A Fresh Look at Judith Goodstein and Donald Babbitt

student of , Eugenio [Segre 55*].1 Although his tenure as Severi’s as- Bertini, and , sistant in from 1927 to 1931 gave him a Francesco Severi is remembered ringside seat as Severi’s politics veered sharply today as one of the key architects from left to right, Segre took pains to remind of the Italian school of algebraic ’s mathematical and scientific communities Ageometry in the first half of the twentieth century. that his mentor had once championed Italy’s (For a brief discussion of some of his most parliamentary democracy, protested the brutal important contributions to , 1924 murder of Giacomo Matteotti (a Socialist see the appendix.) His eagerness to serve the deputy in Parliament), and signed the philosopher Fascist regime after Mussolini became dictator in Benedetto Croce’s anti-Fascist manifesto—actions 1925 has cast a long shadow over his name. Even that forced his resignation in 1925 as rector of though Severi survived multiple investigations the University of Rome. These events, Segre once in Italy, rediscovered his Catholic faith, and said, had led Severi to have “a profound disagree- emphatically denied repeated accusations that he ment with the fascist government, which lasted— was anti-Semitic, the stigma has persisted. if even in a form increasingly attenuated—for Among the first, if not the first, to come to several years, even after having been called to Severi’s defense in the post-World War II era was take part in the Academy of Italy” [Segre 63*]. , who had lost his own academic And, on that sober note, Segre took leave of chair in in 1938 in the wake of the govern- Severi’s political career under Mussolini. ment’s anti-Jewish legislation. Relieved, at Severi’s Our story offers a fuller look at Severi’s politi- behest, of his duties as an editor of Italy’s old- cal dossier during the inter-war years and beyond. est scientific journal in the wake of the regime’s Primary sources range from the personal corre- racial laws, Segre nevertheless insisted that ru- spondence of Beniamino Segre and mors of Severi’s “supposed anti-Semitism” were to Italian government records of the Fascist pe- “flimsy” and based on “some misunderstanding” riod in the Archivio Centrale dello Stato (ACS) to documents in the historical archives of the Uni- Judith Goodstein is university archivist emeritus at Cali- fornia Institute of Technology. Her email address is jrg@ versity of Rome and the Lincei. The whereabouts caltech.edu. of Severi’s personal papers is a mystery, and it is Donald Babbitt is professor of emeritus at possible that he destroyed them. Some mathemati- University of California, Los Angeles. His email address is cians may find a recounting of his activities under [email protected]. Fascism uncalled for, preferring to recall only his 1References with an ∗ can be found at the website: http:// considerable mathematical legacy. (Again, see the www.JudithGoodstein.com. appendix for a nontechnical discussion of some DOI: http://dx.doi.org/10.1090/noti881 of the most important parts of this legacy.) Others

1064 Notices of the AMS Volume 59, Number 8 September back re- brought and group, the died, told he recently them, only membering had colleagues harsh. unduly Some seemed Racism Italian its of issued Manifesto regime Fascist senior the after more years community fifty task mathematical the to Italian thought and the teachers the of own members 90], his [Ves taking of indefinitely” cannot recognition deferred such that be know all closets and we hidden, that if or know [even] forgotten also, all skeletons discipline, we and own exist if his “Even said, about Speaking Vesentini one-day the Italy. at a in racial the laws talk hosted of consequences a cultural which the on in meeting Lincei, himself dei subject Accademia the raised tini in skeletons undisturbed. proverbial remain to the closet allow the to content are first. insignia fascist the but remove frontispiece, to the Segre for asked himself of chose Severi picture this instead. writings a his preparing of in selection help Segre’s Severi Beniamino no, enlisted said Zanichelli in When works, volumes. multiple collected his the publish Enriques, to Federigo opportunity to ties house close publishing with the Zanichelli, activity, offered publishing of Severi years fifty celebrate To Memorie scelte, 1950 (furnished by authors). n18 h tla emtrEoroVesen- Edoardo geometer Italian the 1989 In 2012 oie fteAMS the of Notices i iw.Hwvr eea er fe Mussolini’s after years affected several have However, views. may his ideology, fascist of proponent Severi’s leading and how philosopher clear a Gentile, entirely with association not is It instruction. pub- of lic minister as tenure brief a enjoying was time eaerco fteUiest fRm nthe on Rome Gentile, of Giovanni University of and recommendation the Na- Professors of formed rector University newly became the of of Association president tional as served time He a unions. for Socialist-run and from veterans backing received war and office political for in ning side Allied the on entered military 1915. Italy for once volunteered Italian service quickly supported and which Party, neutrality, Socialist the the connections severed on with He Severi France. intervention and out, urged Britain of who broke side those I for with War alderman sided World Socialist When the commune became education. the and and for Padua Party councilor of Socialist elected the quickly joined In was company. officially water he and gas 1910 municipal presi- the him of appointing dent by allegiance his rewarded mtc tPdai 95 eeiale himself allied Severi 1905, math- left-wing in in the of with rise Padua professor the at took appointed on ematics he being particu- then After boy in movement, Italy. following a socialist politics, as the in lar children, where interest Tus- Arezzo, nine keen the in a of of poverty town in youngest up can the grew Severi 1879 Francesco in Born Politics for Taste A of history the to belong science.” events years those those …because examined of thoroughly events and investigated the being from all, above prevent, “must not added, and he generosity Castelnuovo,” “The of country’s far-sightedness track. the on putting in back role mathematics crucial a noted, played Vesentini had ended, war the after bitterness of lack Castelnuovo’s library. enter math institution’s not their could Enriques they and mathematicians) Castelnuovo Jewish tell (two the to spared forced “been been had least who mathematicians” at those among had being of shame 1945, after age came who of those generation, admiration own his of of ematicians math- the mixture Fortunately, affection.” “a sometimes, and, with along memories acs rtr n rit indi 1925. in signed “The artists leadin and many including writers which fascist Mussolini, wrote Intellectuals”, Fascist he for the fascism”, of tracts Manifesto of political philosopher key “the Of- several as (1922–1924). education to of referred minister ten reforms im- as educational time Gentile his lasting circles, during and philosophical far-reaching Italian plemented in figure major 1 nadn upre ftefsitgvrmn n a and government fascist the of supporter ardent An ewe 98ad12 eeiflre ihrun- with flirted Severi 1925 and 1918 Between lcopplr patavino popolare blocco 1 h tthe at who which , g 1065 1066 usln’ w oiia rjcoy( trajectory political from own lead embellished his Mussolini’s Taking several note. personal articles, flowery a of with of stream spring steady leader the Fascist a the in movement) sending Parliament began fascist year—Severi in that the deputies of the “chief” told as himself for cdm fIay ea otk hp n1926, reserved in slot the shape in interest take keen a Royal to took Severi (The began and insti- Italy) d’Italia of cultural Accademia Academy Reale state-sponsored the new tution, a for Plans d’Italia Accademia The advancement. his considerable promote new to his connections the political used of Severi a life Indeed, play state. intellectual fascist to the his- wanted in he role the prominent that 45*], suggests [Sev record life” torical political active as- “his in forever political participation ended defiance had Matteotti’s 1924 of against in act sassination out his speaking that wrote in later he ambitions. ties political Although his political suited longer socialist Severi no his they socialist), off when a cast have as to career appears political his started iity eaentee oenet We government. 