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Abstract: Abstract A book review of Matematica in Aristotele by Silvio Maracchia, which regards the presence and importance of mathematics and especially geometry in the works of Aristotle. PubDate: 2018-12-01 DOI: 10.1007/s40329-018-0244-2

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Abstract: Abstract Various comments on the book on Giovan Battista Guccia, founder of the Circolo matematico di Palermo, which—besides acknowledging a few of its innovative aspects—aims at reflecting on the present situation of scientific research, along the lines first put forward by Guccia. PubDate: 2018-12-01 DOI: 10.1007/s40329-018-0245-1

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Abstract: Abstract The article introduces the volume Nuclear Italy: an International History of Italian Nuclear Policies during the Cold War. The book analyses the history of Italy’s involvement in nuclear energy during the Cold War, through the perspective of international and comparative history. The 16 essays included here, written by scholars from different disciplines, underline the influence of the international context of the Cold War on Italian nuclear policies, both civilian and military. The essays shed new light on the Italian nuclear experience, thanks in part to archival sources only recently made available. PubDate: 2018-12-01 DOI: 10.1007/s40329-018-0248-y

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Abstract: Abstract Remembering Carlo Bernardini, a few months after his demise; a recollection, devoid of biographical notes, aimed at bringing out unusual and lesser known aspects of his extraordinary personality. PubDate: 2018-12-01 DOI: 10.1007/s40329-018-0246-0

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Abstract: Abstract This paper is the fifth in a series on the theme of the communication of mathematics in Europe. This episode is located is Pisa and features the monologist and mathematical populariser Eduardo Sáenz de Cabezón. The topics covered in the course of the interview include: how to narrate mathematics in a show; how to reconcile research, communication and teaching; the communication of mathematics in Spain; the importance of training to be effective communicators; the interdisciplinary approach to communication; and much more. Eduardo and his versatility allow us to savour the wonders of a world in which the contamination between different fields becomes a richness, and the beauty of mathematics and its message are exalted with wisdom and care by the artistic sensibility that guides his popularisation activities. PubDate: 2018-12-01 DOI: 10.1007/s40329-018-0239-z

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Abstract: Abstract The Mathematical Manuscripts are the least known work of Karl Marx, in which the rediscovery of mathematics coincided with the revival of Hegel’s Logic. They are primarily dedicated to the logical foundation of differential calculus. Marx’s method is historical-genetic, identical to that used in his critique of Political Economy. His aim is to derive the derivative directly from the process of variation of the function, so that its algebraic, real origin is met. In previous methods, the differentials were individual entities with substantial content. In Marx, instead, they are inseparable as numerator and denominator in the differential ratio, which is a unitary operational symbol indicating an ordered set of logical operations. This notion is strikingly similar to the modern concept of algorithm, making Marx a precursor of the modern computational mathematics. PubDate: 2018-12-01 DOI: 10.1007/s40329-018-0241-5

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Abstract: Abstract In the Chinese tradition, linear Diophantine problems can be traced back to two main categories. The first group includes the problems consisting of 2-equation systems with integer coefficients in n unknowns with \(n> 2\) and integer solutions, such as: \(x_1 + x_2 + \dots + x_n = p\) , \(b_1 x_1 + b_2 x_2+ \dots + b_n x_n = q\) . The so-called “100 fowls problem” belongs to this group. The oldest statement can apparently be found in the Zhang Qiujian Suanjing (The Computation Classic of Zhang Qiujian), towards the second half of the 5th century AD (468–486). In the second category there are problems that can be represented through simultaneous linear congruences, which are generally formulated as follows: find a number x that, divided by \(m_1\) , \(m_2\) , \(m_3, \ldots , m_i\) , give as remainders \(r_1\) , \(r_2\) , \(r_3, \ldots , r_i\) . This kind of problem is currently called “Chinese (remainder) problem”. The oldest formulation is attributed to Master Sun Tzu (between 280 and 473). We shall present the different statements of the two problems in their circulation from Asia to Europe and the main proof procedures. PubDate: 2018-12-01 DOI: 10.1007/s40329-018-0242-4

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Abstract: Abstract At the beginning of the nineteenth century, Heidelberg, Königsberg and Göttingen were the main universities in Germany territory, but thanks to the work and convictions of Wilhelm von Humboldt, Berlin became established as a new academic centre. The University of Berlin opened officially in 1810 and, within a few decades, had become central to the education and training system of the whole of Germany, successfully attracting students, researchers and teachers. Research in science was one of the qualifying points of the education and training system of Germany and the new University of Berlin, which included teachers such as Hermann von Helmholtz and Heinrich Hertz, among others. PubDate: 2018-12-01 DOI: 10.1007/s40329-018-0247-z

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Abstract: Abstract The Russian–Italian physicist Gleb Wataghin (1899–1986) lived and worked in Brazil between 1934 and 1949. During his Brazilian residence, he established personal and professional contacts with physicists and mathematicians from countries such as the United States of America, Italy, France, besides Brazil. In this paper, we discuss Wataghin’s participation in a mutual cooperation network of scientists in times of political hostility, in a transnational perspective. As we will argue, Wataghin made use of different tactics in order to help his colleagues to find positions in Brazilian universities and in the scientific field. PubDate: 2018-12-01 DOI: 10.1007/s40329-018-0240-6

