For science and for the Pope-king: writing the history of the exact sciences in nineteenth-century Rome

This paper analyses the contents and the style of the Bullettino di bibliografia e di storia delle scienze matematiche e fisiche (1868–1887), the first journal entirely devoted to the history of mathematics. It is argued that its innovative and controversial methodological approach cannot be properly understood without considering the cultural conditions in which the journal was conceived and realized. The style of the Bullettino was far from being the mere outcome of the eccentric personality of its editor, Prince Baldassarre Boncompagni. Rather, it reflected in many ways, at the level of historiography of science, the struggle of the official Roman Catholic culture against the growing secularization of knowledge and society. While history of mathematics was a well-established discipline by the mid-nineteenth century, no periodical which was entirely devoted to such a discipline existed until 1868. By then, history of mathematics had been the subject of monographic studies, of erudite articles to be included in scientific journals and of memoirs to be included in the acts of scientific academies. An attempt to establish a specific periodical where historians of the exact sciences could publish their work was made by the French mathematician Orly Terquem (1782–1862), director of the Nouvelles annales des matheUmatiques. From 1855 to 1862, the Nouvelles annales included a supplement entitled Bulletin de bibliographie, d ’histoire et de geUographie matheUmatiques, which provided information relative to episodes in the history of mathematics." However, the dimension of the supplement was rather limited, and its contents were little more than a collection of historical curiosities, which is why historians such as George Sarton have described the Bulletin as scarcely an interesting publication.# In 1868 a journal began to be printed which was unprecedented for its remarkable scope, its scientific rigour and its international group of collaborators. * Dibner Institute for the History of Science and Technology, MIT E56-100, Cambridge, MA 02139, USA. I thank David Bloor, John Fauvel, John Henry, Ludovica Serratrice, and the anonymous referees for advice and assistance. Research for this paper was made possible through the support of the Dibner Institute and the resources of the Burndy Library. All translations from non-English sources, unless otherwise indicated, are my own. 1 Terquem’s Bulletin was published as supplement to Volumes 14 to 20 of the first series of the Annales (1855–61), and to the first volume of the Second Series (1862). The Annales were published in Paris by MalletBachelier. 2 G. Sarton, ‘Bibliographie synthe! tique des revues et des collections de livres ’, Isis (1914–1919), 2, 125–61, 133. 258 Massimo Mazzotti Its title was Bullettino di bibliografia e di storia delle scienze matematiche e fisiche, and it was to be remembered as ‘ the first major journal devoted to the history of mathematics ’.$ It may come as a surprise that it was published in Rome, at that time the capital of the ultra-conservative State of the Church, over which Pope Pius IX (r. 1846–78) ruled as an absolute temporal sovereign. In fact, mid-nineteenth century Rome was far from being a leading centre of mathematical research. Its cultural environment has been convincingly described as one hardly favourable to up-to-date literary and philosophical production, let alone advanced scientific research. The Bullettino was exceptional in many respects, beginning with the very fact that it was conceived and published in the Rome of the last Pope-king. Two main issues will be addressed in the present study. The first is the general methodology adopted by those who contributed to the Bullettino. Understanding this should help to make sense of the many peculiarities of the Bullettino, which are to be found in both its contents and its format. We shall see that the journal presented a consistent and paradigmatic example of the general approach to history that came to be known as ‘positivistic historiography’, a methodology based on the centrality of the documents and on the scrupulous analysis of data and sources. Underlying this new attention to data collection was an awareness of the mass of archival material still to be studied, and the basic belief that ‘ the documents ’ would reveal ‘ the facts ’. The second issue addressed in this study