6533b857fe1ef96bd12b46cd

RESEARCH PRODUCT

Pietro Mengoli and the six-square problem

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The aim of this paper is to analyze a little known aspect of Pietro Mengoli's (1625-1686) mathematical activity: the difficulties he faced in trying to solve some problems in Diophantine analysis suggested by J. Ozanam. Mengoli's recently published correspondence reveals how he cherished his prestige as a scholar. At the same time, however, it also shows that his insufficient familiarity with algebraic methods prevented him, as well as other Italian mathematicians of his time, from solving the so-called “French” problems. Quite different was the approach used for the same problems by Leibniz, who, although likewise partially unsuccessful, demonstrated a deeper mathematical insight which led him to look for general algebraic methods. Le but de ce paper est l'analyse d'un aspect peu connu de l'activite de Pietro Mengoli (1625-1686). Plus precisement, nous nous occuperons des difficultees rencontrees par ce mathematicien bolonais pour resoudre quelques problemes d'analyse diophantine proposes part. Ozanam. La correspondence de Mengoli dernierement publiee nous presente l'occasion d'illustrer comment Mengoli tenait a defendre son prestige de savant; mais, en mame temps, elle revele que les methodes algebriques utiles a ce but ne lui etaient pas familieres. Cela lui empechera de resoudre les problemes “francais.” L'approche et la sensibility mathematique de Leibniz a l'egard des měmes problemes etaient differentes, quoique il n'efit que du succes partiel. In questo articolo si esamina un aspetto poco noto dell'attivita matematica di Pietro Mengoli (1625-1686), cioe le sue difficolta a risolvere alcuni problemi diofantei proposti da Ozanam. La recente pubblicazione della corrispondenza mengoliana offre qualche spunto relativo al suo rammarico per to scacco subito e chiarisce a nostro parere la scarsa familiarity the i matematici italiani del periodo avevano con i metodi algebrici. Nelle conclusioni si sottolinea la diversa sensibility matematica di Leibniz di fronte a questi problemi e la sua maggiore attenzione per la ricerca di metodi generali di soluzione, sebbene anch'egli abbia ripetutamente tentato di risolvere quei problemi.