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Testo Completo Università degli Studi di Ferrara DOTTORATO DI RICERCA IN "MATEMATICA E INFORMATICA" CICLO XXVI COORDINATORE Prof. Mella Massimiliano L’INTERNAZIONALIZZAZIONE DEGLI STUDI MATEMATICI IN ITALIA A METÀ OTTOCENTO Settore Scientifico Disciplinare MAT / 04 Dottorando Tutore Dott. Nagliati Iolanda Prof. Borgato Maria Teresa ________________________ ___________________________ (firma) (firma) Anni 2011/2013 1 1 L’internazionalizzazione degli studi matematici in Italia a metà Ottocento Introduction p. 3 Introduzione 17 L’internazionalizzazione degli studi 21 I rapporti di Betti con studiosi stranieri: temi delle lettere Corrispondenti stranieri di Brioschi Corrispondenti stranieri di Tardy La situazione degli esuli: Mossotti da Corfù a Pisa 43 Il ritorno dall’esilio I primi anni dell’attività a Pisa e i rapporti con Betti Vicende politiche, organizzazione degli studi e della ricerca nella corrispondenza tra Brioschi e Tardy 59 L’organizzazione degli studi superiori Gli “Annali” Le equazioni algebriche di quinto grado 73 La teoria degli invarianti 81 Ricerche sui differenziali ad indice fratto 99 Le riviste scientifiche toscane nell’Ottocento 109 Documenti: Lettere di Giorgini a Mossotti 127 Lettere di Mossotti a Tardy 135 Lettere di Mossotti a Betti 139 Carteggio Brioschi-Tardy 191 Lettere a Betti di studiosi stranieri 285 Lettere a Tardy di studiosi stranieri 342 Lettere a Brioschi di studiosi stranieri 369 Bibliografia 371 1 2 Introduction The past few decades have seen several studies carried out by historians of mathematics on mathematics in the post unification period in Italy, further interest being recently stimulated by the celebration of 150 years since the Unification of Italy; this moment brought about a period of renewal of structures and infrastructures suitable for the new state, a sort of modernisation of the economy, which, at the same time, required a new institutional organisation on a national level for the scientific community, to carry on the work already started in the previous decades by single states, like Piedmont and the Grand Duchy of Tuscany. Particular attention was placed on education structures at all levels, the formation of the governing and entrepreneur classes, and the development of research. Before the Unification, during the Restoration and first movements of independence, contacts with the most advanced sectors of European research had already begun and further development would be carried on into the last decades of the XIX century. A greater opening towards the English and German schools of mathematics was seen to take the place of the traditional links with the French school of thought. These studies were enhanced by the publication of numerous inedited works and correspondences, but there is still much material to be studied in university and academy libraries. This thesis aims at casting light on some aspects still under investigation through the use of existing studies as well as new inedited documents. After a brief outline of the theme of the research, the first chapter goes on to provide biographical details of the main protagonists of this study, namely, Enrico Betti, Francesco Brioschi, Ottaviano Fabrizio Mossotti and Placido Tardy. By means of edited and inedited material, the presence of many foreign scholars in Italy will be examined as well as the journeys that Italian mathematicians undertook abroad. Moreover, the contents of inedited correspondences presented in the Documents 3 will be discussed in relation to the theme of the research, or rather the dynamics which contributed to the return of Italian mathematics to the forefront of European scene. The compulsory internationalization of political exile constitutes the subject of the second chapter. Particular study will be devoted to the case of Ottaviano Fabrizio Mossotti, his departure from Italy to the Ionian Academy of Corfu and successive return to the University of Pisa. These years established the first contact with Betti and the scientific formation of the latter, initially directed towards mathematical physics. The Brioschi-Tardy correspondence is the main source of the following chapters which concern the politics of the Risorgimento, the organisation of education and research in the post Unification period, and the lines of research which both Brioschi and Betti and their European interlocutors shared: the resolution of fifth degree equations and the invariant theory of binary forms. The fifth chapter, instead, deals with the research carried out mainly by Liouville and some other English mathematicians in the second quarter of the nineteenth century: expansion of differential and integral calculus to non-integer orders. In Italy it was Tardy, Genocchi and Tortolini who took up the problem. The