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**1 - 3**of**3**### A Self-Contained and Easily . . .

, 2010

"... We present the only proof of PIERRE FERMAT by descente infinie that is known to exist today. As the text of its Latin original requires active mathematical interpretation, it is more a proof sketch than a proper mathematical proof. We discuss descente infinie from the mathematical, logical, historic ..."

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We present the only proof of PIERRE FERMAT by descente infinie that is known to exist today. As the text of its Latin original requires active mathematical interpretation, it is more a proof sketch than a proper mathematical proof. We discuss descente infinie from the mathematical, logical, historical, linguistic, and refined logic-historical points of view. We provide the required preliminaries from number theory and develop a self-contained proof in a modern form, which nevertheless is intended to follow FERMAT’s ideas closely. We then annotate an English translation of FERMAT’s original proof with terms from the modern proof. Including all important facts, we present a concise and self-contained discussion of FERMAT’s proof sketch, which is easily accessible to laymen in number theory as well as to laymen in the history of mathematics, and which provides new clarification of the Method of Descente

### JACQUES HERBRAND: LIFE, LOGIC, AND AUTOMATED DEDUCTION

"... The lives of mathematical prodigies who passed away very early after groundbreaking work invoke a fascination for later generations: The early death of Niels Henrik Abel (1802–1829) from ill health after a sled trip to visit his fiancé for Christmas; the obscure circumstances of Evariste Galois ’ (1 ..."

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The lives of mathematical prodigies who passed away very early after groundbreaking work invoke a fascination for later generations: The early death of Niels Henrik Abel (1802–1829) from ill health after a sled trip to visit his fiancé for Christmas; the obscure circumstances of Evariste Galois ’ (1811–1832) duel; the deaths of consumption of Gotthold Eisenstein (1823–1852) (who sometimes lectured his few students from his bedside) and of Gustav Roch (1839–1866) in Venice; the drowning of the topologist Pavel Samuilovich Urysohn (1898–1924) on vacation; the burial of Raymond Paley (1907–1933) in an avalanche at Deception Pass in the Rocky Mountains; as well as the fatal imprisonment of Gerhard Gentzen (1909–1945) in Prague1 — these are tales most scholars of logic and mathematics have heard in their student days. Jacques Herbrand, a young prodigy admitted to the École Normale Supérieure as the best student of the year1925, when he was17, died only six years later in a mountaineering accident in La Bérarde (Isère) in France. He left a legacy in logic and mathematics that is outstanding.