The first period: 1888 - 1904

The members of the editorial board:

1891: Henri Poincaré entered to belong to “direttivo” of Circolo. (In that way the Rendiconti is the first mathematical journal with an international editorial board: the Acta’s one was only inter scandinavian)

1894: Gösta Mittag-Leffler entered to belong to “direttivo” of Circolo . 1888: New Constitution

Art. 2: [Il Circolo] potrà istituire concorsi a premi e farsi promotore di congress scientifici nelle varie città del regno. [Il Circolo] may establish prize competitions and become a promoter of scientific congress in different cities of the kingdom. Art 17: Editorial Board 20 members (five residents and 15 non residents) Art. 18: elections with a system that guarantees the secrety of the vote. 1888: New Editorial Board

5 from Palermo: Giuseppe and Michele Albeggiani; Francesco Caldarera; Michele Gebbia; Giovan Battista Guccia 3 from Pavia: Eugenio Beltrami; Eugenio Bertini; Felice Casorati; 3 from Pisa: Enrico Betti; Riccardo De Paolis; Vito Volterra 2 from Napoli: Giuseppe Battaglini; Pasquale Del Pezzo 2 from Milano: Francesco Brioschi; Giuseppe Jung 2 from Roma: Valentino Cerruti; Luigi Cremona 2 from Torino: Enrico D’Ovidio; Corrado Segre 1 from Bologna: Salvatore Pincherle A very well distributed arrangement of the best Italian mathematicians! The most important absence is that of the university of Padova: Giuseppe Veronese had joined the Circolo in 1888, Gregorio Ricci will never be a member of it Ulisse Dini and Luigi Bianchi in Pisa will join the Circolo respectively in 1900 and in 1893. The first and the second issue of the Rendiconti

Some papers by Palermitan scholars and papers by Eugène Charles Catalan, Thomas Archer Hirst, Pieter Hendrik Schoute, Corrado Segre (first issue, 1887) and Enrico Betti, George Henri Halphen, Ernest de Jonquières, Camille Jordan, Giuseppe Peano, Henri Poincaré, Corrado Segre, Alexis Starkov, Vito Volterra (second issue, 1888).

Completely international A famous discussion: Veronese and Peano, 1891

On the hyperspaces and non archimedean geometry G. Peano, Lettera aperta al prof. Veronese , 6, 1892. G. Veronese, A proposito di una lettera del prof. Peano , 6, 1892. G. Veronese, Osservazioni sopra una dimostrazione contro il segmento infinitesimo attuale , 6, 1892. G. Peano, Breve replica al prof. Veronese , 6, 1892. Other important contributions on logical problems Cesare Burali Forti, Una questione sui numeri transfiniti , 11, 1897, 154 – 164 (the famous paradox)

Cesare Burali Forti, Il metodo di Grassmann nelle geometria proiettiva , 10, 1896; 11, 1897; 15, 1901. The first contributions of Poincaré

1888, Sur une propiété des fonctions analytiques 189, Sur l’intégration algébrique des équations différentielles du premier ordre et du premier degré 1894, Sur les équations de la physique mathématique 1897, Sur l’intégration algébrique des équations différentielles du premier ordre et du premier degré 1899, Complément à l’Analysis situs 1901, Quelques rémarques sur les groupes continus Picard and the Rendiconti

Three «Revues» from the «Revue Gènerale» 1891 and 1895 (two papers). Particularly « Sur la théorie des surfaces algébriques » in which he presents the papers of Italian geometers. Sur la théorie des groupes et des surfaces algébriques , 9, 1895. Sur les systèmes linéaires de lignes tracées sur une surface algébrique , 13, 1899. The internationalization of the mathematical researches: from 1900

1900: II International Congress (Paris) 1904: III Internazional Congress (Heidelberg) 1908: IV International Congress (Roma) 1904: Congress of Heidelberg

“Il prof. Volterra desidererebbe che il Congresso dei Matematici pel 1908 si tenesse in Italia e precisamente a Roma. Della cosa si parlò ne’ primi di giugno in una riunione di soci Lincei (sezione matematica). Ma da tutti si riconobbe che bisognava intendersi col Circolo Matematico, o meglio con Lei, ed averne i consigli e l’aiuto.” [Cerruti a Guccia 16 luglio 1904]

