# Francesco Severi

### Quick Info

Arezzo, Tuscany, Italy

Rome, Italy

**Severi**'s most important contributions are to algebraic geometry.

### Biography

**Francesco Severi**'s father, Cosimo Severi, was a notary but he had a literary bent and loved writing poems and hymns which he published. He was an Italian patriot who had fought, alongside his three brothers, in Garibaldi's war of independence against the Austrians. Francesco's mother, Licinia Cambi, was [16]:-

... a woman of high religious feelings, hardworking, thrifty, full of wise foresight and affection in reserve, tenacious, courageous and strong-willed though also apparently submissive ...The Severi family was large with Francesco being the ninth of his parents' nine children. He grew up in an austere environment, receiving little affection, where his father saw little, spoke little, but gave all the orders. The eldest son, fifteen years older that Francesco, was the favoured child and badly spoiled by his parents. However, he emigrated to Buenos Aires cutting himself off completely from the family. This sadness, together with financial problems, led to Cosimo committing suicide on 4 January 1889; Francesco was nine years old. His mother Licinia was in severe financial difficulty with a very small pension but too proud to ask for help bringing up the four children (Francesco and three of his sisters) who were still living at home at this time. The hardship, of course, came from the death of Cosimo but one feels that the family should not have had to suffer in this way as they had wealthy relatives. Leonard Roth, in [14], suggests that Francesco's character must have been influenced by this lack of assistance. While at school Francesco had to earn money to help out and did this with a variety of tutoring jobs. It was a childhood of considerable poverty and hard work and Severi said in later life that he had been [16]:-

... sentenced to a life of hard labour in a penal colony.While at school Severi became interested in politics and was attracted to the Socialist movement which at this time was growing in popularity. We note at this point that Severi had rather strange political allegiances, with his political position moving between the left and the right at various times. He completed his secondary education at the Technical Institute of Arezzo in 1896 and he won a university scholarship from the Fraternità dei Laici. He studied at Turin University where, despite the scholarship, he had very little money and had to continue tutoring privately in order to make enough to live. His wealthy relatives could easily have funded his studies but chose not to help him at all. He enrolled in the engineering course, since this had been his father's wish, but soon changed after studying under Corrado Segre who persuaded him to study pure mathematics. Severi had not studied Latin at secondary school and now required that subject to enrol for a degree in pure mathematics. He overcame this problem by learning Latin on his own. Once in the pure mathematics course, Severi was taught by Corrado Segre, Giusepe Peano and Vito Volterra. He became fascinated by geometry and, under Corrado Segre's supervision, he went on to obtain his doctorate in 1900. He was highly appreciative of Corrado Segre describing him as an [5]:-

... incomparable teacher. With assiduous care he trained my intellect [and taught me to appreciate] rigorous scientific investigations ... [stirring my] heart to the highest filial feelings.In addition to his advisor Corrado Segre, Severi also benefited from the friendship of Gaetano Scorza who, although an assistant of Eugenio Bertini in Pisa, spent the year 1899-1900 as an assistant to Corrado Segre. Severi writes:-

I remember the long walks together in Valentino park or on the small, shady, quiet roads in the Turin hills. Solitary walks on cold winter days or intoxicated by the bright and harmonious awakening in spring when nature was bursting into life: spring in the world around and in our lives.Severi contrasts Scorza's personality with his own. He described himself as follows:-

I am restless, impulsive, easy to disdain, to rebuke and forgive, to get enthusiastic, to dream, yes, but tempered by the realistic spirit of my land.His doctoral thesis,

*Sopra alcune singolarità delle curve di un iperspazio*Ⓣ, together with a series of other papers which he published had published while an undergraduate, deal with enumerative geometry, a subject which had been started by Hermann Schubert. After being awarded his doctorate, Severi accepted a post in Turin as assistant to Enrico D'Ovidio for the academic year 1900-01. He had married Rosanna Orlandini on 10 October 1900; she had been a friend from childhood. She was a great support to Severi during the 52 years of their marriage; she died in 1952. From Turin, Severi and his wife moved to Bologna where he became an assistant to Federigo Enriques in 1902. His final post as assistant was in Pisa in 1903 where this time he was assistant to Eugenio Bertini.

