The Work of Fermat Through Law into Mathematics

According to MacTutor's page on Pierre de Fermat¹, following earning his law degree, In Toulouse he bought the offices of Councillor at the parliament and in this town became both a lawyer and government official. From tjis point on Fermat continued to live and work in Toulouse but also found work in both the towns of Beaumont-de-Lomagne and Castres. As of May 14, 1631 Fermat worked within the lower chamber of the parliament until he was promoted to a higher chamber on January 16,1638. He remained at this level until 1652 when he was given the highest rank possible at the criminal court. A plague began to go through the area in the 1650's, sicking Fermat in 1653. Fermat was reported dead but this was later found to be a mistake. After this period of time, Fermat's work in mathematics began to grow.

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1 This source is the only one to tell that his name is actually "Pierre Fermat". He was entitled to "Pierre de Fermat" when he began work as a government official.^↩

Library and Published Works of Pierre de Fermat

While going through the library and looking through some online resources, it became clear that there are no officially published works by Fermat. The only things about Fermat that appear in the library are encyclopedias and other references containing brief articles about his life. Additionally there are a few works written about him by other authors discussing the theorems and principles he came up with. The About Mathematics page tells that he did not publish anything, except for one thing which he did so anonymously. Pierre de Fermat was known for sending his mathematical papers to other mathematicians. He also became well known for sending theorems without proofs, which led to the most famous "Fermat's last theorem" problem which puzzled mathematicians for over 300 years.

Death Of Pierre de Fermat

While trying to find anymore additional information about Pierre de Fermat's death, NNDB verified what other sources have mentioned about his death. Pierre de Fermat died on January 12, 1665, in Castres, France. The cause of death is not directly specified however there are some sources that say the cause of death was the plague that was traveling in the area at this time. Additionally, this source mentions that he left behind a son, Samuel de Fermat, who worked on translating Greek works, wrote books on law, and edited the works of his father.

Fermat "In Mathematical Circles"

While glancing over a book called "In Mathematical Circles" by Howard Eves one can find many interesting discoveries by mathematicians. Oddly enough when examining the book there is no reference of Pierre de Fermat in any section containing Pascal as opposed to most other sources always mentioning them together. Instead, Eves devotes an entire section titled "René Descartes and Pierre de Fermat" to their foundations of analytic geometry, life, and independent mathematical achievements. Fermat is given a section in this portion of the book dedicated to his early life. Pierre de Fermat is stated to be born near Toulouse in 1601 and the son of  leather merchant. Fermat is said to of received his early education at home. The book then jumps to his age of 30 then he obtained the position of Councillor for the parliament at Toulouse. After his retirement he worked in mathematics until he died in Castres in 1665. Due to his contributions in many fields of mathematics he is considered to be the greatest French mathematician of the seventeenth century, and even more so universally considered one of the greatest number theorists to ever live. After discussing some of Decartes work and death, Eves begins to discuss "The Fermat Numbers". In this section Eves states that Fermat believed he had found a formula for finding primes. However this was shown to be false by a counter example created by Leonhard Euler. The formula has been modified to believe to be true for composite numbers. These numbers by this formula are considered to be Fermat Numbers. Other connections have been made with Fermat Numbers.

Fermat also created a method known as "Fermat's method of infinite descent" This is sometimes viewed as a proof method that is the reverse of mathematical induction.

Finally the book concludes with a section of Fermat's last theorem. While this section contains most of the information as seen in the other sources examined, what is interesting about this source is at the time written it had not been solved with. Hence this source talks about math mathematicians sending in proofs for specific values of n, and how many integers n the theorem has been verified for by use of super computers. The book also lists some rewards that were being placed at the time for proofs of the theorem or for just finding if it was true for large values of .

Eves, Howard Whitley. In mathematical circles; a selection of mathematical stories and anecdotes. Boston: Prindle, Weber & Schmidt, 1969. Print.

Pierre de Fermat in the encyclopedia

Looking in the Encyclopedia Americana, Pierre de Fermat is regarded solely as a French Mathematician. On August  20, 1601 he was born in Beaumont-de-Lomangne, France. He studied at the University of Toulouse, followed by the University of Orleans where he received a law degree. While looking at a professional career as a lawyer and legislator, he had activities that also appealed to him. Some of these include mathematics, holding a reputation as a classicist, and also a poet. The encyclopedia entry contains two sections about his mathematical career, one for Algebraic Analysis and the other for Number Theory. 
His work in Algebraic Analysis, inspired by François Viète, was made possible by the recent view of symbolic algebra which allowed arithmetic and geometry to be treated in a similar manner. He had a strong focus on treating problems with respect to the algebraic theory of equations, and combined this with work in Geometry to create analytic geometry at the same time as Descartes. Fermat managed to algebraically with use of geometric information find tangents to curves. Fermat's other discoveries relating to curves and the information that could be found by revolving a solid around a coordinate axis paved the way to what is a big part of Calculus, both differential and integral. However he is discredited of inventing Calculus due to his failure to recognize the relationship between finding the inverse and the area under are inversely related to one another. 
Many of Fermat's most famous contributions stem from his work in Number theory. Two of his proofs mentioned are "Fermat's theorem" and "Fermat's last theorem". While some of these contributions were not made use of during his life, Euler, Legendre, and Gauss and other mathematicians made extensive contributions with them and caused them to be more well known. Fermat also helped found probability theory and although did not focus on many physical applications, used his method to find maxima and minima to develop Fermat's principle.