is an assessment of the socio-cultural situation in which the editorial enterprise of the Bullettino was conceived and realized. I shall argue that the emergence of the new, ‘scientific ’ historiographical methodology, through which history of science was fully legitimated as a truly scientific discipline, can be properly understood only by evaluating the socio-cultural context of its production. That the ‘positivistic ’ methodology promoted by the Bullettino was particularly successful in the Rome of the last Pope-king was indeed far from being a coincidence. A Roman prince’s dream Much has been written on the claustrophobic cultural atmosphere of the years preceding the end of the temporal power of the Church of Rome (1870). ‘Books are not stuff for Christians ’, a priest declaims in a sarcastic sonnet by Roman poet Gioacchino Belli. Similarly, Giacomo Leopardi wrote about ‘Rome, where nothing is understood apart from stones’.% ‘Editorial activity ’, remarked Domenico Gnoli, referring to the middle of the century, ‘was forbidden rather than controlled’ ; there existed indeed ‘a preventive censorship that was both ecclesiastical and political ’.& Exceptional, in this respect, were the highly specialized and remarkably expensive archaeological publications, which continued 3 I. Grattan-Guinness, ‘Talepiece : the history of mathematics and its own history ’, in Companion Encyclopaedia of the History and Philosophy of the Mathematical Sciences I. Grattan-Guinness (ed.), 2 vols., London, 1997, ii, 1667. 4 Quoted in F. Barberi, ‘Libri e stampatori nella Roma dei papi ’, Studi romani (1965), 13, 433–56, 454. 5 D. Gnoli, I poeti della scuola romana (1850–1870), Bari, 1913, 6. For science and for the Pope-king 259 to flourish even in this period. On the other hand, the state of studies on modern literature, history and the sciences has been defined as ‘squalid ’.' It was in such an unpromising environment that the Bullettino first appeared in 1868. By the time the publication ended, in 1887, twenty massive quarto volumes had been completed, for a total of more than thirteen thousand pages. The methodological novelties of this periodical and its substantial contribution to the historiography of the exact sciences make it interesting not only to historians of scientific publishing but also to those working in the history of scientific knowledge tout court. Let us approach the Bullettino by describing the singular figure of its founder, financier and editor, Baldassarre Boncompagni Ludovisi, Prince of Piombino (1821–94). Boncompagni was born into one of the wealthiest and most eminent Roman families, ennobled in 1572 when one of its members was made Pope as Gregorius XIII. He studied under the guidance of some well-known men of science, such as Abbe! Barnaba Tortolini (1808–74), professor of calcolo sublime (higher calculus) at La Sapienza University in Rome, and the Jesuit astronomer Ignazio Calandrelli (1792–1866). Abbe! Tortolini, author of a number of memoirs and of a textbook of calculus (1844), was the most prominent mathematician active in Rome in the middle of the century.( In 1850 he founded the journal Annali di scienze matematiche e fisiche, and it is from a transformation of this periodical that, in 1858, the prestigious Annali di matematica pura e applicata was born.) In 1840, while studying mathematics, Boncompagni began to collaborate with the literary journal Giornale arcadico di scienze, lettere e arti, publishing the biographical notes of the Jesuit astronomer Giuseppe Calandrelli (1749–1827) and of his assistant Andrea Conti (1777–1840). In 1843, Boncompagni ’s first study appeared, in a prestigious journal of mathematics, the Journal fuX r die reine und angewandte Mathematik, directed by August Leopold Crelle. It was a dense memoir on definite integrals ; in fact, it remained 6 Barberi, op. cit. (4), 454. Barberi remarks that in Rome 800 new works were published between 1835 and 1844, while 4900 were published in Milan, 3300 in Venice, 2300 in Turin, 1700 in Naples and 1350 in Florence. Similarly, in the periodical sector, the inferiority of Rome with respect to the northern Italian towns was clear. On the periodical press in Rome in this period see also O. Majolo Molinari, La stampa periodica romana dell ’Ottocento, 2 vols., Rome, 1963. 