In 1904 Severi was appointed to the Chair of Projective and Descriptive Geometry at Parma. Roth writes [14]:-

The interview which led to this appointment must be unique in Italian university annals, for the selection committee insisted on Severi's giving a trial lesson in descriptive geometry at the blackboard (and this at a time when the candidate had publications which placed him in the front rank). After the meeting, Castelnuovo (who was not on the committee) made his way to Rome railway station, sought out Severi, who was sitting in the train for Arezzo, and gave him the good news: again an unusual proceeding.Severi only worked at Parma for one year, accepting the chair at Padua in 1905. In a letter to Beniamino Segre in 1938, Guido Castelnuovo explains how his work and that of Enriques, interacted with that of Severi over the period 1904-08 [6]:-

One last comment regarding the historical issues. ... The notion of a continuous system [now called an algebraic system] of curves on some special surfaces already appears in some works of Enriques and mine that precede the work of Severi. ... In some special cases I suggested the definition of the characteristic series of a continuous system to Severi. But since this suggestion had been given in an unpublished letter, and subsequently Severi brilliantly developed the idea mentioned in it, it is not useful to make a claim of priority here. I only mention this matter to show you how much caution is needed when you assign scientific priorities in periods in which the research was often done in collaboration, or was suggested by elders to their more youthful colleagues. It was the good fortune of the Italian school of algebraic geometry to have this disinterested collaboration between 1890 and 1910. But this makes it necessary to smooth out certain overly clean divisions between the work of one and the other. What is undoubtedly due to Severi in the period 1904-1908 are the following: the theorem that the existence of Picard integrals of the 1st and 2nd kind on an algebraic surface depends on the irregularity of the surface (1904), a theorem that was successively stated precisely by both of us; the theory of the algebraic equivalence of curves on a surface; and the Theorem of the Base [this has evolved into the Néron-Severi Theorem]. That is more than enough to show his great worth.Severi continued his left-wing political position by joining the Blocco Popolare Patavino after taking up the chair in Padua. This led to his appointment as director of the municipal gas and water company in Padua. He joined the Socialist party in 1910 and was immediately elected as a Socialist Party councillor for Padua. He was also the party's education spokesman. In 1914, when Severi held his chair in Padua, World War I broke out but, shortly after hostilities began on 3 August, Italy declared that it would not commit troops to the fighting. This was despite having an alliance with Germany and Austria-Hungary. Italy revoked this alliance on 3 May 1915 and later that month declared war on Austria-Hungary. Severi's tenure of the chair at Padua was interrupted by the war and he volunteered for military service as soon as Italy joined the war in 1915. At this time he resigned from the Socialist Party which had a policy of Italian neutrality. He served with distinction in the artillery for the duration of the war, he was promoted several times and decorated for valour. In May 1916, he was in the Val Lagarina area when the Austrians attacked with a well planned advance. The Italians fought with determination for several days and, although falling back, continued to put up a spirited resistance.

After he was demobbed, Severi returned to his chair in Padua where he remained until 1922 when he was appointed to the Faculty of Mathematical Sciences at the University of Rome. There he began teaching a variety of courses from calculus to higher geometry. In August 1924 he was an invited plenary speaker at the International Congress of Mathematicians in Toronto giving the talk

