Luigi Cremona’s Years in Bologna: From Research to Social Commitment

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 thes…

Remarks on the relations between the Italian and American schools of algebraic geometry in the first decades of the 20th century

Abstract In this paper we give an overview of the interactions between Italian and American algebraic geometers during the first decades of the 20th century. We focus on three mathematicians—Julian L. Coolidge, Solomon Lefschetz, and Oscar Zariski—whose relations with the Italian school were quite intense. More generally, we discuss the importance of this influence in the development of algebraic geometry in the first half of the 20th century.

Intuition and rigor in mathematics education (reaction to Tirosh and Tsamir plenary lecture)

The Annali di Matematica and the Rendiconti del Circolo Matematico di Palermo: two different steps in the dissemination and progress of mathematics in Italy

Luigi Cremona's Years in Bologna: From Research to Social Commitment

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 it 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 d…

The Foundations of Projective Geometry in Italy from De Paolis to Pieri

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 publication of Hilbert's Grundlagen. We are particularly interested in the interrelations between the Italian and the German schools (mainly the influence of Staudt's and Klein's works). We try also to understand the reason of the steady decline of the Italian school during the twentieth century.

Science and Imagination: n-dimensional geometry in 19th century

Picard et les géomètres italiens: histoire des deux prix Bordin

Dans mon intervention je chercherai à mettre au point la question des rapports entre Picard et les géomètres algébriques italiens, en particulier Enriques, Castelnuovo et Severi, en montrant comment si, d'un côté, les thèmes de recherche se croisent, d'un autre ils ont été développés en utilisant des langages mathématiques profondément différents au point de rendre parfois impossible ou presque la compréhension réciproque. Je chercherai aussi à donner un aperçu des rapports en théorie des nombres entre Picard et Bianchi et de l'influence de Corrado Segre et Fano sur Cartan qui à son tour eut une profonde influence sur Benjamin Segre.

Apollonius de Pergé, Coniques. Tome 4: Livres VI et VII. Commentaire historique et mathématique. Édition et traduction du texte arabe by Roshdi Rashed

Review del volume Apollonius de Pergé, Coniques. Tome 4: Livres VI et VII. Commentaire historique et mathématique. Édition et traduction du texte arabe by Roshdi Rashed Berlin/New York: De Gruyter, 2009.

Segre and the Foundations of Geometry: From Complex Projective Geometry to Dual Numbers

In 1886 Corrado Segre wrote to Felix Klein about his intention to study ‘geometrie projective pure’, completing and developing the work of von Staudt. He would continue this research project throughout the whole of his scientific life. In 1889, following a suggestion of Segre, Mario Pieri published his translation of the Geometrie der Lage, and from 1889 to 1890 Segre published four important papers, “Un nuovo campo di ricerche geometriche”, in which he completely developed complex projective geometry, considering new mathematical objects such as antiprojectivities and studying the Hermitian forms from a geometrical point of view with the related ‘hyperalgebraic varieties’. Segre developed …

Introduzione

La Matematica per crescere. Corso di Matematica per la Scuola Secondaria di primo grado

Il programma di Erlangen di Felix Klein: origini e sviluppi successivi

L'opera politica di Luigi Cremona attraverso la sua corrispondenza, Prima Parte. Gli anni dell'entusiasmo e della creatività

Remarks on the Historiography of Mathematics

In this paper, I examine aspects of the methodological debate that originated in 2010, when the distinguished historian of mathematics Sabetai Unguru reviewed Roshdi Rashed’s edition of the Arabic translation of Apollonius’ Conics. In his review, Unguru criticized what Rashed calls “l’usage instrumental d’une autre mathématique pour commenter une oeuvre ancienne”. I consider this debate very important and will try to place it within in the discussion of the so-called “geometric algebra” that goes back to the seventies, by tracing the contributions of the main figures who took part in it. Published Online (2021-04-30)Copyright © 2021 by Aldo Brigaglia Article PDF Link: https://jps.library.ut…

The Luigi Cremona Archive of the Mazzini Institute of Genoa

Abstract Luigi Cremona (1830–1903) is unanimously considered to be the man who laid the foundations of the prestigious Italian school of Algebraic Geometry. In this paper we draw attention to the “Legato Itala Cremona Cozzolino”, which was given to the library of the Mazzini Institute, Genoa, Italy, by Cremona’s daughter, Itala, probably in 1939. This legacy, which contains over 6000 documents, mainly consisting of Cremona’s correspondence with scientific and institutional Italian interlocutors, can help us to understand the connections between the development of Italian mathematics in the second half of the XIX century and the main political issues of Italian history.

L'influenza di Peano sulla matematica palermitana

Historical Notes on Star Geometry in Mathematics, Art and Nature

Gamma: “I can. Look at this Counterexample 3: a star-polyhedron I shall call it urchin. This consists of 12 star-pentagons. It has 12 vertices, 30 edges, and 12 pentagonal faces-you may check it if you like by counting. Thus the Descartes-Euler thesis is not true at all, since for this polyhedron \(V - E + F = - 6\)”. Delta: “Why do you think that your ‘urchin’ is a polyhedron?” Gamma: “Do you not see? This is a polyhedron, whose faces are the twelve star-pentagons”. Delta: “But then you do not even know what a polygon is! A star-pentagon is certainly not a polygon!”