05], a [Bo even regime” not a are are we ministry; not are a dictatorship—“We a of proclamation 1925 Photo from a private collection. n fhsppl tPda hmh are in married he whom Padua, at pupils his of one uloLv-iiaadhswf ieaTrevisani, Libera wife his and Levi-Civita Tullio 94 eert hi ria nNwYr City, York New in arrival their celebrate 1914, lDuce Il Msoiistitle (Mussolini’s oie fteASVolume AMS the of Notices lDuce Il 1933. had dpieorUieste fms ftebest the almost Rome, of remain.” would at perhaps none most faculty would the of added, On he Universities mathematicians. that, our of “deprive mani- short Croce’s Anything signing festo. “nonorthodox those as in indemnify such engaged to demonstrations,” had serve himself, would like that who, oath passage swift an impassioned urging Sev- of himself, and 1929 Mussolini unsolicited to January memo an great in “the dispatched of professors, eri behalf of on an- said, the majority” become was he have oath Speaking, loyalty to swer. Fascist seems a that Severi convinced more the future, only matters Severi. other for stakes and the “Completeness 10]) heightened [B-G the (see of Theorem” feuding proof satisfactory a been over algebro-geometric years had several for Severi Enriques had with family, That Jewish nominated. Italian been an that into secret Federigo born Rome, open Enriques, from an geometer was algebraic It another mathematician. a for tteLne,“leri emtysre opurpose” no serves session 67*] geometry a “Algebraic during Lincei, him the to an at said Volterra, once that had fact al- anti-Fascist, the by advent avowed had along Volterra the helped and rocky, before been Severi ways mathematics between Relations of undisputed Fascism. their school the of lost Italy’s Volterra, and of Vito sign head including to posts, refused courageous 1,250 university Twelve of 1931. out in academicians later years two administered 2 htte hudadsol o etl.Ol na in Only told. be the not should and press, and should ministries, they the what various including stake- and other rank-and-file, matter, the fascist the Gentile manage instruct in to to how holders well about on very length went is at to then Government much reason of He have as I Head disposed.” done and the purpose, have that this I think for powers, could I poor limits as own the my “within Gentile, of in reminded you he told like already person,” with I those, differences “As reward government. their Mussolini’s to resolved had and who regime himself, Fascist to hostile the oath professors reit- loyalty to university by a isolate needed began and badly identify Gentile Italy to that letter erating Severi’s po- tone, practical his more in in emotional, Less instruction, aspirations. public litical of no minister Gentile, Giovanni longer confidant and colleague sity with himself in ingratiate Party to regime. Fascist Mussolini’s begun become Benito the had yet joined he not (he 1932), had member abroad party Severi while a Although Regime” 05]. the inter- to be [G-N contrary remotely criti- as even or could preted anything that done anyone never cized have “I continued, h oat ahrqie faluiest rfsoswas professors university all of required oath loyalty The h oeh huh bu i w political own his about thought he more The nmdFbur,Svr nitdhsuniver- his enlisted Severi mid-February, In . 2 etasrd Severi assured, Rest 59 Number , [Tri 8 brief postscript, in which Severi informed Gentile , both born into Jewish families, that he had marginally patched up a long-standing members of its group. Anti-fascist organizations quarrel with Enriques over competing textbooks had been quick to note the absence of any Ital- (“but with open [and] utter disgust”), did he men- ian Jews among the first members of Mussolini’s tion that Enriques’s Academy nomination might Academy, and in fact the fascist academy was be in trouble [G-N 93*]. Gentile’s response to this never to admit any Jews to its ranks [Good 84]. letter, if there was one, has not survived. The Vatican simply leveled the playing field. Whether by design or chance, Severi had landed That October the thirty successful candidates in the right spot if things veered off track for for the , including the physi- Enriques, which they did. In mid-March, barely one cist Enrico Fermi, the composer Pietro Mascagni, month later, the government deleted Enriques’s and Francesco Severi, the sole mathematician, name from the list of candidates sent to the gathered in the Campidoglio, Rome’s city hall, president-elect of the Academy of Italy. In its place where Prince Francesco Boncompagni Ludovisi, appeared the name Severi. Recalling that period at the city’s governor, proclaimed them the aristoc- Rome, Giorgio Levi della Vida, at the time director racy of Italy’s intelligentsia. Clad in a ceremonial of the Oriental School, wrote, “The Rector then was suit embroidered in gold, a stipend of 3,000 lira a Francesco Severi, a great mathematician and an month lining his pocket, and promoted to the rank energetic man of action …whose antifascism could of “your Excellency”, Severi had been appointed not resist the seduction of the [Royal] Academy the regime’s spokesman for Italian mathematics— of Italy, and as the first error leads to a second and in the eyes of Italy’s new rulers, he was. As one one easily and a third, [the error] turned into of Severi’s assistants in Rome, , enthusiastic support for the regime” [LeviV 66*]. the author of a classic text on integral equations, One of the many congratulatory telegrams Sev- later recalled, Severi was as “exuberantly fascist as eri received in 1929 following the government’s he had earlier been antifascist—who wanted to be public announcement of his nomination came and to a certain extent, was—the ‘boss’ of Italian from the differential geometer Tullio Levi-Civita, mathematics in the fascist period” [Tri 67*]. a colleague at the University of Rome and one of Severi proceeded to play an active role in the Italy’s most distinguished mathematicians. In re- affairs of the fascist academy. Besides diligently sponse, Severi sent Levi-Civita, his friend of more attending sessions, he nominated candidates for than twenty years, a letter marked “confiden- membership, including Levi-Civita in 1933 and tial” from Barcelona, where he was lecturing. He again in 1934, although both he and Levi-Civita expressed “absolute surprise” at his own nomina- knew of the insurmountable obstacles other Jew- tion and remorse over the omission of Levi-Civita’s ish candidates had faced. In addition to serving on name. “I certainly would have loved to see you, various commissions, including one charged with the strongest among the columns of Italian math- purifying