Over a 300-year period, unsuccessful attempts to prove Fermat's Last Theorem led to the discovery of commutative ring theory and other mathematical discoveries.

Pierre de Fermat, a prominent mathematician in the 17th century, made significant contributions to various fields including differential and integral calculus, number theory, optics, and analytic geometry. He also played a key role in the development of probability theory in collaboration with Pascal.

Pierre de Fermat, a French mathematician considered the founder of modern number theory, was born in Beaumont-de-Lomagne, France.

Pierre de Fermat, a lawyer by profession, was baptized on August 20, 1601 in Beaumont-de-Lomagne, France. He later became one of the most influential mathematicians of the seventeenth century, making significant contributions to various fields of mathematics.

Pierre de Fermat, a French mathematician, was born in Beaumont-de-Lomagne, France. He is credited for early developments in infinitesimal calculus and made notable contributions to analytic geometry, probability, and optics.

Pierre de Fermat attended the University of Toulouse for his advanced studies after completing his primary and secondary education at the monastery of Grandsl ve.

In 1623, Pierre de Fermat started studying at the University of Orleans. He later earned a bachelor's degree in civil law in 1626.

In 1626, Pierre de Fermat received a bachelor's degree in civil law from the University of Orléans. This marked an important academic achievement in his early life.

In 1627, at the age of 19, while beginning his legal career in Bordeaux, Pierre de Fermat's interest in high-level mathematics emerged. He became friends with Etienne d'Espagnet, studied works by Franciscus Vieta, and made his first important contributions to mathematics in 1629.

At the age of 20 in 1628, Pierre de Fermat inherited a significant fortune from his father's passing. Instead of abandoning his legal career, Fermat continued working as an attorney while pursuing his passion for mathematics.

In the second half of the 1620s, Pierre de Fermat began his first serious mathematical researches in Bordeaux. He shared his restoration of Appollonius's Plane Loci with mathematicians in Bordeaux and worked on maxima and minima during this time.

Fermat posed the problem that the sum of two cubes cannot be a cube, which is a special case of Fermat's Last Theorem. This may indicate that Fermat realized his proof of the general result was incorrect.

On May 1, 1631, Pierre de Fermat received the degree of Bachelor of Civil Laws from the University of Law at Orléans. This marked a significant milestone in his academic journey.

In 1631, Pierre de Fermat was appointed to the lower chamber of the parliament in Toulouse, where he began his career as a government official and lawyer.

On 1 June 1631, Pierre de Fermat married Louise de Long, a fourth cousin of his mother. The couple went on to have eight children, with five surviving to adulthood.

Wilhelm Boelmans S J presented his theses in 1634, which discussed the sine law of refraction derived from the principle of Fermat.

In 1636, Pierre de Fermat replied to Marin Mersenne's letter, discussing errors in Galileo's description of free fall, his work on spirals, and restoration of Apollonius's Plane loci. Fermat also mentioned his analyses for various numerical and geometrical problems, offering to share his findings with Mersenne.

Fermat's Last Theorem states that for any whole number n greater than 2, the equation x^n + y^n = z^n has no solution with x, y, and z also being whole numbers. Fermat claimed to have proven it for n=4, leaving only odd values of n to be proven. He famously mentioned his proof in the margin of a book, but it was never found.

On 16 January 1638, Pierre de Fermat was promoted to a higher chamber within the parliament in Toulouse, marking a significant advancement in his legal career.

Fermat claimed that all numbers of the sequence 2^(2^n)+1 are prime, but he did not provide a proof for his idea. Euler later disproved Fermat's claim by showing that 2^32 +1 has 641 as a factor.

Fermat's method for determining maxima and minima as well as tangents for curved lines was included in Pierre Hérigone's 1642 work 'Courses in Mathematics'. This work influenced later developments in calculus by mathematicians like Isaac Newton.

In 1648, Pierre de Fermat was promoted to a king's councillorship in the parliament of Toulouse. This was a significant achievement in his career.

In 1651, Pierre de Fermat suffered greatly due to a bout with the plague, affecting his health in his later years.

In 1652, Pierre Fermat reached the highest post at the criminal court after rising through the ranks. He was known for his fluency in multiple languages and his work shared through letters with friends and fellow mathematicians.

In 1653, Pierre Fermat was wrongly reported as dead during a plague outbreak in Beaumont-de-Lomagne, but he managed to survive and continue his duties at the court.

In 1654, Fermat's correspondence with Blaise Pascal on probability led to the establishment of the theory of probability. Pascal and Fermat are now regarded as joint founders of the subject.

In 1656, Pierre de Fermat initiated a correspondence with Christiaan Huygens, which initially focused on Huygens' interest in probability but later shifted to topics of number theory. Fermat shared more of his mathematical methods with Huygens in a letter sent in 1659, including his method of infinite descent and an example of proving primes of a specific form could be written as the sum of two squares.

In 1657, Fermat posed two mathematical problems that were considered unsolvable by many mathematicians of Europe. The second problem involved finding all solutions of Nx^2 + 1 = y^2 for N not a square, which was later solved by Wallis and Brouncker.

In 1658, Pierre de Fermat established the principle of least time, which states that a beam of light traveling between two points will follow the path that takes the shortest amount of time to complete. This idea was developed through Fermat's method for determining minima and maxima.

In 1659, Pierre de Fermat sent a letter to Christiaan Huygens via Carcavi, detailing his method of infinite descent and providing an example of proving primes of a certain form could be expressed as the sum of two squares. Fermat's failure to fully explain the construction of smaller numbers from larger ones led to mathematicians losing interest until Euler later addressed these gaps.

