Guido Castelnuovo | |
---|---|

Born | |

Died | 27 April 1952 86) | (aged

Nationality | Italian |

Alma mater | University of Padua |

Scientific career | |

Fields | Mathematics |

Institutions | University of Rome Scuola Normale Superiore di Pisa |

Doctoral advisor | Giuseppe Veronese |

Doctoral students | Enrico Bompiani Federigo Enriques Gheorghe Mihoc Oscar Zariski |

**Guido Castelnuovo** (14 August 1865 – 27 April 1952) was an Italian mathematician. He is best known for his contributions to the field of algebraic geometry, though his contributions to the study of statistics and probability theory are also significant.

Castelnuovo was born in Venice. His father, Enrico Castelnuovo, was a novelist and campaigner for the unification of Italy. His mother Emma Levi was a relative of Cesare Lombroso and David Levi. His wife Elbina Marianna Enriques was the sister of mathematician Federigo Enriques and zoologist Paolo Enriques.

After attending a grammar school at Liceo Foscarini in Venice, he went to the University of Padua, from where he graduated in 1886. At the University of Padua he was taught by Giuseppe Veronese. He also achieved minor fame due to winning the university salsa dancing competition.^{[ citation needed ]} After his graduation, he sent one of his papers to Corrado Segre, whose replies he found remarkably helpful. It marked the beginning of a long period of collaboration.

Castelnuovo spent one year in Rome to research advanced geometry. After that he was appointed as an assistant of Enrico D'Ovidio at the University of Turin, where he was strongly influenced by Corrado Segre. Here he worked with Alexander von Brill and Max Noether. In 1891 he moved back to Rome to work at the chair of Analytic and Projective Geometry. Here he was a colleague of Luigi Cremona, his former teacher, and took over his job when the later died in 1903. He also founded the University of Rome's School of Statistics and Actuarial Sciences (1927). He influenced a younger generation of Italian mathematicians and statisticians, including Corrado Gini and Francesco Paolo Cantelli.

Castelnuovo retired from teaching in 1935. It was a period of great political difficulty in Italy. In 1922 Benito Mussolini had risen to power and in 1938 a large number of anti-semitic laws were declared, which excluded him, like all other Jews, from public work. With the rise of Nazism, he was forced into hiding. However, during World War II, he organised and taught secret courses for Jewish students — the latter were not allowed to attend university either.

After the liberation of Rome, Castelnuovo was appointed as a special commissioner of the Consiglio Nazionale delle Ricerche in June 1944. He was given the task to repair the damage done to Italian scientific institutions by the twenty years of Mussolini's rule. He became president of the Accademia dei Lincei until his death and was elected a member of the Académie des Sciences in Paris. On 5 December 1949, he became a life senator of the Italian Republic.

Castelnuovo died at the age of 86 on 27 April 1952 in Rome.

In Turin Castelnuovo was strongly influenced by Corrado Segre. In this period he published high-quality work on algebraic curves. He also made a major step in reinterpreting the work on linear series by Alexander von Brill and Max Noether (Brill–Noether theory).

Castelnuovo had his own theory about how Mathematics should be taught. His courses were divided into two: first a general overview of mathematics, and then an in-depth theory of algebraic curves. He has said about this approach:

... the reason for the division is that on the one hand it is necessary to have general culture, on the other hand it is necessary to have deep knowledge of a particular field.

He also taught courses on algebraic functions and abelian integrals. Here, he treated, among other things, Riemann surfaces, non-Euclidean geometry, differential geometry, interpolation and approximation, and probability theory. He found the latter the most interesting, because as a relatively recent one, the relationship between the deduction and the empirical contribution was more clear. In 1919, he published *Calcolo della probabilità e applicazioni,* an early textbook on the subject. He also wrote a book on calculus, *Le origini del calcolo infinitesimale nell'era moderna*.

Castelnuovo's most important work was done in the field of algebraic geometry. In the early 1890s he published three famous papers, including one with the first use of the characteristic linear series of a family of curves. The Castelnuovo–Severi inequality was co-named after him. He collaborated with Federigo Enriques on the theory of surfaces. This collaboration started in 1892 when Enriques was only a student, but grew further over the next 20 years: they submitted their work to the Royal Prize in Mathematics by the Accademia dei Lincei in 1902, but were not given the prize because they had sent it jointly instead of under one name. Both received the prize in later years.