the Italian language of foreign words ematics, in the Academy also,” he wrote. “Let us (e.g. cocktail), he presented numerous papers, his trust in the future” [Sev 29*], a veiled hint perhaps own and others’; and, indeed, when called to ac- that Severi intended to nominate his friend. Later count for his activities later, he proudly noted that year, in fact, when Severi raised the issue with that he had personally introduced thirteen of the his Jewish colleague, Levi-Civita reminded him in fourteen papers authored by Jewish scientists. writing of the obstacles (“two distinct objections, However, in 1931, when Mussolini, with the com- stated or implied”) standing in his way: politics plicity of Academy president Guglielmo Marconi, and religion. As the historian Annalisa Capristo, intervened decisively to prevent the Academy from who has written extensively about the exclusion awarding the first Mussolini Prize in science to of Jews from Italian academies before and af- the militantly anti-fascist and Jewish professor ter the racial laws, writes, “In fact, we have no of human anatomy Giuseppe Levi, Severi did not knowledge of other possible ‘objections.’ On these speak up in defense of Levi, nor did he voice delicate questions, however, the two correspon- any objection to the government for not following dents maintained—at least in their exchange of its own rules [Fabre 08]. (The honor of receiving letters—an understandable discretion” [Cap 03]. the first Mussolini Prize went to a well-known— The Vatican acted first. In February 1929, Mus- and Christian—physiologist and explorer in good solini’s government and the Vatican had signed standing with the regime, Filippo de Filippi.) the Lateran Accords, each recognizing the other’s sovereignty as a state, and in April 1929, only Severi’s Interactions with Colleagues a month after the Reale Accademia d’Italia an- In his dealings with others, Severi often came nounced its first thirty members, the Vatican’s across as arrogant, autocratic, and quick to take Accademia Pontificia delle Scienze elected Levi- offense. There seemed to be no middle ground: he Civita and the world-renowned mathematician either dazzled those around him (“Severi is a man

September 2012 Notices of the AMS 1067 with bewitching hands, when he does something, mathematical reputation, they postponed the de- it is always splendid” [ScorD 62*], the Sicilian cision on his election until they could learn more mathematician Gaetano Scorza once remarked) or about him as a person. The task was entrusted demonstrated “a childlike incapacity either for to an old classmate of Levi-Civita’s, Felix Carli, a self-criticism or for cool judgment,” as Leonard member of both the Sociedad Cientifica Argentina Roth, the English algebraic geometer who spent and the Accademia di Scienze Fisiche e Matem- the year 1930–1931 in Rome, famously observed. atiche di Buenos Aires. “I beg you to give me your Worse still, Roth added, “he meddled in politics, opinion of the man” [Carli 30*], he wrote to Levi- whereas it would have been far better had he left Civita. While we lack Levi-Civita’s reply, Severi’s them alone” [Roth 63]. substantial list of honors and affiliations does not Mathematical collaborations with Severi could include membership in either of Argentina’s sci- also be challenging, recalled Scorza’s son, Giuseppe Scorza Dragoni, who collaborated with entific organizations, which may suggest a tepid Severi on the second and third volumes of Lezioni response on Levi-Civita’s part. di Analisi, magisterial tomes, published in 1942 Serving as Severi’s assistant for four years, and 1951. As the younger Scorza recounted Francesco Tricomi, like Roth, had ready answers in a letter to Segre after Severi’s death, some for those wanting to know what he had experienced of the difficulties arose because the Tuscan in Rome. As a professor and mentor, he reported, mathematician always had a hundred different Severi knew how to push his students along; on obligations to attend to. In fact, he had once the pedagogic side, he ranked as an extraordinary spent his entire vacation in Rome without being teacher, and Tricomi had found his classroom able to meet with Severi once, except on the duties useful, unlike Severi’s other assistants who last day. Scorza also quickly learned that Severi considered them a “waste of time”. However, would not admit to making any mistakes. “But Tricomi also thought that Severi behaved as if he this last obstacle, when I realized it,” Scorza was “the ‘padrone’ [the lord and master], a little continued, “I got around easily: instead of saying overbearing…[although] I never had any real clash where there was a mistake, and how it should with him,” which Tricomi attributed to treating be fixed, I pretended to not understand and I his responsibilities as an extension of his recent continued to not understand until Severi, furious military service. Later, when Tricomi moved up by my artfully directed objections and questions, the academic ladder and became a professor ended by finding the mistakes and [making] the corrections himself” [ScorD 62*]. of mathematics at Florence, he took less kindly Severi believed, according to Roth, “that the to Severi’s requests, reminding him, politely but world at large failed to treat him with due consid- firmly, that “I was no longer under his orders” eration. For, incredible as it may seem, although [Tri 67*]. during the whole period of his maturity honours Beniamino Segre, who became Severi’s assis- were showered upon him and invitations poured tant several years later and who remained closer in,yethe remainedforeverunsatiated…he seemed to him than any of his other pupils, also remem- more or less permanently aggrieved” [Roth 63]. bered him as “ambitious and pugnacious” [Segre Severi’s trip in 1930 to South America is a case 62]. Straining after the events of World War II in point. During his stay there he gave a series of to paint an accurate and fair portrait of Severi technical lectures to a university crowd in Buenos as a man, Segre said, “We need to keep in mind Aires, telling his audience in so many words, that Severi had a complex, intense, tormented na- according to one listener, that he had come to ture, and an exceptional personality,” which Severi Argentina “to civilize and teach mathematics” to himself had described as a “restless energy, which the country’s inhabitants. He also ostentatiously takes away my breath and makes me unhappy” announced in several lectures that he disagreed [Segre 63*]. All in all, Segre concluded, the appear- with Levi-Civita “from several points of view.” ance of fearless confidence that Severi projected Severi’s pronouncements did not sit well with the probably concealed some “mysterious, unjustified mathematicians in the audience, who knew of Levi- Civita’s pioneering work in differential geometry fear of not being appreciated and loved.” Recall- and admired it. Severi further enraged his hosts ing his own dealings with Severi in Rome in the by asking point-blank, “If you have made [French early 1920s, the American mathematician Oscar mathematician Jacques] Hadamard and Enriques Zariski told an interviewer that Severi once said academicians [of Argentina’s scientific society, the to him, “I love you, Zariski, but you don’t love me” Sociedad Cientifica Argentina], why haven’t you [Parikh 91], although the correspondence between done the same for me?” With the society’s mem- the two mathematicians after the war suggests a bers deeply divided over what to make of Severi’s more complicated relationship.

