By Bruno Belhoste
A nice hassle dealing with a biographer of Cauchy is that of delineating the curious interaction among the guy, his occasions, and his clinical endeavors. Professor Belhoste has succeeded admirably in assembly this problem and has therefore written a vibrant biography that's either readable and informative. His topic stands proud as essentially the most incredible, flexible, and prolific fig ures within the annals of technology. approximately 200 years have now handed because the younger Cauchy set approximately his job of clarifying arithmetic, extending it, utilizing it anywhere attainable, and putting it on an organization theoretical footing. via Belhoste's paintings we're afforded an in depth, fairly custom-made photograph of the way a primary cost mathematician labored at his self-discipline - his strivings, his inspirations, his triumphs, his disasters, and primarily, his conflicts and his errors.
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Extra info for Augustin-Louis Cauchy: A Biography
At that time, he was working on number theory, especially on Fermat's theorem on polygonal numbers; and this research was to continue until 1815. In connection with his work in number theory, he made a careful study of Gauss' Disquisitiones Arithmeticae, which had been published in 1801 and translated into French in 1807. He seems to have mastered very quickly the methodology and sense of Gauss; and grasping the importance of the theory offorms that Gauss had used in proving Fermat's theorem on triangular numbers, he managed to simplify it and to generalize some of the results, particularly the ones on discriminants.
Lorsqu'on substitue ces variables it. la place les unes des autres. IIs ont donne plusieurs thcoremes intcressans relatifs it. ce sujet. LIX Il1cll1oires impril11es ell J 77 I • l'un it. Berlin. ['alltre it Paris. Depuis ce temps. quelques gcometres haliens se sont occupes avec slIcces de cette ll1atii:re, et parti-. cuiierell1ent M. Ruffini, qui a consignc: Ie resultat de ses recherches dans Ie tome XII des Memoires de la Societe italienne. et dans sa Thcorie des eqll8tiolls numeriques. Une des :onscquences les pillS j'emarquables des travaux de ces divers gcomCtres, est qu'avec un lIombre donne de lettres on lie peut pas tOlljours former une fonctioll qui ait un nombre detcrmin6 de valeurs.
Cauchy expected to give verbally a concise account of the contents of this paper at the First Class' meeting of May 17. But other readings filled up the meeting. In this account, which he published a few days later, Cauchy intended to pay his respects to Lagrange, 'the great geometer whose passing has saddened learned circles everywhere in Europe as much as it has saddened us', and he presented his own work as a response to a problem that Lagrange had posed in his Traite de la Resolution des Equations Numeriques de tous les Degres.