Matematica per crescere

La similitudine nella scuola secondaria: un percorso didattico multidisciplinare

La conica per nove punti: il contributo di Beltrami. Considerazioni storiche e didattiche

L’avvento dei software di Geometria dinamica ha ridato attualità al valore didattico, ma più in generale formativo, di molti aspetti della Geometria elementare, in voga soprattutto fino ai primi anni dello scorso secolo. Tra i numerosi ed interessanti argomenti di Geometria elementare, intendiamo qui approfondire quello legato alla “conica per nove punti”, soggetto spesso “riscoperto” nel corso del tempo. Lo scopo di questo intervento è duplice: innanzitutto abbiamo provato a ricostruire il reale sviluppo storico dello studio della conica per nove punti, per la sua rilevanza sia sul piano storiografico, sia su quello didattico e divulgativo. In secondo luogo, presentiamo alcune importanti r…

Dalla riga e il compasso alla Geometria Dinamica: considerazioni comparative sull'uso degli strumenti in matematica

Le scienze matematiche in Sicilia dal riformismo settecentesco all'unità nazionale

Il movimento e le macro in Cabri Géomètre

Luigi Cremona e la nuova scuola della nuova Italia: dagli obiettivi ai contenuti e alla loro valutazione

I software geometrici e la tradizione euclidea. Rottura o continuità?

Matematica, Immaginazione, e Modelli: la Comuniocazione dell'Idea di Iperspazio da Helmholtz a Flatland

L'opera matematica

An Overview on Italian Arithmetic after the Disquisitiones Arithmeticae

Thedecades around 1800were not a period inwhich puremathematics in general, and number theory in particular, flourished in Italy, see [Bottazzini 1994]. It is significant in this respect that Joseph Louis Lagrange, whose birth and early studies took place in Torino, finally became a prominent representative of the Frenchmathematical school and that, decades later, Guglielmo Libri still spent most of his academic career in France. Thus, Gauss’s Disquisitiones Arithmeticae did not have an immediate resonance in Italian mathematical circles. Gianfrancesco Malfatti, a professor in Ferrara, already seventy years old at the time of the publication of theDisquisitiones Arithmeticae, was one of the…

Veronese e la teoria degli iperspazi

Il Circolo Matematico che diede lustro e poi Fastidio a Palermo

La mamma dell'algebra

Saccheri vu par Corrado Segre en Italie et par Mansion et Bosmans en Belgique

Brigaglia Aldo, Gaino Bruna, Radelet-de-Grave Patricia. Saccheri vu par Corrado Segre en Italie et par Mansion et Bosmans en Belgique. In: Bulletin de la Classe des sciences, tome 21, 2010. Le Père Henri Bosmans SJ (1852-1928) historien des mathématiques. pp. 83-104.

Mario Pieri e la Scuola di Corrado Segre

Due modi diversi di essere caposcuola

La Matematica per crescere. Corso di matematica per la Scuola Secondaria di primo grado. Il computer per la Geometria

Da Cremona a Castelnuovo. Continuità e discontinuità nella visione della scuola.

Per una biografia scientifica di Corrado Segre

Dall'inversione alle trasformazioni quadratiche

Dall'inversione alle trasformazioni quadratiche Aldo Brigaglia (Università di Palermo) brig@math.unipa.it La inversione (o trasformazione per raggi vettori reciproci) è 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’origine 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’ sulla semiretta AB tale che AB’ 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 è il diametro del…

L'opera politica di Luigi Cremona attraverso la sua corrispondenza II Il crollo delle speranze e il lavoro organizzativo

The Influence of H. Grassmann on Italian Projective N-Dimensional Geometry

On May 29, 1883, Corrado Segre took his doctorate in Turin (Torino), under Enrico D’Ovidio’s guidance. His thesis (Segre 1884a,b) was published one year later in the Journal of the local Academy of Science, and after a short time it became a fundamental starting point for the development of Italian projective n-dimensional geometry.

Emmy Noether. The mother of algebra

Introduzione

Picard and the Italian Mathematicians: The History of Three Prix Bordin

It is usually said that in the transition period between 19th and 20th centuries, French scholars (mainly Picard and Humbert) as well as Italian scholars (mainly Castelnuovo, Enriques and Severi) were interested in the study of algebraic surfaces, though using different methods.

Il Circolo Matematico che dette lustro e poi fastidio a Palermo Seconda Parte

Matematica, dimostrazione, verità: qualche considerazione

The “Circolo Matematico di Palermo” and the First World War: The crisis of scientific internationalism: a view through the unedited correspondence of De Franchis with Edmund Landau and other mathematicians

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.

Foundations of geometry in Italy before Hilbert

I matematici italiani e i "misteri riemanniani". La geometria italiana della prima metà del XX secolo tra intuizione e rigore

La permanenza di Riemann a Pisa, i suoi rapporti diretti con Enrico Betti e, indiretti, con Beltrami, Casorati e Cremona portarono mutamenti profondi in tutti i campi della matematica (e della filosofia della matematica) italiane. Nel mio intervento focalizzerò l’attenzione su alcuni punti, soprattutto riguardo la geometria algebrica italiana e i suoi rapporti con l’analisi complessa nei primi trenta anni del XX secolo, nonché il formarsi di un modo “italiano” di guardare alla geometria. Un esame accurato dello sviluppo storico della geometria italiana non può prescindere dall’esame degli apporti determinanti dati dalle scuole tedesca e francese allo sviluppo dell’interpretazione geometrica…