By Angelo Guerraggio

This ebook describes Italian arithmetic within the interval among the 2 global Wars. We learn its improvement by means of concentrating on either the internal and the exterior affects. Italian arithmetic in that interval used to be formed via a colourful array of sturdy personalities who centred their efforts on a pick out variety of fields and gained foreign attractiveness and admire in an extremely little while. as a result, Italy used to be thought of a 3rd "mathematical strength" after France and Germany, and certified Italian universities turned essential stops at the "tour", geared up for the advance of younger international mathematicians. at the moment, Italy was once additionally ruled via a fascist regime. This political state of affairs and the social and educational constitution of Italian society are integrated within the research as impacts exterior to arithmetic itself. The authors have supplied a desirable examine of a such a lot tough time within the historical past of the area and of mathematics.

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Still in 1965, in a letter to P. Lévy from the 30th July (published in Cahiers du Séminaire d’Histoire des Mathématiques, 1980, n. 1), he clarified that “si je considère que Volterra a réalisé un grand progrès en donnant au moins une définition de la différentielle d’une fonction dont l’argument est une fonction, d’autre part, je considère que sa définition est mauvaise”. 22 Guerraggio Volterra’s other well-known contribution in this period were integral equations, inserted for the first time into a general theory, later taken up and developed by E.

Lebesgue regarding the cogency of some proofs by the latter. Nevertheless, he would mainly concentrate his efforts on algebraic geometry, number theory, logic and the foundations of geometry. In the complex analysis, Eugenio Elia’s research focused on the singular point sets of a holomorphic function of several variables. However, he also wrote on issues relating to: differential geometry, Lie’s groups, partial differential equations and the minimum principle. E. E. Levi would also demonstrate the falsity of Weierstrass’s conjecture according to which given an open A of C2 , a merophormic function will always exist in A which has essential singularities in each point of the border of A, providing further evidence in favour of the differentiation between the theory of the single complex variable and the theory of more than one complex variable.

An article by Rignano, I fattori della guerra ed il problema della pace, was specially worrying; in it the author – Italy had already entered the war with the Allies – had no hesitation in speaking freely about the imperialistic aims of the England, its allies, and their responsibility for the war. Enriques asked Rignano explicitly to withdraw the article, which was not an expression of a free scientific opinion but a real political act, and could offend patriotic feelings. Faced with Rignano’s refusal, Enriques precipitously left the editorship – together with many of the founders – to go back to it only in 1930, after Rignano’s death.