Abstract In this work the situation of the “Circolo Matematico di Palermo” between 1914 and 1928 ... more Abstract In this work the situation of the “Circolo Matematico di Palermo” between 1914 and 1928 is analyzed. It will be observed that during this time the Circolo was among the few European scientific associations with German as well as French associates. During the 1930s, the nationalist politics of Fascism and above all the racial laws dealt a deadly blow to the Circolo as an international scientific association. We will use the rich correspondence in the Circolo's archives to shed some light on this. In particular, the correspondence between M. De Franchis and E. Landau and other recently found documents will figure prominently.
Dall'inversione alle trasformazioni quadratiche Aldo Brigaglia (Universit\ue0 di Palermo) bri... more Dall'inversione alle trasformazioni quadratiche Aldo Brigaglia (Universit\ue0 di Palermo) brig@math.unipa.it La inversione (o trasformazione per raggi vettori reciproci) \ue8 da considerarsi la prima trasformazione birazionale (non lineare) entrata in modo stabile nel novero di quelle trattate dai matematici. La stessa sua naturalezza ha reso nebulosa l\u2019origine di questo concetto. In effetti si tratta della trasformazione che, fissato un punto A e un segmento r, associa ad ogni punto B il punto B\u2019 sulla semiretta AB tale che AB\u2019 sia il terzo proporzionale tra AB e r. Costruzioni di punti di questo genere sono presenti assai spesso: p. es. nella proiezione stereografica, in cui r \ue8 il diametro della sfera, A \ue8 il polo da cui si proietta, B e B\u2019 sono rispettivamente un punto sulla sfera e il suo proiettato nel piano; tali costruzioni sono poi presenti nei classici problemi apolloniani dei Contatti ed usate esplicitamente da Vi\ue9te nel suo Apollonius Gallus. Naturalmente fasi completamente diverse saranno quelle in cui si passa da una visione statica della costruzione di B\u2019 alla considerazione della trasformazione presa nella sua globalit\ue0, all\u2019individuazione delle sue propriet\ue0 fondamentali (l\u2019essere una \u201ctrasformazione circolare\u201d e conforme), e infine l\u2019essere una trasformazione antilineare nella retta proiettiva complessa e le sue connessioni con le forme hermitiane. Mio scopo in questa comunicazione \ue8 quello di vedere come un concetto assai semplice ed elementare quale quello di inversione circolare possa attraverso successive generalizzazioni ed approfondimenti, connettersi a concetti assai pi\uf9 profondi, dar luogo a idee del tutto nuove (quali quelle di trasformazione geometrica generale, di trasformazione birazionale o di forme hermitiane). Esaminer\uf2 in particolare il contributo di Bellavitis in questa direzione, nel quadro di un progetto di ricerca del gruppo di Palermo, mirante ad approfondire le origini storiche del concetto di trasformazione birazionale. Bibliografia: G. Bellavitis, Saggio di geometria derivata, Nuovi Saggi della Imperial Regia Accademia di Scienze Lettere ed Arti di Padova, IV, 1838, pp. 243 \u2013 288; B. Patterson, The origin of the geometric principle of inversion, Isis, 19, 1933, pp. 154 \u2013 180; F. Vi\ue8te, Apollonius Gallus, Paris, 1600. L\u2019uso del Computer come st
In this paper we examine the contributions of the Italian geometrical school to the Foundations o... more In this paper we examine the contributions of the Italian geometrical school to the Foundations of Projective Geometry. Starting from De Paolis' work we discuss some papers by Segre, Peano, Veronese, Fano and Pieri. In particular we try to show how a totally abstract and general point of view was clearly adopted by the Italian scholars many years before the
The correspondence between the mathematician Luigi Cremona (1830-1903) and Quintino Sella (1827-1... more The correspondence between the mathematician Luigi Cremona (1830-1903) and Quintino Sella (1827-1884) highlights aspects of Sella’s political thought and cultural activity. In particular his aims on Rome “capital of science” and on the Accademia dei Lincei as emblem of national culture, encountered difficulties. In spite of some incomprehensions in the initial phase of their relationship, the harmony of ethical, political and cultural intentions for the progress of the country and the synergies implemented by the two friends led to important results. Among them we can mention the renewal of academic membership with prestigious names of scientists and intellectuals, the establishment of prizes to encourage scientific research, the publication of memoirs of the two classes and the exchanges of periodicals with academies and scientific institutions all over the world.
