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 in te rna t iona l iza t ion 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 m e z z i , m e t o d i e o r g a n i z z a z i o n i c h e e s s e n o n 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

“ In 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)

  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)

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

1914: The composition of the members of the Circolo Matematico di Palermo

  Totale: 924

Italian: 306 (33,4%)

Forein: 618 (66,6%)

German: 140

  American: 140

Austrian: 77

  French: 67 0

100

200

300

400

500

600

700

800

900

1000

1904 1908 1914

Totale

Italiani

Stranieri

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