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Abstract: Abstract Monge’s mathematical work (descriptive geometry, analytic geometry, partial differential equations) belongs to the advanced science and teaching of all countries. Monge lived in Italy for almost 2 years as a commissioner for sciences and arts, at the behest of General Bonaparte, and giving the Constitution to the Jacobin Roman Republic of 1798. The small independent Republic of San Marino owes much of its existence to Monge, and even the well-known Parmesan cheese was studied scientifically for the first time by Monge. One section concerns the Monge–Ampère equation, obtained by Monge in 1784, and recently elucidated by Italian mathematicians. PubDate: 2018-12-01 DOI: 10.1007/s40329-018-0243-3

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Abstract: Abstract This paper addresses the Marxian transformation problem of values into prices. According to Marx, the value of commodities is given by the labour embodied in the same commodities. However, given the Marxian assumption of free competition in labour and good markets, the price of commodities may deviate from their labour value. Marx’s “transformation problem” lies precisely in the computation of prices based on their labour content. As we shall see, the solution proposed by Marx is only partial, and subsequent attempts to solve the problem increasingly distance the solution from the Marxian model which is based on labour value and surplus value, leaving the question still open. PubDate: 2018-12-01 DOI: 10.1007/s40329-018-0250-4

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Abstract: Abstract In recent years, the Italian school system has undergone a radical process of evolution that is transforming it, necessitating urgent reflection on the training of mathematics teachers. The book under review aims at offering some basic tools for pedagogical research, which in our opinion is necessary but not sufficient. We believe that the scheme: “teacher training = mathematical contents equal to those for future researchers + a bit of teaching theory and history” does not work and must be replaced by a methodological, historical, formative and foundational integrated approach that focusses on specific, multiple and complex needs of future teachers, which are necessary so that they can securely play their fundamental and irreplaceable social role. To achieve, this it is necessary for researchers in mathematics education, historians of mathematics and mathematicians tout court to work together in an organic way with a view to training future teachers and developing suitable training courses. PubDate: 2018-09-01 DOI: 10.1007/s40329-018-0237-1

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Abstract: Abstract The Italian mathematician Luigi Fantappiè (1901–1956) worked in Brazil from 1934 to 1939 as a member of the Italian Mission that had among its purposes the organisation of the Department of Mathematics and Physics at the Faculty of Philosophy, Sciences and Letters of the University of São Paulo. In this paper, we describe his work in Brazil, taking as our main source his final report to Brazilian and Italian authorities, produced few days before his departure to Italy. We point out some elements of his experience, which involved the organisation of the Department of Mathematics but also debates about Brazilian secondary education and the dissemination of Italian culture abroad in times of fascism. PubDate: 2018-09-01 DOI: 10.1007/s40329-018-0235-3

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Abstract: Abstract The attribution of many Nobel and other scientific prizes to a large number of German scientists is due to the profound reforms of the educational system first in Prussia and then in Germany during the nineteenth century. This article analyses the main reforms adopted mainly by the Prussian State and focusses on some figures who played key roles in the development of university institutions and scientific faculties. PubDate: 2018-09-01 DOI: 10.1007/s40329-018-0230-8

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Abstract: Abstract A review of the book Lo specchio, il labirinto e la farfalla. Il postmoderno in letteratura e matematica by Gian Italo Bischi and Giovanni Darconza, about the parallel courses of mathematics and literature (and especially detective fiction) along the 19th and the twentieth centuries, from an age of certainties to its dissolution with postmodernism. PubDate: 2018-09-01 DOI: 10.1007/s40329-018-0233-5

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Abstract: Abstract We introduce the notion of circle inversion in order to construct tessellations in the Poincaré’s model of non-Euclidean geometry. PubDate: 2018-09-01 DOI: 10.1007/s40329-018-0229-1

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Abstract: Abstract The paper offers a report of the international conference “Transitions in energy history—State of the art and new perspectives”, held in Milan in the winter of 2017 and organised by the Department of documentary, linguistic, philological and geographical sciences of the Sapienza University of Rome, the Leonardo da Vinci National Museum of Science and Technology in Milan, the Fondation EDF, Edison-EDF Group and the Italian section of the World Energy Council. The first part of the paper introduces the overall concept and architecture of the event, exemplifies the different kind of contributions presented at the conference and offers a brief review of the variety of contents and flavours arising from the focus on the category “transition”. The second part of the paper focusses instead on some fundamental reflections, also in the light of related conferences promoted by other museums in the international arena. PubDate: 2018-09-01 DOI: 10.1007/s40329-018-0236-2

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Abstract: Abstract On the occasion of the awarding, in August 2018, of the Fields medals, we present the career and achievements of one of the winners, Peter Scholze. PubDate: 2018-09-01 DOI: 10.1007/s40329-018-0231-7