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Guido Castelnuovo and Francesco Severi: Two Personalities, Two Letters Donald Babbitt and Judith Goodstein

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Guido Castelnuovo and Francesco Severi: Two Personalities, Two Letters Donald Babbitt and Judith Goodstein Guido Castelnuovo and Francesco Severi: Two Personalities, Two Letters Donald Babbitt and Judith Goodstein he Italian school of algebraic geometry letters reflect remarkably the enormous personal- flourished from the latter part of the ity differences between these two giants of Italian nineteenth century through the early mathematics. part of the twentieth century. Some of Guido Castelnuovo (1865–1952) was born and the main contributors were Luigi Cre- raised in Venice, the son of Enrico Castelnuovo, Tmona, Eugenio Bertini, Giuseppe Veronese, Cor- director of the Scuola Superiore di Commercio and rado Segre, Guido Castelnuovo, Federigo Enriques, a popular nineteenth-century author of novels and and Francesco Severi. There were, of course, other short stories. He completed his doctor’s degree at important schools of algebraic geometry in other the University of Padua in 1886 under the direc- countries, but the Italian school stood out because tion of Giuseppe Veronese, one of the leading of its unique mathematical style, especially its algebraic geometers of that period. On the advice strong appeal to geometric intuition. Between of Veronese, Castelnuovo spent the following year 1896 and 1900 two members of this school, Guido in Rome on a postgraduate scholarship and then Castelnuovo and Federigo Enriques, developed the spent three years as assistant to geometer Enrico classification of algebraic surfaces, one of the great D’Ovidio at the University of Turin. In 1890, Castel- achievements of algebraic geometry.1 A few years nuovo won a concorso, or national competition, for later (1904–1908), together with Francesco Severi, a new chair of analytical and projective geometry at they significantly deepened that understanding the University of Rome—an award that was subse- of surfaces. quently withdrawn by the Italian Ministry of Public 2 In this article, we present excerpts from two Instruction on the grounds that the candidate’s letters to Beniamino Segre, a distinguished al- publications did not match the subject matter cov- gebraic geometer in his own right and a distant ered by the chair, although the ministry had judged relative of Corrado Segre: one from Severi in 1932 his work itself to be of higher quality than that of and the other from Castelnuovo in 1938. Severi’s the competition. Thus, Castelnuovo remained in letter provides his frank assessment of his own Turin for another year as D’Ovidio’s assistant, dur- and others’ contributions to algebraic geometry, ing which time he broadened his research interests including those of several of the Italian geometers to include linear systems of curves in a plane and mentioned above. Castelnuovo’s letter discusses the geometry of algebraic surfaces. He won the his collaborations with Enriques and Severi in the next concorso handily, and in 1891, at age twenty- 1904–1908 period and assesses the contributions six, he was appointed to the Rome chair, which he due solely to Severi. The tone and content of the held until his retirement in 1935. A turning point Donald Babbitt is professor of mathematics emeritus at the in Castelnuovo’s scientific life occurred early in his University of California, Los Angeles. His email address is tenure at Rome, in 1892, when Federigo Enriques, [email protected]. a gifted geometer who had earned his degree in Judith Goodstein is university archivist and faculty asso- mathematics at the Scuola Normale in Pisa, came to ciate in history at the California Institute of Technology. Rome to attend a course in higher geometry taught Her email address is [email protected]. by Luigi Cremona, the first occupant of the chair of 1 An accessible account of the classification is given in higher geometry at Bologna and founder of the Ital- [Gray99]. ian school of geometry. Enriques deemed Castel- 2 Translated by Elisa Piccio and edited by the authors. nuovo, only five and a half years his senior, much 2 NOTICES OF THE AMS VOLUME 56, NUMBER 7 more open and “[A]bandoning geometric intuition—the only w e l c o m i n g means that so far has allowed us to find the way than Cremona, in this tangled territory—would mean extinguish- whose lectures ing the feeble flame that can lead us into the dark completely be- forest” [Cast28]. This may have been a criticism of fuddled him. the then-current “algebraizing of algebraic geom- The two young etry” by Emmy Noether and B. L. van der Waerden m a t h e m a t i - [Sch07]. cians quickly A student of his, Oscar Zariski, offers the fol- Turin. of University Mathematics, became friends lowing sketch of the great man [Parikh91]. a n d s e v e r a l y e a r s l a t e r , Castelnuovo was a somewhat distant when Castelnu- fellow, he wouldn’t be chummy with ovo married El- you, he was