“ Prof. Volterra would wish that the Congress of Mathematicians 1908 is held in Italy and precisely in Rome. Of what was said in early June at a meeting of shareholders Lincei (mathematics section). But everyone knew that it was necessary to link up with Circolo Matematico di Palermo, or rather with you, and have the advice and help ”

The Congress approves, by acclamation, entrusting the organization to the mathematics section of the Accademia dei Lincei and of the Circolo Matematico di Palermo (respectively to Castelnuovo e Guccia). A. Guerraggio, P. Nastasi Roma 1908: Il congresso internazionale dei matematici , Bollati Boringhieri, 2008. The editorial board till 1909

From Palermo: Giuseppe Albeggiani (from 1888 till his death 1892); Michele Albeggiani (1888 – 1909); Francesco Caldarera (1888 – 1893); Michele Gebbia (1888 – 1909); Francesco Gerbaldi (1894 – 1905); Gabriele Torelli (1894 – 1909) From Italy: Giuseppe Battaglini (Napoli 1888 – 1893); Eugenio Beltrami (Pavia and Roma 1888 – 1890); Eugenio Bertini (Pavia 1888 – 1893); Enrico Betti (Pisa 1888 – 1893); Luigi Bianchi (Pisa 1897 – 1908); Francesco Brioschi (Milano 1888 – 1896); Alfredo Capelli (Napoli 1894 – 1908); Felice Casorati (Pavia 1888 – 1890); Valentino Cerruti (Roma 1888 – 1908); Luigi Cremona (Roma 1888 – 1903); Riccardo De Paolis (Pisa 1888 – 1893); Pasquale Del Pezzo (Napoli 1888 – 1908); Alfonso Del Re (Napoli 1900 – 1908); Ulisse Dini (Pisa 1900 – 1908); Enrico D’Ovidio (Torino 1888 – 1893 and 1906 – 1908); Giuseppe Jung (Milano 1888 – 1899); Gino Loria (Genova 1894 – 1908); Giovanni Maisano (Messina and Palermo 1894 – 1899); Ernesto Pascal (Pavia and Milano 1900 – 1908); Giuseppe Peano (Torino 1894 – 1908); Salvatore Pincherle (Bologna 1888 – 1908); Corrado Segre (Torino 1888 – 1890); Alberto Tonelli (Roma 1900 – 1908); Vito Volterra (Pisa, Torino, Roma 1888 – 1908) From abroad Gösta Mittag Leffler (Stockholm 1894 – 1908); Henri Poincaré (Paris 1891 – 1908) The preparation and the great progress. New members

1904: Max Noether 1905: F. Klein, H.G. Zeuthen, W. Osgood, G. Cantor, J. Lüroth, O. Veblen, G. Darboux, E. Landau, R. Moore 1906: I. Fredholm, E. Borel, M. Fréchet, D. Hilbert, J. Hadamard, J. Wedderburn, 1907: P. Sylow, P. Duhem, K. Hensel, H. Lebesgue 1908: F. Riesz, M. Dehn, E. Zermelo, H. Weyl, Emmy Noether 1909: A. Hurwitz, H. Bohr, W. Sierpinski 1910: L. Bieberbach, R. Courant, F. Hausdorff, G. H. Hardy, W. Burnside 1911: J. Coolidge, Friedrich Noether 1912: B. Russell, G. Polya 1913: H. Steinhaus, G. D. Birkhoff 1914: S. Lefschetz, A.A. H.Fraenkel 1907: an important lunch

Lunch which was held November 3, 1907 at the Restaurant of the Hotel Continental, Paris. At this lunch took part (as you seen from the manuscript of Guccia): C. Darboux, C. Jordan, H. Poincarè, P. Appel, P. Painlevè, G. Humbert, J. Hadamard, G. Borel, D. Andrè, C. Laisant, G. Fouret, J. Drach, L. Olivier, P. Boutroux, besides Guccia. This meeting laid the foundation for the internationalization of the Circolo Matematico di Palermo. An ambitious program? Dreams?