7 B. Tortolini, Elementi di calcolo infinitesimale, Rome, 1844. The indication ‘Volume 1: differential calculus ’ is added, but no other volumes followed it. Tortolini wrote on the foundations of calculus, on the applications of calculus to geometry and on problems of mathematical physics. He showed particular interest in expanding the application of Cauchy’s methods for the integration of differential equations. Tortolini began teaching calculus at La Sapienza in 1837, in 1846 he was also teaching mathematical physics at the Seminario Romano and in 1856 he added to these duties the direction of the printing office of the Propaganda Fide. As for his ecclesiastical career, in 1866 he became canonico titolare of the Basilica of Santa Maria ad Martyres (hence the title of ‘Monsignore’). On Tortolini ’s life and religious activity see V. Diorio, ‘Cenni intorno alla vita ed ai lavori di monsignore D. Barnaba Tortolini ’, Atti dell ’Accademia Pontificia de’ Nuovi Lincei (1875), 28, 93–106, which includes a complete list of Tortolini ’s memoirs. 8 Tortolini ’s annali ceased publication in 1857. In 1858 Tortolini became one of the four editors of a new journal, the Annali di matematica pura e applicata, together with Enrico Betti in Pisa, Francesco Brioschi in Pavia and Angelo Genocchi in Turin. The foundation of the new journal provided recognition and legitimation to the ‘ Italian school ’ of mathematics. The journal was conceived as the instrument with which to establish fruitful relations with the most advanced European schools, primarily the German school. On the deeply political programme of the new journal, and the less than enthusiastic participation of Tortolini to the enterprise, see U. Bottazzini, Va’ pensiero: immagini della matematica nell ’Italia dell ’Ottocento, Bologna, 1994, 124–7. 260 Massimo Mazzotti Figure 1. Baldassarre Boncompagni (1821–94). his most significant contribution to mathematical research.* After the mid-1840s Boncompagni ’s interest decidedly shifted towards the history of the exact sciences, and in 1846 he published an essay ‘On some advancements of physics in Italy in the sixteenth and seventeenth centuries ’."! Here Boncompagni argued for the importance of studying the history of scientific knowledge, ‘as it is not less important to know about the state of scientific studies in different times and in different countries ’ than to know about political and literary history. ‘The history of sciences ’, he argued, following Francis Bacon, ‘ is the eye of the history of the world’. From around 1850 Boncompagni ’s publications were to be mostly devoted to reconstructing the chronology and the channels of the transmission of mathematical knowledge from the Arabic world to Christian Europe. Such research was articulated in 9 B. Boncompagni, ‘Recherches sur les inte! grales de! finies ’, Journal fuX r die reine und angewandte Mathematik (1843), 25, 74–96. 10 B. Boncompagni, ‘ Intorno ad alcuni avanzamenti della fisica in Italia nei secoli XVI e XVII ’, Giornale arcadico di scienze, lettere ed arti (1846), 109, 3–48. For science and for the Pope-king 261 a number of meticulous studies on scarcely known translators and mathematical practitioners who were active in Italy in the twelfth and thirteenth centuries, such as Guido Bonatti, Platone Tiburtino, Gherardo da Cremona, and Gherardo da Sabbioneta. Boncompagni addressed a number of questions about the chronology of their works, their biographical data and their specific contributions to the mathematical sciences."" But it was Boncompagni ’s essay (1851–2) on Leonardo Pisano, also known as Fibonacci, that earned him the admiration of those working in the history of the exact sciences. Not only did Boncompagni carefully reconstruct the biography of this hitherto obscure figure, but he also assessed his scientific role in all its historical relevance."# In addition to his personal contributions, Boncompagni acted as a supporter and financier of studies in the history of the mathematical sciences. It has been correctly remarked that his role went well beyond that of a patron, and that he rather acted as a ‘cultural organizer ’."$ The main objectives of Boncompagni seem to have been to further the diffusion of the study of medieval mathematics and, as we shall see, to support the pontifical cultural institutions. A crucial instrument of this ambitious project was the Tipografia delle Scienze Matematiche e Fisiche (Printing Office of the Mathematical and Physical Sciences), founded by Boncompagni around 1850."% In this printing office historical and scientific essays were published, and also a number of scientific correspondences, bibliographies and transcriptions of medieval manuscripts."