Mahoney M.S. The Mathematical Career of Pierre de Fermat, 1601-1665

2nd Edition. — Princeton University Press, 1994. — 452 p. — ISBN: 0-691-03666-7.Hailed as one of the greatest mathematical results of the twentieth century, the recent proof of Fermat's Last Theorem by Andrew Wiles brought to public attention the enigmatic problem-solver Pierre de Fermat, who centuries ago stated his famous conjecture in a margin of a book, writing that he did not have enough room to show his "truly marvelous demonstration." Along with formulating this proposition - xⁿ+yⁿ=zⁿ has no rational solution for n 2 - Fermat, an inventor of analytic geometry, also laid the foundations of differential and integral calculus, established, together with Pascal, the conceptual guidelines of the theory of probability, and created modern number theory. In one of the first full-length investigations of Fermat's life and work, Michael Sean Mahoney provides rare insight into the mathematical genius of a hobbyist who never sought to publish his work, yet who ranked with his contemporaries Pascal and Descartes in shaping the course of modern mathematics.Preface (1994)The Personal Touch
Mathematics in 1620
Fermat's Life and Career in Parlement
Motivation to MathematicsNullum Non Problema Solvere: Viete's Analytic Program and Its Influence on Fermat
Algebra, Analysis, and the Analytic Art
Following the "Precepts of the Art"
Fermat's Style of Work and His Influence on His Con temporariesThe Royal RoadFermat's Analytic Geometry, the Ad locos pianos et solidos isagoge
The Origins of the Isagoge: Apollonius' Plane Loci and Conics
Extensions of the System of the Isagoge: The Isagoge ad locos ad superficiem
Uses of the System of the Isagoge: Graphic Solu tion and Classification of EquationsFashioning One's Own LuckThe Roots of an Equation and the Roots of a Method
Of Dubious Parentage: The Method of Tangents
Looking Under the Bed: Descartes vs. Fermat, 1637-38
Archimedes and The Theory of Equations
Between Traditions Contents
The Aftermath: Proceeding By Touch
Learning New Tricks: The Letter to Bnllart
Fine Tuning: The Path Toward Quadrature and RectificationArchimedes and The Theory of EquationsFrom Spirals to Conoids
The Method of Centers of Gravity
The Treatise on Quadrature (ca. 1658)
The Treatise on Rectification (1660)
Fermat and the CalculusBetween TraditionsNumbers, Perfect and Not So Perfect
Triangles and Squares
Reclaiming the Patrimony: The Challenges of 1657
One Final Attempt: The "Relation" to Carcavi (1659) and the Method of Infinite Descent
Infinite Descent and the "Last Theorema"Epilogue: Fermat in RetrospectSidelights on A Mathematical Career
Mechanics
Optics
ProbabilityBibliographical Essay and Chronological Conspectus of Fermat's Works
Index