“Qualche altro anno di tempo mi è necessario (e molto lavoro ancora) prima di battere vittoriosamente tutte e quattro le nostre consorelle di Londra, Parigi, New York e Germania! Ma vi riuscirò, se Dio vuole e se la fiducia degli amici non mi vien meno. Vi riuscirò perché noi disponiamo di mezzi, metodi e organizzazioni che esse non hanno” [Guccia a Cerruti, 15 giugno 1906] “I need a few more years (and a lot of work yet) before beating victoriously all four of our sisters in London, Paris, New York and Germany! But I shall succeed, God willing and if the confidence of the friends I Void. We succeed because we have the means, methods and organizations that they have not ”

400 members (were 195, will be 400 in 1906 and 605 in 1908) Guccia Medal Second journal Divulgation History Guccia Medal

“ Ho deciso di fondare un premio per la geometria, che successivamente diverrà molto probabilmente stabile, ma che per cominciare sarà assegnato nel 1908 … Il premio, con il nome di medaglia Guccia, consisterà in una piccola medaglia in oro e in una somma di 3000 franchi in oro. Il premio sarà internazionale. La commissione giudicatrice sarà composta da un italiano (che sarà Segre), da un tedesco (Noether) e da un francese, che vorrei fosse il nostro amico Poincaré ”. [Guccia a Humbert, 19 luglio 1904]

“I decided to establish a prize for geometry, which later will become very likely stable, but that will be assigned to begin in 1908 ... The award, as the medal Guccia, will consist of a small gold medal and a sum of 3,000 francs in gold. The award will be international. The jury will be composed of an Italian (which will Segre), a German (Noether) and by a Frenchman, that I would like our friend Poincaré ” Journal of Applied Mathematics

“Sorge dunque naturale la idea che anche in Italia qualche cosa di serio si faccia per le matematiche applicate … Vogliamo che le applicazioni si traggano dalle più alte e moderne scoverte delle matematiche pure, non mai dalla matematica elementare o media, perché in tal caso si andrebbe subito giù … si comprenderebbe qualunque cosa ! … I vecchi nostri Rendiconti ( organo per le matematiche pure ) già tanto accreditati, servirebbero ad accreditare in poco tempo i nuovi Rendiconti , che si pubblicherebbero parallelamente, col titolo : « Organo per le matematiche applicate » o altro equivalente .” [Guccia a Cerruti del 11 giugno 1905]

“ Rises therefore the natural idea that even in Italy something serious is done for applied mathematics ... We want that applications be drawn from the highest and modern discoveries of pure mathematics, never from mathematics elementary or middle, because in that case you should straight down ... it would include whatever! ... The old our Rendiconti (journal for the pure mathematics) already so accredited, would serve to credit in a short time the new Rendiconti, which would publish in parallel, with the title: ”Journal for applied mathematics” or equivalent ” The popularization of Mathematics

“Non ho abbandonato l’idea della quale vi ho parlato ultimamente all’Hotel Continental, cioè di pubblicare ogni anno nell’Annuario (che si diffonde gratuitamente in un numero grandissimo di esemplari) un articolo di un maestro della Scienza su di un argomento che possa interessare anche coloro che hanno che una modesta cultura scientifica. … Il legame tra scienza pura e scienza applicata sfugge al grande pubblico e scienza applicata sfugge al grande pubblico e, talvolta, anche agli studiosi. Sarebbe quindi utile, secondo me, di fare bene risaltare (indirizzandosi al grande pubblico) tutto ciò che proviene a pieno diritto dalla matematica superiore nelle grandi scoperte moderne di ordine pratico” [Guccia a Poincaré, 19 dicembre 1905]

He proposed to Mittag Leffler a paper on the work of Weierstrass The popularization of Mathematics

I have not abandoned the idea of which I spoke recently at the Hotel Continental, which is published annually in the Annuario (which spreads for free in a very large number of specimens) an article by a master of Science on a topic that can also interest those who have a modest scientific culture. ... The link between pure science and applied science escapes to the general public and, sometimes, even to researcher. It would therefore be useful, in my opinion, to do well stand (addressing the general public) everything that comes in its own right by the higher mathematics in the great discoveries of modern practical. [Guccia a Poincaré, 19 dicembre 1905]