*La géométrie algébrique*Ⓣ. The Italian Fascist movement had started around 1921 as a nationalist movement. Led by Benito Mussolini, the Fascists came to power in 1923. Giovanni Gentile, a philosopher who became an ardent supporter of the Fascist philosophy, was minister of education from 1922 to 1924. In 1923 Gentile recommended that Severi, in addition to his role in mathematics, be appointed rector of the university. Now Giacomo Matteotti (1885-1924) was a member of the Socialist Party who was elected to the Chamber of Deputies and on 30 May 1924 he made a speech in the Chamber highly critical of the Fascists. Only a few days later, on 10 June, Matteotti was murdered by six Fascist thugs. Severi protested and later declared that he gave up politics at this time. Along with many of his fellow mathematicians in Rome, he also signed Benedetto Croce's anti-Fascist manifesto, a fact made public in 1925. As a consequence, Severi resigned as rector of the University of Rome to avoid becoming criticised in an enquiry which was being set up to investigate these matters. The record shows that Severi, despite his previous membership of the Socialist Party, now began to seek favour with Mussolini and the Fascists [13]:-

Severi began sending the Fascist leader a steady stream of articles, several embellished with a flowery personal note. ... the historical record suggests that he wanted to play a prominent role in the intellectual life of the new Fascist state. Indeed, Severi used his considerable political connections to promote his advancement.For example, on 31 January 1929, Severi sent a document to Mussolini from which we quote (see, for example [2]):-

After having resigned from the socialist party in the first months of 1915, I enrolled as a volunteer when the war broke out, and I was always a fighter at the front. When the war finished, in Padua, where I was Director of that School of Engineers, I faced up to the Bolshevik movement with the fighters. I did not support Fascism, whose structure of admirable coordination of national and economic-social activities, later revealed to me, I had not yet glimpsed; but today I am very close to it, even if on some particular problem, as the press one, my ideas are less orthodox, and agree with what lately an influential fascist Gentile could freely expose. ... I have been abroad several times for scientific reasons and spent a long time, after the accession of Fascism, in America in 1924, in Russia in 1925, in Spain and in Switzerland in 1928. And now I am about to return to Spain. And I never performed any deeds nor pronounced any judgement that, not even for a moment, could be interpreted as adverse to the Regime.It would appear that his changed political views, moving from the Socialist Party to the Fascist Party, had more to do with his desire for advancement that with his political views. In particular he tried to make sure that his name was put forward for the new, state-sponsored Reale Accademia d'Italia. He was nominated in 1929 becoming the only mathematician in the Academy and, three years later, he joined the Fascist Party. In 1933 he published

*Fascismo e Scienza*Ⓣ which extolled the virtues of Italian mathematics and of Fascism telling all Italians it was their patriotic duty to support it. Although the Fascists had not been anti-Semitic at the beginning of the movement, they enacted the Manifesto della razza Ⓣ in July 1938 which forced those of Jewish origins out of the universities. Although Severi would later say that he was appalled to see his Jewish colleagues dismissed, there is considerable evidence that he was leading the call for their dismissal. From this period until Rome was liberated by the Allies in 1944, Severi was the leading Italian mathematician filling leading positions left vacant as his Jewish colleagues were dismissed.

After the end of World War II, various commissions were set up to investigate those who had been active Fascists or who had continued to support Mussolini after he was deposed in September 1943. Severi was suspended from his duties while the investigation took place but the commission cleared him, stating the he:-

... had not received from Fascism anything more than was his due as a distinguished scientist.However, the Accademia dei Lincei dismissed Severi and refused to readmit him even after the favourable findings of the Commission. Only in 1948 when a general amnesty was enacted was Severi re-elected to the Accademia dei Lincei. He strongly defended his actions writing in 1953:-

I have never recanted nor repudiated any of the acts of my life that were, and are, expressions of the strongest attachment to my country.We must not allow the arguments over Severi's political position to detract from his exceptional mathematical contributions. His most important contributions are to algebraic geometry and we have seen in the quote above Castelnuovo's description of Severi's contributions in 1904-08. Severi, who gets the highest praise from some colleagues but severe criticism from others, criticised the work of his contemporaries as lacking rigour and relying too heavily on intuition. However, his own work was, by today's standards, not rigorous. The authors of [13] state:-

