# Mathematician:Pierre de Fermat

## Mathematician

French lawyer, also an amateur mathematician famous for lots of things. Especially:

- Fermat's Little Theorem
- Claimed to have found a proof for what became known as Fermat's Last Theorem, but it has since been doubted that this is in fact the case (he may have been mistaken).

Although he claimed to have found proofs of many theorems, few of these have survived.

It has been suggested, with some justification, that it was Fermat, not Descartes, who was the true inventor of analytic geometry.

It has also been suggested that he shared the creation of the discipline of probability theory with Blaise Pascal.

He rarely published, and most of his output was in the form of letters, mainly through the correspondence he started with Marin Mersenne in $1636$.

Father of Clément-Samuel Fermat, who became his scientific executor.

A member of the informal Académie Parisienne.

## Nationality

French

## History

- Born: 17 August 1601 or 1607/8 (exact date unknown), Beaumont-de-Lomagne, France
- Died: 12 January 1665, Castres, France

## Theorems and Definitions

### Definitions

- Fermat Pseudoprime
- Fermat Number
- Fermat's Equation
- Fermat Prime
- Fermat Quotient
- Fermat Set
- Fermat's Spiral
- Fermat-Torricelli Point (with Evangelista Torricelli), also known as either a Fermat Point or a Torricelli Point

Definitions of concepts named for **Pierre de Fermat** can be found here.

### Theorems and Conjectures

- Fermat's Little Theorem (otherwise known as Fermat's Theorem)
- Fermat's Right Triangle Theorem
- Fermat's Two Squares Theorem (also known as Fermat's Christmas Theorem)
- Fermat's Principle of Least Time
- Fermat Prime Conjecture (false): that all integers of the form $2^{\paren {2^n} } + 1$ are prime
- Fermat Problem (also known as Steiner's Problem for Jakob Steiner)

- Claimed to have found a proof for what became known as Fermat's Last Theorem, but it has since been doubted that this is in fact the case (he may have been mistaken).

Results named for **Pierre de Fermat** can be found here.

## Publications

- c. 1629: Reconstructed what he could of
*On Plane Loci*by Apollonius of Perga

- 1636:
*Methodus ad Disquirendam Maximam et Minimam et de Tangentibus Linearum Curvarum*("Method for determining Maxima and Minima and Tangents to Curved Lines") (circulated in manuscript form)

- 1637:
*Introduction to Plane and Solid Loci*- 1679:
*Ad Locos Planos et Solidos Isagoge*("Introduction to Plane and Solid Loci") (posthumous)

- 1679:

- 1659:
*New Account of Discoveries in the Science of Numbers* - 1670:
*Arithmetica*(posthumous)

## Notable Quotes

*The equation $x^n + y^n = z^n$ has no integral solutions when $n > 2$. I have discovered a perfectly marvellous proof, but this margin is not big enough to hold it.*

## Critical View

*A master of masters.*

*le premier homme du monde*(the foremost man of the world)

*Look elsewhere for someone who can follow you in your researches about numbers. For my part, I confess that they are far beyond me, and I am competent only to admire them.*- -- Blaise Pascal, in a letter to Fermat

*[***Fermat**] invented analytic geometry in 1629 and described his ideas in a short work entitled*Introduction to Plane and Solid Loci*, which circulated in manuscript form from early 1637 on but was not published during his lifetime. ... nothing that we would recognize as analytic geometry can be found in Descartes' essay, except perhaps the idea of using algebra as a language for discussing geometric problems.**Fermat**had the same idea, but did something important with it: He introduced perpendicular axes and found the general equations of straight lines and circles and the simplest equations of parabolas, ellipses, and hyperbolas ... it may be surmised that much of what [ Descartes ] knew he learned from**Fermat**.- -- 1992: George F. Simmons:
*Calculus Gems*

- -- 1992: George F. Simmons:

## Sources

- John J. O'Connor and Edmund F. Robertson: "Pierre de Fermat": MacTutor History of Mathematics archive

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{IV}$: The Prince of Amateurs - 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $1$: The Nature of Differential Equations: $\S 6$: The Brachistochrone. Fermat and the Bernoullis - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**Fermat, Pierre de**(1601-65) - 1991: David Wells:
*Curious and Interesting Geometry*... (previous) ... (next): A Chronological List Of Mathematicians - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.13$: Fermat ($\text {1601}$ – $\text {1665}$) - 1992: David Wells:
*Curious and Interesting Puzzles*... (previous) ... (next): Henry van Etten - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Fermat, Pierre de**(1601-65) - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Fermat, Pierre de**(1601-65) - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $6$: Curves and Coordinates: Fermat - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $7$: Patterns in Numbers: Fermat - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**Fermat, Pierre de**(1601-65)