1068 Notices of the AMS Volume 59, Number 8 Public Acts Unlike Enrico Fermi, his colleague at Rome, who never talked politics, Severi actively cooperated with Mussolini’s government. In an article aptly titled “Fascismo e Scienza”, published in 1933 in L’Illustrazione Italiana, a popular weekly maga- zine, Severi dismissed those who remained mired in the past (“a wretched preoccupation with con- ventional analytical politics and trifling doctrines from other times”) while extolling, in the name of patriotism, loyalty to the regime for its goal of restoring the grandeur of Rome and reclaiming Italy’s place in the world of science, starting with mathematics [Sev 33*]. The Italian school of math- Photo courtesy ©Archivio Storico Luce. ematics was a matter of deep national and personal Inaugural session of the fascist Academy of pride for Severi, who told his readers: “Not every- Italy, Farnesina Palace, 1930. Guglielmo Marconi, one knows that…Italy, in fact, occupies one of the in ceremonial uniform, is seated next to foremost places, if not the first, in mathematics Mussolini. Other academicians gathered around in the world today. Foreign mathematicians ev- the table include Francesco Severi, Cesare erywhere,” he continued, “recognize this and as Bazzani (first and second from left), and Francesco Giordani (third from right). and as fascists we are legitimately bound to be proud of it.” More importantly, he concluded, “we export many ideas, nay many more than those my science…this would distress me greatly, we import.” Even after the war ended, Severi per- and if I am induced to do something that sisted in believing that Italian mathematics (and costs me some sacrifice (no one likes to talk by extension, his own achievements) did not re- about himself), it is because I believe I have ceive the recognition they deserved outside Italy.3 to do it not so much in my own interest as “Thank you for the draft …of [Fabio] Conforto’s in defense of my School, which follows me review,” Severi began one letter to Ralph Boas, faithfully and which, like the majority of executive editor of the Mathematical Reviews, in Italians, is working to restore our country, March of 1949, after the great disaster, to a high interna- I note, however, that the last lines of the tional level in the intellectual and spiritual original review, which had expressed a realm, which is the realm where Italy has sensible opinion of my work, have been always distinguished itself throughout the deleted. I would not point this out if I had centuries. [Sev 49*] not been very hurt by the way my works Enacted in 1938, Italy’s anti-Jewish legislation are generally reviewed in MR. This is the altered abruptly Segre’s relationship with Severi. first time, after a half-century of intense, “You already know of the whirlwinds that have nonstop work in science, that I find my- shocked us over the past several months, inflict- self having to express such grievances to ing unspeakable moral pain on us,” Segre wrote a publication. Publishing …Conforto’s final to Zariski from Bologna on October 16, the day comments would perhaps have served to after the racial laws had banished him from the reaffirm that the Directors of MR do not classroom, expelled him from numerous scientific share the unfavorable attitude of certain academies and organizations, and relieved him reviewers, which is something you kindly of his duties as a managing editor of Annali di mentioned to me and which I certainly be- Matematica Pura ed Applicata [Segre 38*]. “Still lieve.…In any case, in your position…you more distressing,” he added, “is the apathetic—if have connections with many mathemati- not to say hostile—attitude of certain individuals cians and frequent opportunities to bring of our common acquaintance,” being careful not people together. Therefore I have faith in to mention anyone by name. That same day, Segre your efforts to restore the reputation of sent a letter to Levi-Civita, also a member of the Italian mathematics, which is alive and ac- journal’s editorial board, in which he identified tive.…As one [who] loves my country and Severi as the chief instigator behind their dis- missal. In it, he wrote: “The initiative was started 3Nor, for that matter, does the recent authoritative refer- ence treatise The Princeton Companion to Mathematics by S[everi], who—some time ago—indicated to the [Gowers 08] cite the contributions of the Italian school of President of the [organization unidentified] the algebraic geometers by name. situation in the editorial office of the Annali. Said

September 2012 Notices of the AMS 1069 President then wrote to Dr. [unidentified name], reserving to myself to come and greet you as soon requesting advice and this person left the mat- as it will be possible for me” [Sev 40*]. History ter completely up to Severi’s decision” [N 96*]. does not reveal if Severi kept the appointment. Of the journal’s four editors, three were Jewish By the end of the decade, Severi had con- (Guido Fubini was also dismissed), leaving Severi, solidated his leadership position within Italy’s who had joined the editorial board in 1925, as mathematical community. In spring 1938, Severi the journal’s sole editor. “In no other case up to petitioned Mussolini to underwrite an Institute of now has anything similar happened,” he told Levi- Higher Mathematics in Rome [INDAM], which was Civita. Recalling the event in an article dedicated inaugurated in 1940, with the Duce; the minis- to Giovanni Sansone and published many years ter for national education, Giuseppe Bottai; and later in the Annali, Severi noted the “deplorable a host of other Fascist dignitaries in attendance. decree” that left him remaining “alone on the Not surprisingly, Severi also became the institute’s scientific committee of the ‘Annali’, becoming au- first president. In the wake of the racial laws, he tomatically, without my desire, the only managing had succeeded Enriques as professor of higher editor” [Sev 60]. His colleague Giovanni Sansone, geometry at the University of Rome; he had also added Severi, had been the very first to share with replaced Enriques as director of Rome’s school of him the duties of running the journal. post graduate studies in the history of science. When the publisher of Springer ordered its 4 One of the few items still missing from his lengthy editor, Otto Neugebauer, in 1938 to remove list of honors and appointments was member- Levi-Civita’s name from the masthead of the ship in the Pontifical Academy of Sciences, whose Zentralblatt, the renowned international review roster had recently expanded to include Robert journal in mathematics founded by Neugebauer, Millikan, Max Planck, Erwin Schrödinger, and other on the grounds that according to Italy’s racial laws notable scientists. In 1939 an opening occurred. he was no longer a university professor, Severi’s As one of four scientists in the running for the name quickly appeared in his place. While planning one vacant seat, Severi’s credentials were hard to for the second meeting of the Italian Mathematical top. As one academy member wrote to Caltech’s Union in Bologna in 1940, the organizers debated Millikan, highlighting the advantages that Severi’s whether Levi-Civita, a former member and an ex- election would confer on the Pontifical Academy, pert on theory, could be invited “[W]e all have a great interest in concentrating to speak on that topic as a guest. Severi is re- our designation on the name of H[is] E[xcellency], ported to have said, “Please! We just got rid of Professor Severi, not only because he is a prince that race.”5 The historians of Italian mathematics among the mathematicians, and probably the most Giorgio Israel and Pietro Nastasi, who have writ- prominent in the world in the branch of