pierre de Fermat para niños
- Diagonal form
- Euler's theorem
- List of things named after Pierre de Fermat