Severi, perhaps more than any other major mathematician of his day, stated more true theorems whose proofs were "irreparable" by modern standards or "almost true" theorems that required modifications to make them true or that were just plain false "theorems".Roth, in [14], summarises Severi's contributions in the following way:-

Severi's scientific work presents several features which, when taken together, must make his career a rarity. To begin with, there is the uniformly high level of his very considerable scientific production: as a rule Severi attacks only important questions of general character and usually of great difficulty. ... In the second place, one cannot fail to observe an essential unity of outlook. Severi maintains a balance between geometry and analysis - he has actually made outstanding contributions to function theory. But within his geometrical work itself the same unity is manifest ...After work on enumerative geometry, Severi turned to birational geometry of surfaces, a topic which Castelnuovo and Enriques has spent ten years developing before Severi began to work on it. He introduced many concepts into geometry, for example the notion of algebraic equivalence. He gave necessary and sufficient conditions for the linear equivalence of two curves on a surface in 1905. Some rate Severi's discovery of a base of algebraically independent curves on any surface as his most important contribution. He published this in

*Mathematische Annalen*in 1906 and Max Noether wrote to Severi concerning these results saying:-

You have shed a great light on geometry.In 1907 Enriques and Severi won the Prix Bordin from the French Academy of Sciences for a work on hyperelliptic surfaces. We have only scratched the surface for it is impossible to give in this short article any real indication of the range of the contributions which Severi made. For example, in [13] Beniamino Segre lists over 400 publications by Severi. Six volumes of

*Opere matematiche: memorie e note*Ⓣ contain 196 of these papers. J S Joel writes in a review:-

... the first four of a planned six, contain 142 mathematical papers of Severi (1879-1961), principally concerning algebraic geometry (surfaces) and function theory of two (or more) complex variables. ... One remarkable thing is that topics touched upon in the first volume recur later on (with deeper results); inversion theorems, theories of equivalence, correspondences, surfaces admitting a continuous group of birational transformations, base loci, intersection multiplicities, Riemann-Roch theorems, enumerative problems.Roth describes Severi's teaching abilities in [14] writing:-

... it was as a teacher of geometry that Severi excelled. His lectures on his own work were unforgettable, the style was beautifully simple ... and the presentation masterly. He was greatly interested in teaching for its own sake, and his didactic skill found an outlet in a whole stream of books ...Despite the incredible output of mathematics from Severi, he had an amazing number of outside interests. Again we quote [14]:-

As he approached middle age, mathematics came to occupy less and less of his time, it had to compete with a host of other occupations. For Severi by then was (among other things) President of an Arezzo bank, head of the engineering faculty at Padua, an expert agriculturist who managed his own estate.His most impressive work came before he went to Rome but, despite spending less time on mathematics, after this he still managed to produce work of the greatest importance like the solution of the Dirichlet problem and his development of the theory of rational equivalence. We have already seen much of Severi's character in the above biography but let Roth [14] give us this summary:-

[He considered] that the world at large failed to treat him with due consideration. For, incredible as it may seem, although during the whole period of his maturity honours were showered upon him and invitations poured in, yet he remained forever unsatisfied. Intellectually, materially and socially, he had nearly everything a man could hope for; he possessed a towering presence, with a leonine head, he was a superb talker - and writer, a connoisseur of art and the humanities in general, a world traveller - but despite all this he seemed more or less permanently aggrieved. He was fond of appearing as a martyr, a part that he played with conviction. ... Personal relationships with Severi, however complicated in appearance, were always reducible to two basically simple situations: either he had just taken offence or else he was in the process of giving it - and quite often genuinely unaware that he was doing so. Paradoxically, endowed as he was with even more wit than most of his fellow Tuscans, he showed a childlike incapacity either for self-criticism or for cool judgement. Thus he meddled in politics, whereas it would have been far better had he left them alone.Among the honours given to Severi we have already mention his election to the Accademia dei Lincei in 1910. He was elected to the Paris Academy of Sciences in 1957 and was made an honorary member of the London Mathematical Society in 1959. He was elected to the National Academy of Sciences of Italy (the "Academy of XL") in 1919 and served as its president from 1949 to 1955, and re-elected from 1955 to 1961. He was awarded the gold medal from the National Academy of Sciences of Italy, the Guccia gold medal and, as we mentioned above, the Bordin prize from the Paris Academy of Sciences.