algebraic ten extensively about science and race in fascist geometry…but on account of his great authority Italy, have also reported that Severi personally intervened to deny his Jewish colleagues access and his political position in Italy, we are in need to the University of Rome’s mathematics library of his help as a friendly link between the Italian after the racial laws went into effect.6 Two years authorities and the Pontifical Academy” [Giorgi later, Severi wrote Levi-Civita a friendly, if short, 39*]. One wonders if Severi, who won the election, note in which he apologized for not being able appreciated the irony of listening to papers pre- to personally deliver a recent issue of the Annali, sented by its long-time members Levi-Civita and “but since I see that it is late, I am sending it to you, Vito Volterra, both of whom had paid dearly for being both Jews and anti-fascists in Mussolini’s 4Neugebauer subsequently resigned from all editorial du- Italy. ties at Springer journals, left Germany, and joined the Brown faculty in 1939, where he became the founding Investigation and Rehabilitation editor of the AMS’s new abstracting journal, MR (Mathe- After the liberation of Rome in June 1944, Italy’s matical Reviews). newly installed provisional government estab- 5“Per carità, ci siamo appena liberati di quella razza.” The story has been passed down from the mathematician lished a High Commission for Sanctions against Ugo Amaldi, present at the meeting, to Edoardo Amaldi, Fascism to investigate allegations of wartime his son, who played a central role in rebuilding Italian collaboration against party members, either for physics after World War II, to , a distin- taking an active part in Fascist political life or for guished algebraic geometer in his own right and former remaining loyal to Mussolini after he was deposed president of the Lincei, private communication, Tullio G. in September 1943. That year, at the behest of Ceccherini-Silberstein to the author (JG), November 11, 2011. the Ministry of Public Instruction, the commis- 6Enzio Martinelli, a pupil of Severi, is the principal source sion took up the case against Severi, the only for this story, private communication, Giorgio Israel to the mathematician dealt with in this fashion. When it author (JG), Oct. 28, 2011. initially suspended him from university teaching,

1070 Notices of the AMS Volume 59, Number 8 effective August 1, 1944, Severi appealed the rul- nature with respect to a scientist who has honored ing. To the charge that he had been an apologist Italy such as you” [Cast 45*]. for the regime during the war, Severi countered According to the commission, Severi’s trans- by saying that he’d given scientific talks in Spain gression had been to accept an invitation from his and Portugal, not political speeches, and that he old friend Gentile, at the time the Academy of Italy had made a 1943 trip to Germany for the sole president, to attend a celebration there in honor purpose of collecting a medal in connection with a of the eighteenth-century political philosopher Gi- Copernican anniversary. In May 1945, Severi’s sus- anbattista Vico. “I have no reason to correct any pension was annulled and replaced by a sanzioni page from the book of my life,” Severi replied, after minori, a simple censure that involved a letter reading Castelnuovo’s letter [Sev 45*]. Far from placed in his university personnel file, but that did admitting any wrongdoing, Severi defended his not prevent him from teaching a course on higher visit, but thought it important to add a postscript geometry at INDAM during the 1945–46 academic in which he pointed out that “among the impor- year [Rog 05]. tant examples of his behavior with respect to the When pressed on the issue of anti-Semitism, racial laws,” he had seen to it that Castelnuovo’s Severi pointed to his repeated efforts on behalf of book on the origins of the calculus remained in Levi-Civita (who had died in 1941) for membership circulation after 1938. in the Academy of Italy [Cap 03] and his continued Gentile was unavailable to shed any further friendship with Segre, whom he described as light on the matter, having been assassinated by having always been his favorite student. Neither communists in Florence in August 1944 while the central commission nor a separate commission riding his bicycle. Four years later, Italy’s minister assignedin1945toexaminethebehaviorofformer of justice, Palmiro Togliatti, declared a sweeping members of the Academy of Italy found anything amnesty, and in July 1948, Severi was reelected to condemn in Severi’s personal or professional a member of the Lincei. Severi, who had lost his conduct. In its report on Severi’s conduct, in fact, position as president of INDAM, also recovered the commission noted: “The moral rectitude and that post following the amnesty and held it until good services of [P]rofessor Severi as a person his death. and as a scientist are beyond discussion and on Although Severi emphatically denied being anti- Semitic at the end of the war, he saw evidence the other hand no one could doubt it” [ACS 45*]. of others “paint[ing] me, especially in the Anglo- Faced with a new investigation the following year Saxon world, as anti-Semitic…[and presuming] involving former Fascist academicians, Severi told racial preconceptions that I have never had,” he Segre, “Naturally, I’ll come out from this painful wrote in one letter to Segre [Sev 49*], adding, “And trialasimmaculateasIhavealwaysbeen”[Sev46*]. you and many other Israelites know this well.” Severi’s prediction proved true but only up to A case in point was Oscar Zariski,7 born into a a point. In 1945 a separate committee, appointed Russian-Jewish family and an algebraic geometer by the provisional government to reconstitute at Harvard, who seemed in no rush to resume Italy’s storied Academy of the Lincei, homed in contact with Severi after 1945. “I am very sorry on members who had belonged to the Academy that he didn’t answer [my letter],” Severi told of Italy. The chairman of that commission went Segre, out of his way to note that the range of Severi’s activities demonstrated “a marked independence I had sent him [in 1948] many of my pa- and courageous conduct to ensure that science pers including books, together with a very warm letter…I did the same with [Solomon] prevailed over the dominant politics” [ACS 45*]. Lefschetz, who has already answered…ex- In so many words, as the central commission had pressing his deep appreciation. No answer, previously concluded, Severi “had not received instead from Zariski, to whom I won’t send from Fascism anything more than was his due anything more from now on, unless things as a distinguished scientist.” Nevertheless, that summer the committee members unanimously 7Zariski attended high school in Chernigov (Ukraine) and decided to purge from the Lincei any members the University of Kiev (1918–1920). Admitted to the Uni- who had taken part in a March 1944 meeting versity of Rome in 1921 as a third-year student, Zariski held in German-occupied Florence, regardless of received his doctor’s degree in 1924 under the supervi- the reason behind their attendance. Severi had sion of Castelnuovo. Zariski later said that Castelnuovo been present at that meeting, and so he was out. chose a problem that would suit him (Galois theory, solv- ing by radicals) because he could see that Zariski was not, As , a committee member and at heart, a geometer in the sense of the Italian school of al- Jewish mathematician who had gone into hiding gebraic geometry. He did postgraduate work at Rome on during the war, wrote to Severi that June, “It pains a Rockefeller fellowship (1924–1926) before going to Johns me that it is necessary to take a step of such a Hopkins University in 1927.