& Among the periodicals which were published by Boncompagni were not only the Bullettino but also, from 1871, the Atti dell ’Accademia Pontificia dei Nuovi Lincei (Acts of the Pontifical Academy of the New Lincei), official organ of the scientific culture of the Vatican, and the Bullettino metereologico, periodical of the observatory of the Collegio Romano, edited by the Jesuit Angelo Secchi. In addition to this publishing activity, Boncompagni assembled a remarkable library specializing in the history of the exact sciences. The library reached the size of around 11 B. Boncompagni, Della vita e delle opere di Guido Bonatti, astrologo e astronomo del secolo decimoterzo, Rome, 1851; idem, ‘Delle versioni fatte da Platone Tiburtino, traduttore del secolo duodecimo’, Atti dell ’Accademia Pontificia dei Nuovi Lincei (1850–1), 4, 247–86; idem, ‘Della vita e delle opere di Gherardo Cremonese, traduttore del secolo decimo secondo, e di Gherardo da Sabbioneta, astronomo del secolo decimoterzo’, ibid. 387–493. 12 B. Boncompagni, ‘Della vita e delle opere di Leonardo Pisano, matematico del secolo decimoterzo’, Atti dell ’Accademia Pontificia dei Nuovi lincei (1851–2), 5, 208–45. Boncompagni also edited Leonardo Pisano’s writings ; see B. Boncompagni (ed.), Opuscoli di Leonardo Pisano, Florence, 1856; and idem (ed.), Scritti di Leonardo Pisano, matematico, 2 vols., Rome, 1857–62 (the first volume contains the Liber Abbaci, the second the Practica Geometriae and other minor essays). This last work was published by the Tipografia delle Scienze Matematiche e Fisiche, founded by Boncompagni. For a presentation of the main achievements of Boncompagni ’s medieval studies, and for a contextualization of his work with respect to contemporary European scholarship, see G. Codazza, ‘ Il principe Boncompagni e la storia delle scienze matematiche in Italia ’, Il politecnico (1864), 91, 5–27. 13 Chiara Lefons, ‘Un capitolo dimenticato della storia delle scienze in Italia : il Bullettino di bibliografia e di storia delle scienze matematiche e fisiche di Baldassarre Boncompagni ’, Giornale critico della filosofia italiana (1984), 63, 65–90, 74. 14 See Vincenzo Cappelletti, ‘Baldassarre Boncompagni ’, in Dizionario biografico degli italiani, Rome, 1969. 15 In addition to Boncompagni’s work, in this printing office such works were published as medieval treatises of arithmetic (1857), unpublished works and letters by Pietro Cossali (1857) and a magnificent edition in ottavo grande of La composizione del mondo, by Ristoro d’Arezzo (1859). 262 Massimo Mazzotti twenty thousand volumes and six hundred manuscripts."' Its strength was in the collection of medieval abbaci and early treatises of arithmetic, but it also included texts on the natural sciences, archaeology and history, and contained a rich theological section. The assembling of the library was made possible by a network of Boncompagni ’s correspondents, which covered the whole of Europe. Upon receiving information of the presence of an interesting book or manuscript, Boncompagni would send one of his many secretaries to purchase the piece or, when this was impossible, to realize a facsimile. The collection was intended primarily as an instrument to reconstruct the complex modalities of the transmission of mathematical knowledge from the Arabic world to Christian Europe, and it was constantly open to scholars from every country. The foundation of the Bullettino was another step in Boncompagni ’s cultural project. The periodical was designed to provide a space where complete studies, work-in-progress pieces, notes, letters and discussions could be published, providing a specific forum for the scattered community of the historians of the exact sciences. From the very beginning the Bullettino was an authoritative and highly international journal, with contributions from many of the most eminent historians of mathematics of the period: the Germans Moritz Cantor, Maximilian Curtze, Sigmund Gu$ nther and Hermann Hankel ; the Belgian Paul Mansion; the Frenchman Charles Henry; the Dutchman David Bierens de Haan, and the Italians Antonio Favaro, Angelo Genocchi, Domenico Chelini and Pietro Riccardi. Wellknown orientalists such as Louis Sedillot and Moritz Steinschneider also offered contributions. Boncompagni was assisted in the direction by strict collaborators such as Enrico Narducci, Timoteo Bertelli and Ferdinando Jacoli. Articles appeared in Italian and French, rarely in Latin; German, Dutch, Swedish and Russian contributions were translated. A yearly volume included up to ten memoirs, and a variable number of notes, reviews and abstracts, concluded by a section where new publications in the field were listed. Boncompagni contributed with fifty-five memoirs and seventy-seven ‘notes ’ in which he critically analysed pieces by other contributors. In fact, he personally edited almost any piece published in the Bullettino. Boncompagni invited the contributors to strictly follow guidelines derived from the methodology of the philological and palaeographic sciences."