# Pierre de Fermat

> French mathematician and lawyer

**Wikidata**: [Q75655](https://www.wikidata.org/wiki/Q75655)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Pierre_de_Fermat)  
**Source**: https://4ort.xyz/entity/pierre-de-fermat

## Summary
Pierre de Fermat was a French mathematician and lawyer known for foundational contributions to number theory and for formulating several results and principles that bear his name, including Fermat's Last Theorem and Fermat's little theorem. He combined a legal career (affiliated with the Parliament of Toulouse) with major mathematical work spanning number theory, probability, analysis, analytic geometry, and optics.

## Biography
- Nationality: France
- Known for: Formulating Fermat's Last Theorem (inception 1637), Fermat's little theorem (inception 1640-10-18), Fermat's principle (inception 1662), and numerous concepts in number theory and mathematics that bear his name
- Employer(s): Parliament of Toulouse
- Field(s): Mathematics (number theory, probability theory, mathematical analysis, analytic geometry, optics), Law (lawyer, jurist, judge)
- Aliases: Fermat; Pierre Fermat
- Wikipedia title: Pierre de Fermat
- Wikidata description: French mathematician and lawyer
- Sitelink count: 114

## Contributions
- Fermat's Last Theorem (inception: 1637): Formulated the theorem in number theory stating there are no nontrivial integer solutions of x^n + y^n = z^n for integer n > 2. The formulation is attributed to him in the provided material.
- Fermat's little theorem (inception: 1640-10-18): Stated the congruence property for primes that later played a foundational role in number theory and modular arithmetic.
- Fermat's principle (inception: 1662): Formulated the principle of least time in optics, a foundational idea in the study of light propagation.
- Fermat's theorem (calculus): Introduced a method to find local maxima and minima of differentiable functions on open sets.
- Fermat's theorem on sums of two squares: Stated the characterization for when an odd prime is expressible as a sum of two squares.
- Fermat's factorization method: Described an algorithmic approach for integer factorization.
- Fermat point: Identified the point in a triangle that minimizes the sum of distances to the three vertices.
- Fermat numbers and Fermat primes: Defined the family of integers of the form 2^(2^n) + 1 and the related concept of Fermat primes.
- Fermat's spiral and Fermat cubic: Studied and/or lent his name to plane curves and cubic surfaces (Fermat spiral; Fermat cubic: x^3 + y^3 + z^3 = 1).
- Fermat–Catalan conjecture: Associated name in a conjecture in number theory.
- Fermat's right triangle theorem: Left the only complete proof he provided for a non-existence result in number theory (the right triangle theorem).
- Legacy namesakes and honors: A lunar crater (Fermat), the Fermat Prize (inception: 1989; country: France), and the lycée Pierre-de-Fermat (inception: 1806; Toulouse, France) are all named after him.
- Connections to later results: Euler's theorem is identified as a generalization of Fermat's little theorem.

## FAQs
Q: What were Pierre de Fermat's main occupations?
A: He was a mathematician and a lawyer; the available material also associates him with roles and categories such as jurist and judge and notes his affiliation with the Parliament of Toulouse.

Q: Which mathematical areas did Fermat work in?
A: He worked in number theory, probability theory, mathematical analysis, analytic geometry, and optics, and he formulated results that influenced these areas.

Q: What are the best-known theorems or principles attributed to Fermat?
A: The most prominent are Fermat's Last Theorem (formulated 1637), Fermat's little theorem (1640-10-18), and Fermat's principle (1662). Other named results include Fermat's theorem on maxima/minima, Fermat's theorem on sums of two squares, and Fermat's factorization method.

Q: Where did Fermat work as a legal professional?
A: He was affiliated with the Parliament of Toulouse, a regional appellate court in the Kingdom of France.

Q: Are there awards, institutions, or objects named after Fermat?
A: Yes. The Fermat Prize (established 1989 in France), lycée Pierre-de-Fermat (inception 1806 in Toulouse), and a lunar crater named Fermat are all named in his honor.

Q: Who are some mathematicians or figures associated with Fermat in the records?
A: The provided material lists Diophantus of Alexandria, Gerolamo Cardano, François Viète, Leonhard Euler, and Gilles de Roberval as key people related to him.

## Why They Matter
Pierre de Fermat's formulations and discoveries established core problems, methods, and principles that reshaped several branches of mathematics. His work in number theory produced named objects and conjectures (Fermat numbers, Fermat primes, Fermat's Last Theorem, Fermat's theorem on sums of two squares) that became central threads in the development of modern arithmetic and algebra. Fermat's little theorem provided an elementary congruence that led directly to later generalizations, including Euler's theorem, thereby creating a foundation for modular arithmetic and later applications in number theory and cryptography. In analysis and geometry, his theorem for maxima and minima presaged methods of calculus; in optics, Fermat's principle expressed a variational formulation (principle of least time) that became a fundamental concept. The multiplicity of mathematical objects and results that carry his name — points, curves, factorization methods, and conjectures — indicates a broad and durable influence across disciplines. Institutions and awards named after him (a lycée, a prize, and lunar nomenclature) reflect a lasting recognition of his impact; without his formulations many subsequent generalizations and named results (for example Euler's generalization) would not have developed along the same historical lines.