In 1660, Fermat published a paper titled 'De Linearum Curvarum cum Lineis Rectis Comparatione' where he demonstrated that certain algebraic curves, including the semicubical parabola, were strictly rectifiable, disproving the widely held belief that the length of algebraic curves could not be precisely determined.

Fermat derived Snell’s Law of Refraction by assuming that light passes between two points in the least possible time, leading to the principle of least action in modern physics.

Pierre de Fermat, the renowned French mathematician known for his contributions to calculus, the law of refraction, and number theory, passed away on January 1, 1665 in Castres, France. Despite his reluctance to publish his work, Fermat is still remembered as a great mathematician.

Pierre de Fermat died on January 12, 1665 in Castres. He was a French mathematician known for his contributions to number theory.

Fermat's Last Theorem, proposed by Pierre de Fermat, states that the equation xn+yn=zn has no non-zero integer solutions for x, y, and z when n is greater than 2. Fermat famously claimed to have a proof for this theorem in the margin of Bachet's translation of Diophantus's Arithmetica, which was only revealed after his son Samuel published an edition of the translation in 1670.

Fermat's work on loci, which laid the foundation for Cartesian geometry along with Descartes, was published posthumously in 1679.

In 1849, A.-H.-L. Fizeau experimentally verified Fermat's principle of least time, which stated that the law of refraction (the sines of the angles of incidence and refraction of light passing through media of different densities are in a constant ratio) is in agreement with the assumption that light travels less rapidly in denser media.

J E Hofmann presents new insights into Fermat's number-theoretical challenges from 1657, including two previously unknown original pieces by Fermat, in Abh. Preuss. Akad. Wiss. Math.-Nat. Kl.

C B Boyer's work on Fermat's integration of Xˆ was published in the National Mathematics Magazine in 1945.

J Itard discussed the methods used by Fermat in number theory in his paper published in 1950 in the Revue d'Histoire des Sciences.

C B Boyer's article on Fermat and Descartes was published in Scripta Mathematica in 1952, discussing the mathematical contributions and interactions between these two prominent figures.

A note on Pierre de Fermat's methods of factorization in 1957.

J E Hofmann delves into the connections and significance of number-theoretical methods of Fermat and Euler in the publication Arch. Hist. Exact Sci.

J E Hofmann's book 'Geschichte der Mathematik' provides a historical account of the development of mathematics, including the period leading up to the emergence of mathematicians like Fermat and Descartes, offering insights into the evolution of mathematical thought.

J A Lohne discussed the influence of Fermat on Newton, Leibniz, and the anaklastische problem in 1966 in the Nordisk Matematisk Tidskrift.

P Chabbert's work on Fermat in Castres was published in the Review of History of Science and its Applications in 1967.

L S Freiman's work on Fermat, Torricelli, and Roberval was published in a collection of articles on classical science by 'Nauka' Moscow in 1968.

C Jensen delved into Pierre Fermat's method of determining tangents of curves and its application to the conchoid and the quadratrix in 1969 in the journal Centaurus.

J E Hofmann's scientific historical sketch on Pierre de Fermat was published in the journal Science History in 1971.

M S Mahoney explored Fermat's mathematics, including proofs and conjectures, in 1972 in the journal Science.

In 1973, Michael Sean Mahoney published 'The Mathematical Career of Pierre de Fermat,' shedding light on the mathematical journey of Pierre de Fermat.

The correspondence between Blaise Pascal and Pierre de Fermat on questions of probability theory in 1976.

A P Kauchikas examined double equations in the work of Diophantus and Pierre Fermat in 1982 in the Istoriko-Matematicheskie Issledovaniya.

A comment on Fermat's 'Observations on Diophantus' in 1983.

André Weil, a 20th-century mathematician, praised Fermat's methods for dealing with curves of genus 1, stating that they are still the basis for modern theory. Weil highlighted Fermat's innovative approach and his significant contributions to the field of number theory.

Discussion on the conceptual direction of Pierre de Fermat's works in 1988.

E Brassinne's work 'Précis des oeuvres mathématiques de P Fermat et de l'Arithmétique de Diophante' sheds light on Pierre de Fermat's mathematical contributions and his connection to Diophantus' Arithmetica, providing valuable insights into the history of mathematics.

J-B Hiriart-Urruty explored the historical associations of Fermat in Beaumont and Toulouse, France in 1990 in the Mathematical Intelligencer.

C R Fletcher's reconstruction of the Frenicle - Fermat correspondence of 1640 was published in the journal Historia Mathematica in 1991.

In June 1993, British mathematician Andrew Wiles proved the truth of Fermat's assertion, but later withdrew the claim due to problems. However, in November 1994, Wiles claimed to have a correct proof which was eventually accepted.

Fermat's Last Theorem, which eluded mathematicians for centuries, was finally proven in 1994 by Sir Andrew Wiles. This groundbreaking proof utilized advanced mathematical techniques that were not available during Fermat's time.

After over 300 years of attempts to prove Fermat's Last Theorem, Andrew Wiles, a professor of mathematics at Princeton University, published a complete proof in 1995. This breakthrough finally solved the theorem that had puzzled mathematicians for centuries.

In his book 'Against the Gods', Peter L. Bernstein described Fermat as a mathematician of rare power who independently invented analytic geometry, contributed to calculus, and made significant advancements in various areas of mathematics. Bernstein highlighted Fermat's crowning achievement in the theory of numbers.

K Barner's article 'How old did Fermat become?' was published in the International Journal for History and Ethics of Natural Sciences, Technology and Medicine in 2001, discussing aspects of Fermat's life and age.