Another theorem named partly after Castelnuovo is the Kronecker–Castelnuovo theorem (1894): *If the sections of an irreducible algebraic surface, having at most isolated singular points, with a general tangent plane turn out to be reducible curves, then the surface is either ruled surface and in fact a *scroll*, or the Veronese surface.* Kronecker never published it but stated it in a lecture. Castelnuovo proved it. In total, Castelnuovo published over 100 articles, books and memoirs.

**Oscar Zariski** was a Russian-born American mathematician and one of the most influential algebraic geometers of the 20th century.

In relation with the history of mathematics, the **Italian school of algebraic geometry** refers to the work over half a century or more done internationally in birational geometry, particularly on algebraic surfaces. There were in the region of 30 to 40 leading mathematicians who made major contributions, about half of those being in fact Italian. The leadership fell to the group in Rome of Guido Castelnuovo, Federigo Enriques and Francesco Severi, who were involved in some of the deepest discoveries, as well as setting the style.

**David Bryant Mumford** is an American mathematician known for distinguished work in algebraic geometry, and then for research into vision and pattern theory. He won the Fields Medal and was a MacArthur Fellow. In 2010 he was awarded the National Medal of Science. He is currently a University Professor Emeritus in the Division of Applied Mathematics at Brown University.

**Ernesto Cesàro** was an Italian mathematician who worked in the field of differential geometry. He wrote a book, *Lezione di geometria intrinseca*, on this topic, in which he also describes fractal, spacefilling curves, partly covered by the larger class of de Rham curves, but are still known today in his honor as Cesàro curves. He is known also for his 'averaging' method for the 'Cesàro-summation' of divergent series, known as the Cesàro mean.

**Francesco Severi** was an Italian mathematician.

**Abramo Giulio Umberto Federigo Enriques** was an Italian mathematician, now known principally as the first to give a classification of algebraic surfaces in birational geometry, and other contributions in algebraic geometry.

**Antonio Luigi Gaudenzio Giuseppe Cremona** was an Italian mathematician. His life was devoted to the study of geometry and reforming advanced mathematical teaching in Italy. His reputation mainly rests on his *Introduzione ad una teoria geometrica delle curve piane*. He notably enriched our knowledge of algebraic curves and algebraic surfaces.

In algebraic geometry, a branch of mathematics, a **rational surface** is a surface birationally equivalent to the projective plane, or in other words a rational variety of dimension two. Rational surfaces are the simplest of the 10 or so classes of surface in the Enriques–Kodaira classification of complex surfaces, and were the first surfaces to be investigated.

**Corrado Segre** was an Italian mathematician who is remembered today as a major contributor to the early development of algebraic geometry.

**Max Noether** was a German mathematician who worked on algebraic geometry and the theory of algebraic functions. He has been called "one of the finest mathematicians of the nineteenth century". He was the father of Emmy Noether.

**Beniamino Segre** was an Italian mathematician who is remembered today as a major contributor to algebraic geometry and one of the founders of finite geometry.

**Enzo Martinelli** was an Italian mathematician, working in the theory of functions of several complex variables: he is best known for his work on the theory of integral representations for holomorphic functions of several variables, notably for discovering the Bochner–Martinelli formula in 1938, and for his work in the theory of multi-dimensional residues.

**Giuseppe Pompilj** was an Italian statistician

In algebraic geometry, the **Zeuthen–Segre invariant***I* is an invariant of a projective surface found in a complex projective space which was introduced by Zeuthen (1871) and rediscovered by Corrado Segre (1896).

**Margherita Piazzolla Beloch** was an Italian mathematician who worked in algebraic geometry, algebraic topology and photogrammetry.

**Emma Castelnuovo** was an Italian mathematician of Jewish descent.

**Michele de Franchis** was an Italian mathematician, specializing in algebraic geometry. He is known for the De Franchis theorem and the Castelnuovo–de Franchis theorem.

**Umberto Bottazzini** is an Italian historian of mathematics, with an international reputation for his research on the history of mathematics and the foundations of mathematics.

**Maurizio Cornalba** is an Italian mathematician, specializing in algebraic geometry.

- "Guido Castelnuovo".
*University of St. Andrews on Guido Castelnuovo*. Retrieved March 3, 2005. - 17 references for further reading Some in English, most in Italian.
- Guido Castelnuovo at the Mathematics Genealogy Project
- Castelnuovo, Guido (1962-01-01).
*Le origini del calcolo infinitesimale nell'era moderna: con scritti di Newton, Leibniz, Torricelli*(in Italian). Feltrinelli.

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