September 2012 Notices of the AMS 1071 change. I know that Zariski had a grudge consequence of your temperament” [Sev 53*]. Sev- [against me]; [Tomás Rodriquez] Bachiller, eri then turned to mathematical matters. Judging who was there [at Harvard] …wrote to me from their later correspondence, the subject never that he had…explained to Zariski the real came up again. facts and that he seemed to be persuaded. One year later, when Severi’s name was point- Does he still perhaps believe in my anti- edly omitted from the list of speakers for an Semitism, the most disgusting calumny that international symposium on algebraic geometry has been circulated underground, without in 1954, Zariski wrote to the chair of the organiz- ever having the bravery to pronounce it ing committee: “I am particularly worried about publicly, it being so far from the truth? Why the omission of the name of Severi. I think that would he keep considering the polemics I Severi deserves a place of honor in any gathering had with Enriques in the past as a display of algebraic geometers as long as he is able and of anti-Semitism? Can’t anyone have a bone willing to attend such a meeting. We must try to to pick with a Muslim without being against avoid hurting the feelings of a man who has done Mohammed. [Sev48*] so much for algebraic geometry” [Zar 54*]. An Severi also felt that these accusations had done invitation was duly issued to Severi.8 great damage to the reputation of his own field Severi died in Rome on December 8, 1961, at of mathematics. As he wrote to Segre in an- the age of eighty-two; he remained proud of the other letter, “The attack that has been conducted fact that, as he once wrote, “I have never recanted against me has ended by damaging Italian geom- nor repudiated any of the acts of my life that were, etry abroad and especially in America [Sev 49*]. and are, expressions of the strongest attachment You have only to look, continued Severi, at the to my country” [Sev 53*]. “very hostile attitude towards us” by Zariski’s group of abstract algebraists, despite the fact that Appendix: Severi the Mathematician Zariski “formed his outlook (that I always guided) Francesco Severi, who contributed in fundamental in Italy.” ways to several areas of mathematics in the first Severi also found that some French mathemati- half of the twentieth century, is generally acknowl- cians continued to harbor hard feelings toward edged as one of the three great Italian algebraic him in the postwar period. Mounting a spirited geometers of that era, together with Guido Castel- defense of his aging mentor, in 1955 Segre wrote a nuovo and Federigo Enriques. A hugely prolific letter to the French mathematician René Garnier, author, Severi’s bibliography contains 415 items, in which he stated unequivocally that rumors of including 34 books that range from elementary to Severi’s anti-Semitism did not square with what advanced monographs. He was gifted with extra- he knew. In the paragraphs that followed, Segre ordinary geometric intuition; however, when this reiterated many of the arguments Severi had used was combined with the Italian algebraic geome- in the past to defend himself, including Segre’s ters’ imprecise mathematical language and their own interactions with Severi. In his reply, Garnier notion of what they considered a proof, it led said that he was personally satisfied by Segre’s him many times to either state a true theorem for narrative, but others might not be, given that “in which it was impossible to convert his proof to Paris, there is strong resistance” [Ga 55*]. an acceptable modern one (e.g., see the article of There is little correspondence between Severi JosephHarris [Ha86]),or to state as a true theorem and Zariski in Zariski’s papers, which are deposited one that was “almost true” but which later mathe- in the Harvard University Archives. There is none maticians had to modify in order to obtain a true from before World War II, and the few letters they theorem (e.g., see the article by Robert Lazarsfeld exchanged after 1948, when the correspondence [Laz 81]). Ironically, Severi’s own ideas in another seems to have resumed, at times turned testy. In context have often been utilized to furnish the response to a letter written by Zariski in summer correct proofs. For an authoritative discussion of 1953, Severi demanded to know why Zariski had Italian algebraic geometry and algebraic geome- brought up Hitler and Mussolini: “Do I have per- ters, including Severi, between the two world wars, haps some responsibility in front of those who see the book by Aldo Brigaglia and Ciro Ciliberto had to flee from paradise from the first and did [B-C 95]. not find asylum in the second?…Your references In 1949 Severi presented a paper at the Colloque demonstrate to me that in certain areas of the de géométrie algébrique, held in Liège [Sev 49], mathematical world this non benevolent attitude entitled “La géométrie algébrique italienne: sa towards me, from which I have greatly suffered, rigueur, ses méthodes, ses problèmes”. In it he has not ceased.…On your part I have often had an impression of coldness, which at times I was 8It was at this symposium where the famous exchange with not expecting. But it could be that it is only a André Weil took place (see next page).