He proposed to Mittag Leffler a paper on the work of Weierstrass

The History

“Percorrendo il suo opuscolo «Carteggio di Paolo Ruffini» … ho ripensato ad una mia vecchia idea, cioè la ristampa di tutte le opere di Ruffini nei nostri Rendiconti … Di ciò ebbi a scrivere, or fa un anno, al Vailati, ma questi occupato come era ed è … mi scrisse di non potersene occupare. Sarebbe ella disposta di raccogliere e ordinare le opere di Ruffini e di curarne la ristampa nei nostri Rendiconti ?” [Guccia a Bortolotti 3 dicembre 1906]

“Going through your brochure "Correspondence of Paolo Ruffini”... I thought back to an old idea, that is the reprint of all the works of Ruffini in our Rendiconti ... Of what I wrote a year ago, to Vailati, but he was busy as and he is ... he wrote me not being able to occupy. Would you be willing to collect and sort the works of Ruffini and to have reprinted it in our Rendiconti ?

The cultural policy of Rendiconti after 1904: Opening to the young

“ I n any case - and this is one of the most remarkable among the great and immortal merits of Guccia - he always judged mathematicians solely from their papers, without worrying about their age, or their official position; he has helped many beginners - as I was a dozen years ago - to publish their research in his important journal and to have confidence in themselves. I came here to thank the Circolo Matematico – that is Guccia – for the fact that he has created, to many mathematicians, their position in science” [E. Landau, 14 Aprile 1914]

M. Fréchet, Sur quelques points du calcul fonctionnel , 1906 Introduction axiomatic of metric spaces. E. Borel, Les probabilités dénombrables et leurs applications arithmétiques , 1909 The cultural policy of Rendiconti after 1904: Applied Mathematics

Levi – Civita: Sopra un problema di elettrostatica che si è presentato nella costruzione di cavi , 20, 1905 G. Colonnetti: Sul moto di un liquido in un canale , 32, 1911

“Io spero di poter dare ai Rendiconti maggiore estensione nel campo delle applicazioni delle matematiche superiori moderne. La memoria di Levi Civita fu il primo passo verso questo ordine di idee; come un altro importantissimo lavoro [di Poincaré]che comparirà[…] ” [Guccia a Colonnetti, 24 febbraio 1906] “I hope to extend the contributions of the Rendiconti in the field of modern higher applied mathematics, following a continually growing trend. The paper by Levi Civita was a first step taken in this order of ideas; as well as another very important paper [of Poincaré]…. which will pubblished […]” The cultural policy of Rendiconti after 1904: The Theory of Relativity

H. Poincaré, Sur la dynamique de l’électron, 21, 1906 M. Abraham, Zur Elektrodynamik bewegter Korper, 28, 1909 M. Abraham, Sull’elettrodinamica di Minkowski, 30, 1910 T. Levi Civita, Nozione di parallelismo su una varietà qualunque, 42, 1917 A. Palatini, Sui fondamenti del calcolo differenziale assoluto, 43, 1919 A. Palatini, Deduzione invariantiva delle equazioni gravitazionali dal principio di Hamilton, 43, 1919 Two comments: A. Logunov 1984, G. Weinstein 2012

Why to such a far away paper that is not even a physics newspaper ? Above all because the Director of this journal was his friend, but also because the physicists of this time considered Henri Poincaré as a mathematician, and a mathematician cannot write in a physics journal! Consequently that work - the founding work of relativity - will remain almost ignored during the beginning of the twentieth century. [A. Logunov, 1984]

“A very strange note: On July 23, 1905 Poincaré submitted the second paper – published only in 1906 – to an obscure Italian journal by the name, Rendiconti del Circolo matematico di Palermo.” [G. Weinstein, 2012]

