Born: c. 1607 · Beaumont-de-Lomagne, France

Died: 12 January 1665 · (aged 57) · Castres, France

Education: University of Orléans (BCL, 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)

Fields: Mathematics and law

Major contributions of Pierre de Fermat include:

• Fermat's principle for light propagation

• Fermat's Last Theorem in number theory

• Developing a method to calculate maxima and minima

• Contributions to differential and integral calculus

• Initiating the development of probability theory in correspondence with Pascal

Problem/events that influence Pierre de Fermat's mathematical ideas:

Pierre de Fermat's mathematical ideas were influenced by a combination of his personal interests, professional life, and exposure to earlier works in mathematics. Fermat, a lawyer by profession, pursued mathematics as a passion, often solving problems for intellectual pleasure rather than formal recognition. His legal career provided him with analytical skills and a methodical approach to problem-solving, which translated into his mathematical work. Fermat was heavily inspired by the works of ancient Greek mathematicians, particularly Diophantus, whose Arithmetica motivated Fermat’s explorations into number theory. This inspiration famously led to his marginal note proposing "Fermat’s Last Theorem," a conjecture that puzzled mathematicians for centuries.

Fermat also benefited from the intellectual climate of the 17th century, a period marked by advancements in science and mathematics. His correspondence with other mathematicians, including Blaise Pascal, fueled his interest in probability theory, leading to the foundation of modern probability. Additionally, the influence of René Descartes’ work on analytic geometry prompted Fermat to develop his own methods for calculating tangents and areas under curves, which became foundational to calculus. His curiosity and independent study of mathematical problems, combined with the collaborative exchange of ideas during his time, significantly shaped his contributions to mathematics, particularly in number theory, analytic geometry, and probability.

His Impact on the modern mathematics: 

Pierre de Fermat’s impact on modern mathematics is profound, as his work laid the groundwork for several key areas in the field. Known as one of the pioneers of modern number theory, Fermat introduced concepts and problems that remain central to mathematical research today. His famous Fermat's Last Theorem inspired generations of mathematicians and led to advancements in algebraic geometry and modular forms, ultimately culminating in its proof by Andrew Wiles in the 1990s. Fermat’s work in probability theory, developed through correspondence with Blaise Pascal, formed the foundation of modern statistics and probability, which are essential in fields ranging from economics to data science.

Fermat also made significant contributions to calculus, independently developing methods for finding tangents and extrema, which prefigured the work of Newton and Leibniz. His work in analytic geometry, alongside René Descartes, helped unify algebra and geometry, enabling more complex mathematical modeling. Fermat’s principle of least time in optics also demonstrates his influence beyond mathematics, impacting physics and engineering. His problem-solving approach and his visionary ideas continue to shape mathematics, inspiring innovations and serving as a cornerstone for modern mathematical thought and application.