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Francesco Severi

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13 April 1879

Arezzo, Italy

8 Dec 1961

Rome, Italy

Francesco Severi studied at Turin University where he had very little money and had to tutor privately in order to make enough to live. The hardship came from the sad loss of his father when he was nine years old but one feels that he should not have had to suffer in this way as his wealthy relatives could easily have funded his studies but chose not to help him at all.

His ideas of becoming an engineer soon changed after studying under Corrado Segre at Turin. Severi became fascinated by geometry and, under Corrado Segre 's supervision he went on to obtain his doctorate in 1900. His doctoral thesis, together with a series of other papers which Severi published at this time, deal with enumerative geometry, a subject which had been started by Schubert .

After being awarded his doctorate, Severi accepted a post in Turin as assistant to D'Ovidio . From there he moved to Bologna where he acted as assistant to Enriques . His final post as assistant was held in Pisa where this time he was assistant to Bertini .

In 1904 Severi was appointed to the Chair of Projective and Descriptive Geometry at Parma. He only worked at Parma for one year, accepting the chair at Padua in 1905. World War I interrupted Severi's tenure of the chair at Padua and during the war he served with distinction in the artillery.

From 1922 Severi worked at the University of Rome. His most important contributions are to algebraic geometry . He criticised the work of his contemporaries as lacking rigour and relying too heavily on intuition. Roth , in , 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.

Severi introduced many concepts into geometry, for example he notion of algebraic equivalence. He gave necessary and sufficient conditions for the linear equivalence of two curves on a surface F 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.

It is impossible to give any real indication of the contribution which Severi made in a short article. In Beniamino Segre lists over 400 publications by Severi.

Roth describes Severi's teaching abilities in 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 :

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 the 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.

For his character we again quote Roth :

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.

Source:School of Mathematics and Statistics University of St Andrews, Scotland