The contributions of Poincaré to the Rendiconti, 1904 – 1912

1904, Cinquième complément à l’Analysis situs (famous conjecture) 1906, Sur la dynamique des électrons 1907, Les fonctions analytiques de deux variables et la représentation conforme 1908, Nouvelles rémarques sur les groupes continus 1908, L’avenir des mathématiques 1909, Sur la réduction des intégrales abéliennes et les fonctions fuchsiennes 1910, Sur la diffraction des ondes hertziennes 1911, Rapport sur le prix Bolyai 1912, Sur un théorème de géométrie Poincaré su Les Temps

“For about thirty years the mathematician activity in Italy is very intense ... seeing them together in this congress we realize better than it has been in recent times the activity of the Italian scientific life ... I can not, however, appoint ... Volterra, the famous analyst, or Castelnuovo, Enriques and Severi that they are doing to make a decisive step to the theory of surface nor especially Guccia ... who founded an international mathematics society and one of the most renowned mathematics journal around the world .” April, 21, 1908 A bitter disappointment «Quant au Congrès de Rome, ainsi que vous l’avez pu remarquer sur la place, notre Société c’est effacée dès que dans la Séance d’inauguration l’Académie des Lincei a fait annoncer par son President qu’elle prenait la direction du Congrès. Cette circonstance, aussi imprévue que bizarre, étant en désaccord avec les circulaires précédents, a un peu étonné le public. Il fallait donc, sans faire du bruit, sauvegarder la dignité de notre grande association internationale … qui jouit, à tous les points de vue, d’une grande indépendance, et à laquelle appartiennent les plus illustres et célèbres mathématiciens du monde entier. Je ne crois pas donc avoir mal agi, dans ma qualité de délégué du Circolo au Congrès, en résiliant, sous un prétexte avouable et vraisemblable … nos accords avec le Comité d’organisation … La seule chose qui m’est vraiment pénible dans cette affaire, c’est que, parmi les membres du Comité “organisateur” (le seul responsable vis-àvis du public) il y avait trois membres du Conseil de Direction du Circolo, qui sont de mes bons et excellents amis, mais qui, dans la circonstance, ont oublié tout à fait notre Société! Entre l’Accademia dei Lincei, illustre et célèbre qui s’occupe de tout, même du fromage «Gorgonzola» et notre modeste société qui ne s’occupe d’autre que des mathématiques le choix n’était pas douteux pour eux: ils se sont tournés vers l’Académie, pour accroître sa gloire à l’occasion du Congrès.» [Guccia a Mittag-Leffler 12 luglio 1908] A bitter disappointment

“Regarding the Congress of Rome, as you may have noticed, our Society has been troubled because, during the inaugural session, the President of the Accademia dei Lincei announced that it had undertaken the organization of the Congress. This fact, unexpected and strange, contradicted the previous circular letters and amazed the audience. It was necessary, without any fuss, to safeguard the dignity of our great international association…which is, from every point of view, greatly autonomous, and which has among, its members the most famous and illustrious mathematicians in the world. I don’t think that I have done anything wrong, in my capacity as representative of the Circolo at the Congress, in recinding, advancing a likely excuse, …our agreements with the organizational Committee…The only thing that I find really painful in this affair is that among the members of the the organizational Committee…there were three members of the Circolo’s editorial board, who are my good friends, but who on this occasion completely forgot our Society! Between the Accademia dei Lincei (renowned and famous) which is interested in everything, even Gorgonzola cheese, and our modest Society which is interested only in mathematics, they had no doubt: they sided with the Accademia, to advance its reputation on the occasion of the Congress .” [Guccia a Mittag-Leffler 12 luglio 1908]

The answer: the “direttivo” of 1909 Even more internationalization

From Palermo: G. B. Guccia, E. Ovazza, G. Scorza, M. Gebbia Italian 15 : G. Bagnera (Palermo), M. De Franchis (Catania), C. Segre e C. Somigliana (Torino), G. Loria (Genova), G. Vivanti (Pavia), T. Levi-Civita e F. Severi (Padova), F. Enriques e S. Pincherle (Bologna), E. Bertini, L. Bianchi e U. Dini (Pisa), R. Marcolongo ed E. Pascal (Napoli) French 5 : È. Borel, J. Hadamard, G. Humbert, È. Picard e H. Poincaré (Paris) German 6: D. Hilbert, E. Landau e F. Klein (Göttingen), C. Caratheodory (Hannover), M. Noether (Erlangen), P. Stæckel (Karlsruhe) The answer: the “direttivo” of 1909 Even more internationalization