### References (show)

- B Segre, Biography in
*Dictionary of Scientific Biography*(New York 1970-1990). See THIS LINK. - A Guerraggio and P Nastasi,
*Italian mathematics between the two World Wars*(Birkhäuser Verlag, Basel, Boston, Berlin, 2000). - B Segre,
*L'opera scientifica di Francesco Severi*(Rome, 1962). - B Segre,
*L'opera scientifica di Francesco Severi (1879-1961)*, Ricerca Sci. Parte I 3 (1962). - F Severi,
*Dalla scienza alla fed*(Edizioni Pro Civitate Christiana, 1959). - D Babbitt and J Goodstein, Guido Castelnuovo and Francesco Severi: Two Personalities, Two Letters,
*Notices Amer. Math. Soc.***56**(7) (2009), 800-808. - D C Demaria, Francesco Severi's contribution to topology (Italian), P
*roceedings of the mathematical congress in celebration of the one hundredth birthday of Guido Fubini and Francesco Severi, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur.***115**(1981), 161-165. - S Doleck and G H Greco, Tangency vis-à-vis differentiability by Peano, Severi and Guareschi,
*J. Convex Anal.***18**(2) (2011), 301-339. - A Ellero and A Sorato, The cones of George Bouligand and Francesco Severi (Italian),
*Lett. Mat. Pristem No.***37**(2000), 20-24. - G Fichera, The contributions of Francesco Severi and Guido Fubini to the theory of functions of several complex variables (Italian),
*Proceedings of the mathematical congress in celebration of the one hundredth birthday of Guido Fubini and Francesco Severi, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur.***115**(1981), 217-233. - Francesco Severi (Italian),
*Accad. Naz. dei XL Annuario Generale**1953*(1953), 13-30. - D Galletto, The ideas of Einstein in the works of Guido Fubini and Francesco Severi (Italian),
*Proceedings of the mathematical congress in celebration of the one hundredth birthday of Guido Fubini and Francesco Severi, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur.***115**(1981), 205-216. - J Goodstein and D Babbitt, A Fresh Look at Francesco Severi,
*Notices Amer. Math. Soc.***59**(8) (2012), 1064-1075. - L Roth, Francesco Severi,
*J. London Math. Soc.***38**(1963), 282-307. - B Segre, L'opera scientifica di Francesco Severi,
*Rend. Mat. e Appl.*(5)**21**(1962), 524-584. - B Segre, Francesco Severi (13 aprile 1879-8 dicembre 1961),
*Ann. Mat. Pura Appl.*(4)**61**(1963), i-xxxvi. - B L van der Waerden, Francesco Severi and the foundations of algebraic geometry,
*Symposia mathematica***XXVII**(London-New York, 1986), 239-244. - S Xambó-Descamps, Francesco Severi and the principle of conservation of number, in
*Algebra and geometry (1860-1940): the Italian contribution, Cortona, 1992, Rend. Circ. Mat. Palermo*(2) Suppl. No. 36 (1994), 255-277. - G Zappa, The Francesco Severi school of mathematics around 1940 (Italian),
*Riv. Mat. Univ. Parma*(4)**10**(1984), 11-14.

### Additional Resources (show)

Other websites about Francesco Severi:

### Honours (show)

Honours awarded to Francesco Severi

### Cross-references (show)

Written by J J O'Connor and E F Robertson

Last Update May 2013

Last Update May 2013