not that type. He was very bina Enriques, dignified, long beard. He looked like brothers-in- the Moses of Michelangelo. When he law. As they smiled, his face was transformed. But strolled the mostly he was very serious. Fonti iconografiche, Biblioteca Matematica Giuseppe Peano, Department of of Department Peano, Giuseppe Matematica Biblioteca iconografiche, Fonti s t r e e t s o f Beniamino Segre paints a rather more attractive Rome, talking picture, describing Castelnuovo’s house in the Via Guido Castelnuovo, ca. 1890. mainly about Veneto section of Rome as “modest but welcom- algebraic ge- ing”, and as an academic gathering place [Segre54]. o m e t r y , E n - riques would update his new friend daily on his … a center where every Saturday for progress, while Castelnuovo listened attentively several years colleagues and students, and offered critical comments. “It is probably not Italians or foreign visitors, gathered for an exaggeration to assert that the theory of alge- friendly conversation on a wide variety braic surfaces from the Italian point of view was of subjects; his influence on those pres- created during these conversations,” Castelnuovo ent was enormous, with his display notes in a eulogy delivered at the Accademia Nazio- of calm wisdom, his interest in each nale dei Lincei following Enriques’ death in 1946 idea expressed, his offering of serene [Cast47]. The Castelnuovo-Enriques collaboration and objective opinions and thought- culminated in their classification of algebraic sur- ful advice, his courtly presence, his faces, which has been hailed as “one of the lasting genuine modesty. These qualities, even contributions to mathematics made by the Italian if chastely veiled by a certain reserve, geometers of a century ago” [Gray99]. made him loved and appreciated by Castelnuovo eventually stopped working ac- everybody: you can be certain that he tively in algebraic geometry. After 1906 he pub- did not have any enemies or detractors. lished only two original papers relating to the Francesco Severi (1879–1961) was a man of a field, including his notable 1921 paper on Abelian very different stripe. His personality is described functions [Cast21]. Although best known outside thus in an obituary in the Journal of the London Italy for his contributions to algebraic geometry, Mathematical Society [Roth63]. Castelnuovo explored other fields, including prob- ability, mathematical pedagogy, and the philosoph- Personal relationships with Severi, ical implications of Einstein’s theories of special however complicated in appearance, and general relativity (an interest he shared with were always reducible to two basically Enriques)—lecturing, writing, and publishing on all simple situations: either he had just these topics. Nevertheless, he continued to keenly taken offence or else he was in the follow the developments of algebraic geometry at process of giving it—and quite often home and abroad and made penetrating judgments genuinely unaware that he was doing on them throughout his life. so. Paradoxically, endowed as he was Castelnuovo was an unabashed champion of with even more wit than most of his the role of intuition in the success of the Ital- fellow Tuscans, he showed a childlike ian school. At the 1928 International Congress incapacity either for self-criticism or of Mathematicians held in Bologna, he delivered for cool judgment. Thus he meddled in one of the major addresses, an overview of the politics, whereas it would have been far work in algebraic geometry not just in his own better had he left them alone. country but in Germany, France, and the United Oscar Zariski’s biographer, Carol Parikh, States. At the end of his talk, he issued the follow- describes her subject’s relations with Severi ing warning with regard to its future development: [Parikh91]. AUGUST 2009 NOTICES OF THE AMS 3 A tall heavy man from Tuscany, he culus to higher lectured in a way that was particularly geometry, and in disquieting to Zariski. Lacking both the 1923 he became playfulness of Enriques…and the me- rector of the uni- Civilta dele dele Civilta ticulous formality of Castelnuovo, Se- versity as well, a veri’s dictatorial style seemed designed position he re- to make it impossible for his students signed to protest to distinguish between guesses and the assassination assertions, hunches and hypotheses. of the Socialist deputy Giacomo Outside of mathematics Severi was also Matteotti by Fas- a forceful and disquieting presence. ‘I cist thugs in June love you, Zariski, but you don’t love of the following me,’ he once said, a surprising state- year. ment from a man as vain as he seemed Severi also , 1957 (furnished by authors). by (furnished 1957 , to be. His wild driving was legendary; signed (as did his oblivious to the pleading of his passen- Rome colleagues Photographs of Francesco Severi previously published in in published previously Severi Francesco of Photographs Macchine gers, he would careen through the hills Vito Volterra, above Rome.
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