English 2: A. R. Forsyth (Cambridge) e A. Love (Oxford) Austria-Hungary 3: L. Fejer (Koloszovar), F. Mertens e W. Wirtinger (Vienna) U.S.A. 2: E. H. Moore (Chicago) e W. Osgood (Cambridge- Mass) Russian 2: A. Liapunov e A. Steklov (S. Pietroburgo) Sweden 2: E. I. Fredholm e G. Mittag-Leffler (Stoccolma) Greece 1: Stéphanos (Atene) Belgium 1: C. J. de la Vallée Poussin (Lovanio) Denmark 1: H. G. Zeuthen (Copenhagen) 1914: The composition of the members of the Circolo Matematico di Palermo

Totale: 924 1000 Italian: 306 (33,4%) 900 800 Forein: 618 (66,6%) 700 600 German: 140 Totale 500 Italiani 400 American: 140 Stranieri 300 Austrian: 77 200 100 French: 67 0 1904 1908 1914 Comparison between the principal mathematical associations (1914)

Circolo matematico di Palermo 924 Deutsche Mathematiker Vereinigung 769 American Mathematical Society 703 London Mathematical Society 320 Société Mathématique de France 298 30° anniversary of Circolo Matematico of Palermo

“We celebrate the jubilee of a company that has only a minority of its members in the city where he lives, but which brought together nearly a thousand mathematicians around the world and, among these, the greatest and most distinguished researcher of Italy, of Germany, of England, of France, of United States, of Hungary and of all the nations where it is grown our science. It is the only permanent organization that we have; so we consider Palermo as the center of the mathematical world. The reason lies mainly in the journal, the Rendiconti, which the Circolo Matematico public under the direction of its founder, Mr. Guccia, which enshrined in this direction the work of the last thirty years. Aware of all the chapters of mathematics, no one better than he could devote himself to this task. The statements are now the best mathematical journal in the world .

[E. Landau, 14 Aprile 1914. On the occasion of the 30th anniversary of the founding of Circolo Matematico ]

The reasons for the success: Palermo Liberty

The Sicily at the end of the XIX century: an international atmosphere

The Florio family and industrial development: shipyards, shipping, furniture, Marsala, sulfur.

The intellectual side: the architect Ernesto Basile, Luigi Pirandello (Nobel prize)

1893: The international exhibition

1897: The opening of the Teatro Massimo The Circolo Matematico of Palermo Liberty The reasons for the success: the development of the italian mathematics

National independence and international insertion Francesco Brioschi (1824-1897): Foundation of the “Politecnico of Milano” 1863 Enrico Betti (1823-1892): diffusion of the Galois theory and of the work of Riemann Luigi Cremona (1830-1903) Felice Casorati (1835-1890): The work of Weierstrass. Eugenio Beltrami (1836-1890): non-euclidean geometry Two main aspects: political commitment and strong international links To conclude: the «testament» of Poincaré

December 1911 To conclude: the «testament» of Poincaré

My dear friend, I told you, during your last visit, about a paper in which I was behind by more than two years. I don’t moved on and I decided to leave him temporarily to give him the time to mature. Everything would be fine, if I were sure to being able to resume; at my age, I can no longer answer; and the results obtained, are susceptible to put researchers on a new and unexplored direction, appear to me too full of promise, despite the disappointments that have given me, and therefore I resign myself to sacrifice them. In these conditions, would you find a convenient publish a Memoria in which I would lay the goal that I pursued, the problem that I have proposed, and the results of the efforts that I made to solve them? This would be a little unusual, but perhaps it can be useful. What embarazzed me is that I would be have to put many figures, because I was not able to find a general rule, but I've only accumulated the particular solutions. Tell me, I pray yoy, what you do you think and what do you recommend. Your devoted friend, Poincaré . December 1911