By Bruno Belhoste

A nice hassle dealing with a biographer of Cauchy is that of delineating the curious interaction among the fellow, his occasions, and his medical endeavors. Professor Belhoste has succeeded admirably in assembly this problem and has therefore written a brilliant biography that's either readable and informative. His topic stands proud as probably the most superb, flexible, and prolific fig ures within the annals of technology. approximately 2 hundred years have now handed because the younger Cauchy set approximately his job of clarifying arithmetic, extending it, using it anyplace attainable, and putting it on an organization theoretical footing. via Belhoste's paintings we're afforded a close, fairly custom-made photograph of ways a primary fee mathematician labored at his self-discipline - his strivings, his inspirations, his triumphs, his disasters, and specifically, his conflicts and his errors.

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Memoire sur Ie nombre des valeurs qu'une fonction peut acquerir, lorsqu'on y permute de to utes les manieres possibles les quantites qU'elle renferme', Journal de I'Ecole Poly technique, 10, 1815, pp. 1- 28. Published by permission of the Ecole Poly technique. 3. The Waiting Room of the Academy 34 In the proof of this result he introduced new concepts, notations, and methods, directly inspired by Gauss' Disquisitiones. He denoted as the substitution transforming the permutation Ar of n letters into the permutation As of the same letters and (lX,f3) as the transposition of two letters IX and 13 in a given permutation.

At his lecture on November 14, 1811, he declared: What can I say about the exact sciences? Most of them seem to have already been carried forth to their highest stage of development. Arithmetic, geometry, algebra, and higher mathematics are sciences that can rightly be regarded as having been completed, as it were; and nothing more remains to be done with them except to find new areas of useful applications (26). This opinion was widely held in France's scientific community at that time. Most decidedly, the future seemed to belong to the engineering sciences (27).

In January 1814, when Augustin-Louis' sick-leave was due to expire, LouisFranc;:ois wrote to Baron Costaz asking that an additional three months' leave be granted his son whose health had been 'profoundly undermined by his work load' during the three years of service at Cherbourg (19). Following this supplementary leave, it seems that Augustin-Louis resumed his duties at the Ponts et Chaussees in March 1814, although the relevant records are silent on 40 3. The Waiting Room of the Academy this point (20).

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