1072 Notices of the AMS Volume 59, Number 8 defended the Italian approach to what consti- and Castelnuovo made related and key contribu- tuted a satisfactory proof. Here are two samples tions to the proof of the Fundamental Theorem of what Severi had to say. In his opening para- of Smooth Surfaces over C, one of the most graph he writes: “For many years a legend has beautiful and deepest contributions of early twen- run through a certain part, fortunately limited, of tieth century algebraic geometry. The theorem the mathematical community that Italian algebraic states the equality of two apparently different bi- geometry, while being ingenious and rich in im- rational invariants associated with the surface F: portant results, has not yet attained the necessary the dimension of the space of closed holomorphic rigor”. He then goes on to discuss “substantial 1-forms on F (called Picard integrals of the first rigor”, i.e., the sense of rigor of the Italian school, kind) and the irregularity q ≡ pg − pa of F, where and “formal rigor,” i.e., the sense of rigor of the pg is the geometric genus and pa is the arith- Franco-American school of André Weil and Oscar metic genus of F. See, e.g., [Kl 05, pp. 243–244] Zariski. for a more thorough discussion of this theorem, Later in his talk (p. 41), while discussing a including the relative contributions of the two recent letter from “an eminent foreign geometer” mathematicians. (not named, but almost certainly Zariski), he says: Principle of the Conservation of Number and Enu- “Personally, I believe that our methods, when care- merative Geometry. Severi in 1912 made an ex- fully analyzed, give the same sense of assurance haustive analysis of the validity of the Principle as the purely algebraic methods.” Here by “alge- of the Conservation of Number, a very important braic methods” he seems to be referring to the tool in enumerative geometry [Sev 12]. However, Franco-American school’s methods of proof. For he did this utilizing the foundational language and the response of the “formal proof” community, tools available in 1912. Further progress required a see the critical and very interesting review of more refined foundational language, which indeed this paper by Claude Chevalley in Mathematical evolved in the following decades and consequently Reviews, 1951 [MR 0038094; 12, 353f]. led to significant additional progress in enumer- What might be correct to say is that Severi, per- ative geometry and Schubert’s calculus (Hilbert’s haps more than any other major mathematician of 15th problem). See [Kl 76] for a definitive history, his day, stated more true theorems whose proofs including Severi’s contributions. were “irreparable” by modern standards or “al- Rational Equivalence of Algebraic Cycles and Inter- section Theory on Smooth Projective Varieties over most true” theorems that required modifications C. Severi’s contributions here consist both of deep to make them true or that were just plain false insights and serious missteps. He first introduced “theorems”. But sorting through his triumphs and the notions of rational equivalence of algebraic missteps is a story for another day. cycles and studied its relationship to the inter- section of algebraic cycles [Sev 33]. Early on, he Some of Severi’s Main Contributions to became aware of difficulties with his definition Algebraic Geometry of rational equivalence and its relationship to the Theorem of the Base. Severi’s most cited work is intersection theory of algebraic cycles, and as a almost certainly his Theorem of the Base, which result, he continued to modify his definitions as he proved early in his career and is now usually time went on. At the 1954 International Confer- referred to as the Néron-Severi Theorem [Sev 06]. ence of Mathematicians (as related by B. L. van der It was one of the major results of early twenti- Waerden), Severi presented a new exposition of his eth century algebraic geometry over the complex theory, which Andre Weil famously (and correctly) numbers C, and the paper itself was explicitly criticized in the discussion session. Subsequently, 9 solicited for the Math. Annalen by . in 1970 van der Waerden [Waer 70] showed to his The theorem says that a certain important abelian satisfaction that Severi’s definitions and results group NS(F) naturally associated with an algebraic could in fact be adjusted to meet the modern stan- surface F over C is finitely generated. Specifically, dards of rigor. Precise and satisfactory definitions NS(F) is the quotient of the free group generated of rational equivalence in the rigorous language by the irreducible curves (divisors) on F by the of the “French” school were given independently. subgroup of divisors algebraically equivalent to See, e.g., Claude Chevalley [Chev 58]. To summa- the zero divisor. Néron [Ner 52] showed that the rize the significance of Severi’s contributions to theorem also holds for surfaces over any field, rational equivalence and intersection theory, we which is the reason that his name is also attached 9There were many exchanges over the years between Sev- to it. For more detail on the theorem and Severi’s eri and van der Waerden concerning various aspects of contribution, see [Zar 71, Ch. 5.6]. algebraic geometry, including rational equivalence. For a Contribution to the Proof of the Fundamental Theo- description of some of these interactions, see the fascinat- rem of Smooth Surfaces over C.Both Severi[Sev05] ing article by Norbert Schappacher [Sch 07].

September 2012 Notices of the AMS 1073 1074

Courtesy of Istituto Nazionale di Alta where ojcue1. Conjecture 69]. [Mum Mumford these and Kodaira the 52] of [Kod papers true, of well-known as two Both false—in settled—one other been below. have false, examples conjectures some many the made true, Sev- also including some theorems he conjectures, proved, of have interesting multitude to the claimed eri to addition In Conjectures Severi Some the of few would survive.” equivalence work, rational on Severi’s papers are subsequent ignoring and errors of for forgotten; presence were grounds the area and incompleteness this pi- if in Severi’s wrote: if work subject, however, oneering unfortunate, the who, be on 25–26], would work pp. “It authoritative 98, [Ful his Fulton in William to turn etv ait fdmninn n[e 9,Severi 09], [Sev In that n. conjectured dimension of variety jective ojcue2. Conjecture false. be to Severi h ieso ftevco pc fholomorphic of space j vector the of dimension the eciesm fSvr’ ok trigwt his with starting work, Severi’s of they some Interestingly, describe 04]. Ciliberto, ex- [B-C-P C. Pedrini Severi Brigaglia, Claudio A. that and by article topics the see related plored, other several and equivalence. of en- systems almost Severi’s based on is tirely conjecture this of disproof of dimensional. finite equiv- is rational modulo alence 0-cycles of group the Then Matematica “Francesco Severi”. frson -forms ih)i h nvriyo oesmathematics Rome’s of University the in right) ufr rvdtefloigcnetr of conjecture following the proved Mumford o necletdsuso fti conjecture this of discussion excellent an For method the Mumford, paraphrasing Ironically, eioMsoiiadFacsoSvr o the (on Severi Francesco and Mussolini Benito p a p a = steaihei eu of genus arithmetic the is g V n hswspoe yKdiai 1954. in Kodaira by proved was This . − Let Let g n − V 1 F + easot reuil pro- irreducible smooth a be easot ufc over surface smooth a be g n − 2 · · · − oie fteASVolume AMS the of Notices ( − 1 irr,1939. library, ) V n − and 1 g 1 , g j C is . B 05] [Bo GN05] [G-N 08] [Gowers Cp03] [Cap BG10] [B-G References assistance. and valuable advice their editorial provided in Aspaturian materials help Heidi from their repositories. quote for to permission Archives and California Technology the of and Institute Archives, Lincei, University dei Nazionale Harvard Accademia the medioevo, per Sapienza, il italiano storico della Istituto the Storico Roma, di Archivio Università the dello (EUR), Centrale Archivio Stato the at Zanatta, staffs the and Rita Erwin, Papers; Charlotte Romanello, Zariski Alessandro Panetta, down Susanna the tracking in for Frankfort documents Michelle in and research archival Rome for Rosa Francesca Arezzo; in discussions useful for Farnetani Italo and Annalisa Biagianti Ivo Piccio, friendship; their for Elisa Fabre Giorgio and comments; Capristo, key helpful Fulton translated William his Boas; for who to letter Bowers, Severi’s of passages Maryse thank We Acknowledgments algebraic in interest an current motives, geometry. of of study topic has the that to important relevant 1932, be in to equivalence proved rational of theory BC95] [B-C Ce 58] [Chev BCP04] [B-C-P Fbe08] [Fabre Go 84] [Good ol Wars World .Gowers T. .Capristo A. .Babbitt D. niussqett rv h “Complete- the prove Theorem”, to ness quest Enriques’s .J .Bosworth B. J. R. 295–347. pp. 2004, Berlin/Heidelberg, Springer-Verlag, Abel in and legacy, geometry Abel’s algebraic of school Italian The Ciliberto C. Brigaglia, A. rneo,2008. Princeton, Mathematics to 607–617. Fabre G. d’Italia, 2005. York, New Group, 1915–1945 Dictatorship, Fascist the otrasworld, Volterra’s Goodstein J. .Brigaglia A. 21) 240–248. (2010), inleI I éiar .Cealy2 Chevalley in C. Séminaire II, I, tionelle Chevalley C. 20) 237–56. (2003), rnl rmteIainb .Dflt Queen’s Duflot, 1995. J. Kingston, by University, Italian the from Wars World transl. Two the between Geometry braic oii ncs iAtsmtsodl1931, del Antisemitismo storia di di Quaderni caso Un solini, oml uéiue ai,1958. Paris, Supérieure, Normale neu eCo tApplications et Chow de Anneaux lvA adladRgiPee eds., Piene, Ragni and Laudal A. Olav , , tla ahmtc ewe h Two the between Mathematics Italian aRsen esl iIsrael di mensile Rassegna La oetrs olbrtr iMus- di collaboratori volenterosi I , ed., , ikäsrVra,Bsl 2005. Basel, Verlag, Birkhäuser , uloLv-iiael’Accademia e Levi-Civita Tullio , and and e lse ’qiaec ra- d’équivalence classes Les , h ieadfl fVito of fall and rise The , rneo nvriyPress, University Princeton , oie mr ah Soc. Math. Amer. Notices h eayo il Henrik Niels of Legacy The , h rneo Companion Princeton The usln’ tl:Lf under Life Italy: Mussolini’s .Ciliberto C. .Hs.Ideas Hist. J. 68 .Goodstein J. 20) 89–122. (2008), 59 and Number , , tla Alge- Italian .Pedrini C. Federigo , 45 Penguin , e (1984), École , année, 58 69 8 , , [Ful 98] W. Fulton, Intersection Theory, 2nd ed., [Sev 60] , Fondamenti della Geometria sulle va- Springer-Verlag, New York, 1998. rietà algebriche, Annali di Matematica, 49 [Ha 86] J. Harris, On the Severi problem, Invent. (1960), 283–298. Math. 84 (1986), 445–461. [Waer 70] B. L. van der Waerden, The theory of [Kl 76] S. L. Kleiman, Rigorous foundation of equivalence systems of cycles on a vari- Schubert’s enumerative calculus, Proc. of ety, 1971 Symposia Mathematica, INDAM, Symposia in Pure Math. 28, Amer. Math. Soc., Rome, 1969/70), Academic Press, London, Providence, RI, 1976, pp. 445–482. pp. 255–262. [Kl 05] , The Picard scheme, Math. Surveys and [Ves 90] E. Vesentini, Il caso della Matematica, Conse- Monographs 123, Amer. Math. Soc., 2005, pp. quenze culturali delle leggi razziali in Italia, 237–331. Accademia Nazionale dei Lincei, Rome 84 [Kod 52] K. Kodaira, Arithmetic genera of algebraic (1990), 97–105. varieties, Proc. Nat. Acad. Sci. U.S.A. 38 [Zar 71] O. Zariski, Algebraic Surfaces (second sup- (1952), 527–533. plemented ed.), Springer-Verlag, New York- [Laz 81] R. Lazarsfeld, Excessive intersection of Heidelberg, 1971. divisors, Comp. Mathematica 43 (1981), 281–296. [Mum 69] D. Mumford, Rational equivalence of 0- cycles on surfaces, J. Math. Kyoto 9 (1969), 195–204. [Nér 52] A. Néron, La théorie de la base pour les diviseurs sur les variétés algébriques, Deux- ième Colloque de Géométrie Algébrique Liège, Masson & Cie, Paris, 1952, pp. 119-126. [Parikh 91] C. Parikh, The Unreal Life of Oscar Zariski, Academic Press, Boston, 1991. [Rog 05] Gino Roghi, “Materiale per una Storia dell’Istituto Nazionale di Alta Matematica dal 1939 al 2003”, serie La Matematica nella Soci- età e nella Cultura, Bollettino U.M.I., Bologna, Serie VIII, Vol. VIII-A, Dicembre 2005/2. [Roth 63] L. Roth, Francesco Severi, J. London Math. Soc. 38 (1963), 282–307. [Sch 07] N. Schappacher, A historical sketch of B. AMERICAN M ATHEMATICAL S OCIETY L. van der Waerden’s work in algebraic geometry: 1926–1946, Jeremy J. Gray and Karen Hunger Parshall, eds., in Episodes in the History of Modern Algebra (1800–1950), American Math. Soc., Providence, 2007, pp. 245–283. [Segre 62] , L’opera scientifica di Francesco Sev- eri, Rend. Mat. (5) 21 (1962), 524–584. [Sev 05] F. Severi, Sulla differenza fra i numeri degli integrali di Picard della prima e della seconda specie appartenenti ad una super- ficie irregolare, Atti Acc.Torino 40 (1905), 288–296. [Sev 06] , Sulla totalità delle curve algebriche tracciate sopra una superficie algebrica, Math. Annalen 62 (1906), 194–225. [Sev 09] , Fondamenti per la geometria sulla va- TheTh e AMSA o ers over 2,500 pure rietà algebriche, Rend. del Circolo Matematico and applied mathematics titles di Palermo 28 (1909), 33–87. in eBook form via Google Play. [Sev 12] , Sul principio della conservazione del numero, Rend. del Circolo Matematico di Palermo 33 (1912), 313–327. [Sev 33] , Über die Grundlagen der algebrais- Your favorite texts (even the chen Geometrie, Abhandlungen aus dem outofprint ones!) are now fully math. Seminar der Hamsburgischen Univer- searchable and easily readable sität 9 (1933), 335–364. on webbrowsing devices. [Sev 49] , La géométrie algébrique italienne: sa rigour, ses méthodes, ses problèmes, in Col- loque de géométrie algébrique, Liège, 1949, Start reading today at: play.google.com/store Misson et Cie, Paris, 1950, pp. 9–55.

September 2012 Notices of the AMS 1075