The correspondence between the mathematician Luigi Cremona (1830-1903) and Quintino Sella (1827-1... more The correspondence between the mathematician Luigi Cremona (1830-1903) and Quintino Sella (1827-1884) highlights aspects of Sella’s political thought and cultural activity. In particular his aims on Rome “capital of science” and on the Accademia dei Lincei as emblem of national culture, encountered difficulties. In spite of some incomprehensions in the initial phase of their relationship, the harmony of ethical, political and cultural intentions for the progress of the country and the synergies implemented by the two friends led to important results. Among them we can mention the renewal of academic membership with prestigious names of scientists and intellectuals, the establishment of prizes to encourage scientific research, the publication of memoirs of the two classes and the exchanges of periodicals with academies and scientific institutions all over the world.
If things had gone according to plan, it should have been an Italian to voice the new ideas since... more If things had gone according to plan, it should have been an Italian to voice the new ideas since no one had come closer to those ideas than the [Italian] school. … In fact it was also an Italian. I realised that only after having completed this essay. Fano had already got there in 1892. He introduces his axiomatic system with words that resonate with Hilbert’s own words that we have quoted above. (Freudenthal 1957) This quotation shows that Italian school had elaborated a point of view on foundations of geometry resonant with Hilbert’s about ten years before the publication of Hilbert’s work. In this talk I will try to reconstruct the link between the Italian geometric tradition on the foundations of geometry, from the work of De Paolis (1881) to the first appearance of Hilbert’s masterpiece (1899). Before beginning, I give a short list of the main features of Italian school:
Luigi Cremona (1830–1903), unanimously considered to be the man who laid the foundations of the p... more Luigi Cremona (1830–1903), unanimously considered to be the man who laid the foundations of the prestigious Italian school of Algebraic Geometry, was active at the University of Bologna from October 1860, when assigned by the Minister Terenzio Mamiani (1799–1885) to cover the Chair of Higher Geometry, until September 1867 when Francesco Brioschi (1824–1897) called him to the Politecnico di Milano. The “Bolognese years” were Cremona’s richest and most significant in terms of scientific production, and, at the same time, were the years when he puts the basis for its most important interventions in the social and political life of the “newborn” kingdom of Italy. In this article we present these different aspects of Cremona’s life, with particular emphasis on the relationship of the geometer of Pavia with the academic life in Bologna, with students and colleagues.
Abstract In this work the situation of the “Circolo Matematico di Palermo” between 1914 and 1928 ... more Abstract In this work the situation of the “Circolo Matematico di Palermo” between 1914 and 1928 is analyzed. It will be observed that during this time the Circolo was among the few European scientific associations with German as well as French associates. During the 1930s, the nationalist politics of Fascism and above all the racial laws dealt a deadly blow to the Circolo as an international scientific association. We will use the rich correspondence in the Circolo's archives to shed some light on this. In particular, the correspondence between M. De Franchis and E. Landau and other recently found documents will figure prominently.
Dall'inversione alle trasformazioni quadratiche Aldo Brigaglia (Universit\ue0 di Palermo) bri... more Dall'inversione alle trasformazioni quadratiche Aldo Brigaglia (Universit\ue0 di Palermo) brig@math.unipa.it La inversione (o trasformazione per raggi vettori reciproci) \ue8 da considerarsi la prima trasformazione birazionale (non lineare) entrata in modo stabile nel novero di quelle trattate dai matematici. La stessa sua naturalezza ha reso nebulosa l\u2019origine di questo concetto. In effetti si tratta della trasformazione che, fissato un punto A e un segmento r, associa ad ogni punto B il punto B\u2019 sulla semiretta AB tale che AB\u2019 sia il terzo proporzionale tra AB e r. Costruzioni di punti di questo genere sono presenti assai spesso: p. es. nella proiezione stereografica, in cui r \ue8 il diametro della sfera, A \ue8 il polo da cui si proietta, B e B\u2019 sono rispettivamente un punto sulla sfera e il suo proiettato nel piano; tali costruzioni sono poi presenti nei classici problemi apolloniani dei Contatti ed usate esplicitamente da Vi\ue9te nel suo Apollonius Gallus. Naturalmente fasi completamente diverse saranno quelle in cui si passa da una visione statica della costruzione di B\u2019 alla considerazione della trasformazione presa nella sua globalit\ue0, all\u2019individuazione delle sue propriet\ue0 fondamentali (l\u2019essere una \u201ctrasformazione circolare\u201d e conforme), e infine l\u2019essere una trasformazione antilineare nella retta proiettiva complessa e le sue connessioni con le forme hermitiane. Mio scopo in questa comunicazione \ue8 quello di vedere come un concetto assai