## The Mathematical Career of Pierre de Fermat, 1601-1665Hailed 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 - x(superscript n) + y(superscript n) = z(superscript n) 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. |

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### Contents

The Personal Touch | 1 |

Nullum Non Problema Solvere Vietes Analytic Program And Its Influence On Fermat | 26 |

The Royal Road | 72 |

Fashioning Ones Own Luck | 143 |

Archimedes and the Theory of Equations | 214 |

Between Traditions | 283 |

### Common terms and phrases

algebraic aliquot analysis analytic art analytic geometry Apollonius Appendix applied Archimedes arithmetic axis Beaugrand Brulart Carcavi center of gravity Chap Chapter circle classical clearly contains correspondence cossist cube cubic equation curve demonstration derived Descartes determination Diophantus Dioptrics equal example expression Fermat to Mersenne Fermat's mathematical Fermat's method form 4k Frenicle Galileo geostatics given number Greek Hence Huygens hyperbola indeterminate equations infinite descent integers Introduction lemma letter to Mersenne mathe mathematicians maxima and minima Mersenne method of maxima method of quadrature method of tangents notation number theory original Pappus parabola Paris perfect numbers Pierre de Fermat Plane Loci prime number proof proposition qu'il quadratic quadrature ratio rectangle rectification reduced right triangle Roberval roots Schooten segment solid solution solve spiral square straight line syncrisis technique theorem theory of equations tion Toulouse translation Treatise on Quadrature unknown Viete Viete's Wallis