( This meant that great attention was paid to the handling of the original sources, which had to be carefully reconstructed, transcribed (often the facsimile was published) and integrated with a massive apparatus of references. Characteristic was the way in which reference and quotations were given. Following the erudite tradition of philological and humanistic studies, Boncompagni asked contributors to render always the complete front page as title, including indications of the line breaks, and to list every 16 In his last years, Boncompagni contacted both the city council of Rome and the Vatican Library in order to find an appropriate collocation for his library. A series of minutiae prolonged the negotiations until suddenly the prince died, in 1894. Four years later the heirs dispersed the collection. On Boncompagni ’s library see E. Narducci, Catalogo di manoscritti ora posseduti da don B. Boncompagni, Rome, 1862; idem, Catalogo di edizioni del secolo XV possedute da D. Baldassarre Boncompagni, Rome, 1893; Catalogo della insigne biblioteca appartenuta alla chiara memoria del Principe D. Baldassarre Boncompagni, 2 vols., Rome, 1895–6; and the impressive catalogue of the 1898 sale : Catalogo della biblioteca Boncompagni, 6 vols., Rome, 1898. 17 See A. Favaro, ‘Don Baldassarre Boncompagni e la storia delle scienze matematiche e fisiche’, Atti del Regio Istituto Veneto di Scienze, Lettere ed Arti (1894–5), 6, 509–21, 514. For science and for the Pope-king 263 Figure 2. The Bulletino’s notorious footnotes (from Volume 1, 1868). edition of a given book or every known copy of a given manuscript as well as the libraries where these exemplars could be found. This unusual attention to the philological study of the original sources had already characterized Boncompagni’s early essays, and it was now to shape the entire production of the Bullettino.") It is in relation to the unusual degree of formal accuracy displayed by the editor of the Bullettino that anecdotes about the ‘exaggerations’ of the Roman prince began to circulate. Collaborators such as Moritz Cantor and Paul Mansion commented on the 18 It should be noted that the philological methodology that inspired Boncompagni can be considered an ‘old’ model, one centred on text revival and restoration, and as such one proper of classical philologists and humanistic scholars. ‘Modern’ philology, which emerged at the end of the eighteenth century, was characterized instead by a new conception of ‘ interpretation’, i.e. the historical understanding of cultures through textual analysis. For the traditional methodology see D. Kelley, The Foundations of Modern Historical Scholarship, New York, 1970, 53–86. On the origins of the ‘modern’ methodology, see R. Leventhal, ‘The emergence of philological discourse in the German States, 1770–1810’, Isis (1986), 77, 243–60. 264 Massimo Mazzotti erudition of Boncompagni and on the richness of his overlong footnotes."* George Sarton was clearly drawing on this when he underlined ‘the extreme exactness of the prince’, one negative consequence of which was that ‘ the prince used to interrupt the printing of his journal in order to make further corrections in the remaining copies! As a result, there are numerous differences among the copies of the Bullettino that are spread around the world’.#! In Italy, such a judgement was echoed in Aldo Mieli ’s bibliographical essay on the history of science (1916), where the application of the rules of diplomatic transcription to the history of science is defined as ‘pedantic ’.#" In 1923, writing about the life of the prince, an Italian biographer concluded, ‘ famous collector of mathematical books, cultivator of the history of the mathematical and physical sciences, very diligent bibliographer, indeed a too diligent one, as in his later years such a diligence reached the most bizarre excesses ’.