## Notable For
- Being identified in Wikidata and reference material as a French mathematician and lawyer.
- Formulating Fermat's Last Theorem (inception: 1637).
- Stating Fermat's little theorem (inception: 1640-10-18), later generalized by Euler.
- Formulating Fermat's principle in optics (inception: 1662).
- Establishing Fermat's theorem on maxima and minima in analysis.
- Defining Fermat numbers and the concept of Fermat primes.
- Developing Fermat's factorization method for integers.
- Naming the Fermat point in triangle geometry and Fermat's theorem on sums of two squares.
- Having the Fermat Prize (est. 1989, France), lycée Pierre-de-Fermat (est. 1806, Toulouse), and a lunar crater named after him.
- Being affiliated with the Parliament of Toulouse.
- Appearing under aliases “Fermat” and “Pierre Fermat”; recorded Wikipedia title: Pierre de Fermat; sitelink_count: 114.

## Body

### Identity and official records
- Name and aliases: The subject is recorded under the primary name Pierre de Fermat and is also known as Fermat and Pierre Fermat.
- Metadata: The Wikipedia title for this subject is "Pierre de Fermat." Wikidata describes him succinctly as a "French mathematician and lawyer." The sitelink_count in the provided material is 114.

### Occupations and affiliations
- Mathematics: Classified as a mathematician; associated mathematical domains in the source include number theory, probability theory, mathematical analysis, analytic geometry, and optics.
- Law: Classified as a lawyer and jurist; the source also lists judge as a related category.
- Employer / affiliation: Affiliated with the Parliament of Toulouse, identified as a regional appellate court in the Kingdom of France.

### Major named results and objects
- Fermat's Last Theorem (inception 1637): Attributed formulation in the source as a central number-theoretic statement concerning the nonexistence of nontrivial integer solutions to x^n + y^n = z^n for n > 2.
- Fermat's little theorem (inception 1640-10-18): Recorded as a key theorem asserting a congruence property for primes; later generalized by Euler (Euler's theorem is cited as a generalization).
- Fermat's principle (inception 1662): Noted as the principle of least time in optics.
- Fermat's theorem (calculus): Identified as a method to find local maxima and minima of differentiable functions on open sets.
- Fermat's theorem on sums of two squares: Listed as a theorem characterizing odd primes expressible as sums of two squares (primes of form 4n + 1).
- Fermat's factorization method: Documented as an integer factorization algorithm bearing his name.
- Fermat point: Recognized as the point in a triangle minimizing the sum of distances to its vertices.
- Fermat numbers and Fermat primes: The family of integers 2^(2^n) + 1 and the subset that are prime are both identified in the material.
- Fermat spiral and Fermat cubic: Both appear among mathematical objects named after him (the Fermat cubic given by x^3 + y^3 + z^3 = 1).
- Fermat–Catalan conjecture: Included in the list of conjectures associated by name.
- Fermat's right triangle theorem: Cited as "the only complete proof left by Pierre de Fermat" in the source material. The result concerns non-existence in number theory.

### Namesakes and honors
- Fermat Prize: A prize named after him, with inception year 1989 and country France specified in the source data.
- lycée Pierre-de-Fermat: A French high school in Toulouse bearing his name; inception given as 1806.
- Lunar crater: A crater on the Moon named Fermat is listed among eponyms.

### Connections to other mathematicians and developments
- Diophantus of Alexandria: Listed among key people connected in the source; historically associated with problems in arithmetic that informed later number-theoretic work.
- Gerolamo Cardano, François Viète, Gilles de Roberval: Included as significant mathematical figures related in the provided material.
- Leonhard Euler: Explicitly connected through the statement that Euler's theorem generalizes Fermat's little theorem; Euler is listed among key people.
- Influence chains recorded: The provided material documents a chain where Fermat's little theorem led to Euler's generalization (Euler's theorem).

### Miscellaneous factual entries
- Categories and related concepts recorded include mathematician, lawyer, judge, polyglot, jurist, and human.
- Geographic and political context: Nationality is France; the Parliament of Toulouse is noted as a regional appellate court in the Kingdom of France (headquarters and country metadata appear in the affiliation entry).
- Items bearing the Fermat name span pure mathematics (theorems, conjectures, numbers, curves, points), physical optics (Fermat's principle), educational institutions (lycée), awards (Fermat Prize), and astronomical nomenclature (lunar crater).

### Summary of scope
- The provided material ties Pierre de Fermat to foundational mathematical results across number theory, analysis, geometry, and optics. 
- His legal career is recorded through affiliation with the Parliament of Toulouse and descriptors such as lawyer, jurist, and judge. 
- Multiple theorems, methods, and mathematical objects carry his name; later mathematicians (explicitly Euler) extended or generalized some of his statements. 
- Commemorations (prize, lycée, crater) demonstrate a recognized legacy reflected in institutional and eponymous honors.

## References

1. EB-11 / Fermat, Pierre de
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