semplice ed elementare quale quello di inversione circolare possa attraverso successive generalizzazioni ed approfondimenti, connettersi a concetti assai pi\uf9 profondi, dar luogo a idee del tutto nuove (quali quelle di trasformazione geometrica generale, di trasformazione birazionale o di forme hermitiane). Esaminer\uf2 in particolare il contributo di Bellavitis in questa direzione, nel quadro di un progetto di ricerca del gruppo di Palermo, mirante ad approfondire le origini storiche del concetto di trasformazione birazionale. Bibliografia: G. Bellavitis, Saggio di geometria derivata, Nuovi Saggi della Imperial Regia Accademia di Scienze Lettere ed Arti di Padova, IV, 1838, pp. 243 \u2013 288; B. Patterson, The origin of the geometric principle of inversion, Isis, 19, 1933, pp. 154 \u2013 180; F. Vi\ue8te, Apollonius Gallus, Paris, 1600. L\u2019uso del Computer come st
In this paper we examine the contributions of the Italian geometrical school to the Foundations o... more In this paper we examine the contributions of the Italian geometrical school to the Foundations of Projective Geometry. Starting from De Paolis' work we discuss some papers by Segre, Peano, Veronese, Fano and Pieri. In particular we try to show how a totally abstract and general point of view was clearly adopted by the Italian scholars many years before the
The correspondence between the mathematician Luigi Cremona (1830-1903) and Quintino Sella (1827-1... more The correspondence between the mathematician Luigi Cremona (1830-1903) and Quintino Sella (1827-1884) highlights aspects of Sella’s political thought and cultural activity. In particular his aims on Rome “capital of science” and on the Accademia dei Lincei as emblem of national culture, encountered difficulties. In spite of some incomprehensions in the initial phase of their relationship, the harmony of ethical, political and cultural intentions for the progress of the country and the synergies implemented by the two friends led to important results. Among them we can mention the renewal of academic membership with prestigious names of scientists and intellectuals, the establishment of prizes to encourage scientific research, the publication of memoirs of the two classes and the exchanges of periodicals with academies and scientific institutions all over the world.
The correspondence between the mathematician Luigi Cremona (1830-1903) and Quintino Sella (1827-1... more The correspondence between the mathematician Luigi Cremona (1830-1903) and Quintino Sella (1827-1884) highlights aspects of Sella’s political thought and cultural activity. In particular his aims on Rome “capital of science” and on the Accademia dei Lincei as emblem of national culture, encountered difficulties. In spite of some incomprehensions in the initial phase of their relationship, the harmony of ethical, political and cultural intentions for the progress of the country and the synergies implemented by the two friends led to important results. Among them we can mention the renewal of academic membership with prestigious names of scientists and intellectuals, the establishment of prizes to encourage scientific research, the publication of memoirs of the two classes and the exchanges of periodicals with academies and scientific institutions all over the world.
If things had gone according to plan, it should have been an Italian to voice the new ideas since... more If things had gone according to plan, it should have been an Italian to voice the new ideas since no one had come closer to those ideas than the [Italian] school. … In fact it was also an Italian. I realised that only after having completed this essay. Fano had already got there in 1892. He introduces his axiomatic system with words that resonate with Hilbert’s own words that we have quoted above. (Freudenthal 1957) This quotation shows that Italian school had elaborated a point of view on foundations of geometry resonant with Hilbert’s about ten years before the publication of Hilbert’s work. In this talk I will try to reconstruct the link between the Italian geometric tradition on the foundations of geometry, from the work of De Paolis (1881) to the first appearance of Hilbert’s masterpiece (1899). Before beginning, I give a short list of the main features of Italian school:
Luigi Cremona (1830–1903), unanimously considered to be the man who laid the foundations of the p... more Luigi Cremona (1830–1903), unanimously considered to be the man who laid the foundations of the prestigious Italian school of Algebraic Geometry, was active at the University of Bologna from October 1860, when assigned by the Minister Terenzio Mamiani (1799–1885) to cover the Chair of Higher Geometry, until September 1867 when Francesco Brioschi (1824–1897) called him to the Politecnico di Milano. The “Bolognese years” were Cremona’s richest and most significant in terms of scientific production, and, at the same time, were the years when he puts the basis for its most important interventions in the social and political life of the “newborn” kingdom of Italy. In this article we present these different aspects of Cremona’s life, with particular emphasis on the relationship of the geometer of Pavia with the academic life in Bologna, with students and colleagues.
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