subject, which had been put aside for several decades, came back to the forefront towards the end of the XX century. Although the influence of the foundation of the Annali di Matematica Pura ed Applicata was a determining factor in the renewal of scientific research in Italy, several other journals contributed to the dissemination of results and information to Italian scholars, as well as to the formation of new technical and scientific professions: as an example we may recall the Giornale by Battaglini, the Annali by Majocchi or the Politecnico for engineers and architects. Academic publications also played their part, and the last chapter provides a detailed examination of the scarcely studied scientific periodicals linked to the University of Pisa during the XIX century. The second part of the thesis contains either inedited or partially published documents recovered from various archives during this three-year doctorate. They include six letters from Gaetano Giorgini to Mossotti, four letters from Mossotti to Tardy and fifty to Betti, sixty-three letters 4 exchanged between Brioschi and Tardy, fifty-two letters from various foreign mathematicians and physicists to Betti and thirty letters from mathematicians and physicists to Tardy, or transmitted to him by other recipients; a further profile of letters from foreign mathematicians and physicists to Brioschi is reported. 5 6 The internationalization of Italian mathematicians in the mid nineteenth century It is the opinion of historians that the journey 1 undertaken in the autumn of 1858 by Enrico Betti, Francesco Brioschi and Felice Casorati 2 with the aim of getting to know the main European universities, their scholars and organisational models marks the turning point in the return of the Italian mathematic faculty to the European scene 3, whose position since the Napoleonic period was only second to that of France in undergoing a remarkable reassessment. This thesis examines some aspects of the internationalization process taking place during the XIX century, focussing on two of the protagonists of the journey, Enrico Betti and Francesco Brioschi, and on two scholars who were closely linked to them, namely, Ottaviano Fabrizio Mossotti and Placido Tardy, by means of their inedited correspondences and scientific works. A reconstruction of personal and scientific relationships is proposed through their direct contact during the journey, the influence of foreign research models, editorial activity and the choices made in the organisation of secondary school education. Enrico Betti (Pistoia, 21st October 1823 - Soiana PI, 11th August 1892) was one of the most important Italian mathematicians of the XIX century, achieving important results in his research in various fields: algebra with studies on the resolution of fifth degree equations, Galois’s theory and invariants, topology where he introduced numerical invariants which bear his name, the theory of elasticity and potential. In 1846 he graduated from the University of Pisa, having studied under Ottaviano Fabrizio Mossotti and Carlo Matteucci (1811-1868); he taught for several years in 1 The journey has been widely studied [Bottazzini 1994], [Borgato 1992, 2012]; as early as 1900, on the occasion of the second International congress of mathematicians in Paris, Volterra underlined the importance of the journey for the development of analysis in Italy [Volterra 1900]. 2 Felice Casorati (Pavia, 1835 - Casteggio, 1890), a graduate in civil engineering and architecture in 1856, was nominated assistant to the chair of Geodesy and hydrometry and applied mathematics, held by Brioschi, was since that time professor at Pavia University. His participation in the journey was decided at the last moment when both Cremona and Tardy did not confirm their presence. 3 [Giusti - Pepe 2001], [Pepe 2002], [Martini 2006], [Bottazzini - Nastasi 2013]. 7 secondary schools, and in 1857 he was nominated to teach algebra of finites at the University of Pisa; two years later he obtained the chair of Higher Analysis, and took over the course on Mathematical Physics on the death of Mossotti. From 1865 he was the Director of the Scuola Normale , where he taught, among others, Ulisse Dini (1845-1918) and Vito Volterra (1860-1940). He was also involved in politics, after direct participation as Corporal of the University Guards, headed by Mossotti now in his sixties in the battle of Curtatone and Montanara in May 1848; he held the position of Parliamentary Deputy in the Collegio of Pistoia, and was nominated Senator of the Kingdom in 1884, and from 1864 to 1885 he held various positions in the Ministry of Education. He was also a member of the most prestigious academies and scientific societies. Francesco Brioschi (Milan 22nd December 1824 – 13th December
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