## Gino Loria, in his important 1946 essay on the historiography of mathematics, recommended reading the Bullettino on the ground that there modern historiographical methods ‘reached the highest degree of rigour and precision’. But at the same time he noted that such precision was excessive. To have an idea of Boncompagni ’s methods, Loria wrote, one should read his memoir on Smeraldo Borghetti, author of a medieval treatise on arithmetic : It is a 284-page work, entirely devoted to a scientist so insignificant that, even after the enormous effort of the excellent bibliographer, historians (such as Cantor, for instance) do not mention him at all. In this piece one finds the biographical data of every author being cited, and they are derived from different sources ; every citation includes a complete transcription of the title, every single edition of the main works is described, and libraries where copies can be found are listed. ‘As a consequence’, Loria continues, ‘ footnotes are not an appendix to the text, but rather the most essential part of it ’. Boncompagni ’s remarkable efforts seemed not to be justified by the final result ; rather, Loria noted, ‘ they look like sportive manifestations, the goal of which is to strengthen the muscles ’, or like those laboratory experiments which are not relevant in themselves but designed to train young scientists. Loria concluded by noting that Boncompagni ’s work proved to be a remarkable source of inspiration for the following generation of historians, who improved on it by directing their attention to more relevant historical figures, and by reducing to the essential the apparatus of notes and quotations.#$ Even in the most recent literature Boncompagni ’s work is given an ambivalent judgement: on the one hand its innovative nature is acknowledged, but on the other the 19 M. Cantor, ‘Fu$ rst Baldassarre Boncompagni Ludovisi. Ein Nachruf ’, Zeitschrift fuX r Mathematik und Physik (1894), 39, 201–3; P. Mansion, note in Revue des questiones scientifiques (1894), 6, 242. 20 ‘Le prince interrompıWt le tirage de sa revue pour apporter encore des corrections dans les exemplaires restant a[ tirer ! Il en reU sulte d ’assez nombreuses differences entre les divers exemplaires du Bullettino qui sont eUparpilleU s dans le monde ’. G. Sarton, ‘Bibliographie synthe! tique des revues et des collections de livres ’, Isis (1914–19), 2, 133. 21 A. Mieli, La storia della scienza in Italia. Saggio di bibliografia e di storia della scienza, Florence, 1916, 57. 22 G. Fumagalli, La bibliografia, Rome, 1923, p. xxi. 23 Quotations from G. Loria, Guida allo studio della storia delle matematiche. Generalita[ , bibliografia, Milan, 1946, 74–6. The memoir Loria is referring to is B. Boncompagni, ‘ Intorno ad un trattato di aritmetica del P. D. Smeraldo Borghetti Lucchese, canonico regolare della Congregazione del SS. Salvatore ’, Bullettino (1880), 13, 1–80, 121–200, 245–368. For science and for the Pope-king 265 excessive attention paid to formal issues and to secondary figures in the history of science is underlined. So, for instance, Ivor Grattan-Guinness defines the Bullettino as the first important journal in the history of mathematics and recognizes that ‘ its twenty annual volumes contain a mass of invaluable research, especially for the Renaissance period’, but he also refers to Boncompagni as ‘a rich prince able to indulge his eccentricities, he even changed text while passing proofs (so that not all copies are the same), and insisted on authors indicating line-breaks when rendering titles of works! ’.#% Once again, the overly meticulous and indiscriminate use of the methodological instruments of philology and palaeography is recognized as the main characterizing aspect of Boncompagni ’s work. Once again, the explanation for the general methodology of the studies published in the Bullettino is found in the eccentric personality of its founder, in his maniacal precision. But, I suggest, this is not a satisfactory historical explanation for a complex phenomenon such as the Bullettino. It is precisely this ‘style ’, this minuzionsaggine (minuteness) – as his collaborator Favaro called it – that should be problematized and made the object of further investigation.#& The remainder of this paper is devoted to investigating the cultural significance of such a historiographical methodology, going beyond the usual recognition of the ‘eccentricity of the prince’.