Mahoney, Michael. "Fermat, Pierre de." Encyclopedia Americana. International ed. ed. 2006. Print.

What does the Dictionary of Scientific Biography have to say?

Upon looking for a very credible bibliographical source, I came across the Hutchinson Dictionary of Scientific Biographies. The biography gives a fairly brief overview of the entire life of Pierre de Fermat. It begins giving a brief overview by skipping most of his early life, only really acknowledging that he was a French lawyer and magistrate who treated mathematics as a hobby, but contributed greatly to a variety of mathematical fields. Pierre de Fermat was born on August 20, 1601 in Beaumont de Lomagne. This biography does not try to exactly pinpoint where he received his early education from. It simply says he received a "classical education locally". After receiving his early education, believed to be between the ages of 20 and 30 he relocated to Bordeaux where he may have studied at the University of Toulouse. While here, Fermat was introduced to mathematics discovered by François Viète. Fermat became especially interested in the field of Number Theory, which is where many of his well known contributions came from. However, his studies at school were not devoted to the field of mathematics. Instead he studied law, and at the age of 30 received a bachelor's degree in civil law from the University of Orleans. After maintaining a legal practice in Toulouse, he was moved higher over time by parliament and finally ended as the king's counselor until 1665.

Fermat's accomplishments in mathematics may have came from an attack of the plague because after he suffered through the illness, much of his time was dedicated tot his study. Through his own works and working to redo some early Greek work. While he did not publish his works, he did create and publish problems for other mathematicians to solve. In fact, Fermat is most likely known for "Fermat's last theorem" which was the final one to be proved and was done so in 1993 by Andrew Wiles. The theorem states:

Fermat's techniques led rise to his interest in Geometry, from which he provided much insight into Analytic Geometry which was discovered at the same time by René Descartes. From Analytic Geometry Fermat proceeded to move towards curves and found a method of finding the tangent line to equations. The results he achieved were verified due to the same result being obtained from what is modern day Calculus. Fermat also worked with Blaise Pascal to develop the foundation of probability theory, mainly the probability of two independent events occurring. Fermat also provided some insight in Optics despite conclusions disagreed with by Descartes, Fermat produced "Fermat's principle".
Fermat died on January 12, 1675 in Castres.

"Fermat, Pierre De (1601-1675)." The Hutchinson Dictionary of Scientific Biography. Abington: Helicon, 2013. Credo Reference. Web. 26 April 2014.

Mathematics of the Time

During the time period that Pierre de Fermat lived there were many developments occurring in mathematics. Fermat lived during the period of 1601-1665. Using a device designed after a toy, which became known as the telescope, Galileo developed the telescope. Since then, this device has become modified to see the universe in ways people of the time never thought possible. Using the telescope he was capable of observing orbits, specifically the moons of Jupiter as they traveled around the planet. However, the use of mathematics for astronomical reasons did not stop there. Tycho Brahe began gathering mathematical data regarding how the planets moved throughout the sky. Brahe during his calculations had an assistant named Johannes Kepler. Kepler began combining the mathematics behind logarithms with planetary motion to create mathematical laws regarding orbits. While these laws were being laid out through calculations, earlier mathematicians created a way of graphing the movement. René Descartes and his development of analytic geometry led to the plotting of orbits using Cartesian coordinates. Simon Stevin developed the foundation for our current decimal system so that all numbers in nature were "treated equally". This allowed all rational and irrational numbers to be described in a similar manner.

Other mathematicians were working on branches of math that would tie together many mathematical applications. Issac Newton began founding the laws of modern day physics which aided in the explanation of the mathematics that Johannes Kepler was working on. At this point, Issac Newton also began putting together many pieces of what became modern day Calculus. Applied mathematics became worked on more heavily along with the foundation of Probability Theory by Pierre de Fermat and Blaise Pascal. Science and mathematics became a phenomenon all over the world and started exponential progress began occurring in the field.

Fermat's Education

Fermat's early education appears to be a bit of a mystery. The University of St. Andrews gives a rather vague response to his school. From this source, it is labeled that his school education was  a the local Franciscan monastery. Cross referencing sources, two of which are Famous Mathematicians and Totally History, many sources get more specific as to say he attended College de Navarre in Montauban. From this point his education become more agreed upon. Fermat attended the University of Toulouse, followed by the University of Orleans where he received his Bachelor of Civil Laws in 1626. Leen Veirman, Ine Weyn, and Sophie Verhaert offer additional information by stating that Fermat's mother was a member of a famous family which praticed law. This conclusion is not strongly backed up, especially since his mother is not definitely known. However, this is a possible reason to Fermat's decision to take up the study of law. They also dispute the fact that he received his Bachelor degree in 1626 by arguing he earned it in 1631. 

Who is Pierre de Fermat?

From Wolfram Research we manage to get a beginning overview on Fermat's life. Pierre de Fermat [pyer duh fer-mah]is best known as a French mathematician, however what may be less known is that he was only an amateur mathematician¹.Fermat was primarily a lawyer who did work in mathematics on the side.  A nice beginning piece of early life history for Fermat comes from the credible University of St. Andrews. Fermat was born on August 17, 1601 in the French city Beaumont-de-Lomagne.  His father, Dominique Fermat, was a merchant selling cattle and wheat and made a very good living while his was not definitely known. Along with Pierre de Fermat, Dominique also had a brother and two sisters.

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1 Fermat's work specifically in number theory is what earned him most of his recognition. ^↩