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

Born | Venice | 14 August 1865

Died | 27 April 1952 86) Rome | (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.

**Italy**, officially the **Italian Republic**, is a country in Southern Europe. Located in the middle of the Mediterranean Sea, Italy shares open land borders with France, Switzerland, Austria, Slovenia and the enclaved microstates San Marino and Vatican City. Italy covers an area of 301,340 km^{2} (116,350 sq mi) and has a largely temperate seasonal and Mediterranean climate. With around 61 million inhabitants, it is the fourth-most populous EU member state and the most populous country in Southern Europe.

A **mathematician** is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

**Algebraic geometry** is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros.

Castelnuovo was born in Venice. His father, Enrico Castelnuovo, was a novelist and campaigner for the unification of Italy.

**Venice** is a city in northeastern Italy and the capital of the Veneto region. It is situated on a group of 118 small islands that are separated by canals and linked by over 400 bridges. The islands are located in the shallow Venetian Lagoon, an enclosed bay that lies between the mouths of the Po and the Piave rivers. In 2018, 260,897 people resided in the *Comune di Venezia*, of whom around 55,000 live in the historical city of Venice. Together with Padua and Treviso, the city is included in the Padua-Treviso-Venice Metropolitan Area (PATREVE), which is considered a statistical metropolitan area, with a total population of 2.6 million.

**Enrico Castelnuovo** was an Italian writer who had an active role in the Italian unification movement.

A **novelist** is an author or writer of novels, though often novelists also write in other genres of both fiction and non-fiction. Some novelists are professional novelists, thus make a living writing novels and other fiction, while others aspire to support themselves in this way or write as an avocation. Most novelists struggle to get their debut novel published, but once published they often continue to be published, although very few become literary celebrities, thus gaining prestige or a considerable income from their work.

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.

The **University of Padua** is a premier Italian university located in the city of Padua, Italy. The University of Padua was founded in 1222 as a school of law and was one of the most prominent universities in early modern Europe. Padua is the second-oldest university in Italy and the world's fifth-oldest surviving university. In 2010 the university had approximately 65,000 students, in 2016 was ranked "best university" among Italian institutions of higher education with more than 40,000 students, and in 2018 best Italian university according to ARWU ranking.

**Giuseppe Veronese** was an Italian mathematician. He was born in Chioggia, near Venice.

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.

**Rome** is the capital city and a special *comune* of Italy. Rome also serves as the capital of the Lazio region. With 2,872,800 residents in 1,285 km^{2} (496.1 sq mi), it is also the country's most populated *comune*. It is the fourth most populous city in the European Union by population within city limits. It is the centre of the Metropolitan City of Rome, which has a population of 4,355,725 residents, thus making it the most populous metropolitan city in Italy. Rome is located in the central-western portion of the Italian Peninsula, within Lazio (Latium), along the shores of the Tiber. The Vatican City is an independent country inside the city boundaries of Rome, the only existing example of a country within a city: for this reason Rome has been often defined as capital of two states.

**Enrico D'Ovidio** (1842-1933) was an Italian mathematician who is known by his works on geometry.

The **University of Turin** is a university in the city of Turin in the Piedmont region of north-western Italy. It is one of the oldest universities in Europe, and continues to play an important role in research and training. It is steadily ranked among the top 5 Italian universities and it is ranked third for research activities in Italy, according to the latest data by ANVUR.

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 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.

**Benito Amilcare Andrea Mussolini** was an Italian politician and journalist who was the leader of the National Fascist Party. He ruled Italy as Prime Minister from 1922 to 1943; he constitutionally led the country until 1925, when he dropped the pretense of democracy and established a dictatorship.

**Antisemitism** is hostility to, prejudice, or discrimination against Jews. A person who holds such positions is called an **antisemite**. Antisemitism is generally considered to be a form of racism. It has also been characterized as a political ideology which serves as an organizing principle and unites disparate groups which are opposed to liberalism.

**Law** is a system of rules that are created and enforced through social or governmental institutions to regulate behavior. It has been defined both as "the Science of Justice" and "the Art of Justice". Law is a system that regulates and ensures that individuals or a community adhere to the will of the state. State-enforced laws can be made by a collective legislature or by a single legislator, resulting in statutes, by the executive through decrees and regulations, or established by judges through precedent, normally in common law jurisdictions. Private individuals can create legally binding contracts, including arbitration agreements that may elect to accept alternative arbitration to the normal court process. The formation of laws themselves may be influenced by a constitution, written or tacit, and the rights encoded therein. The law shapes politics, economics, history and society in various ways and serves as a mediator of relations between people.

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.

The **Accademia dei Lincei** is an Italian science academy, located at the Palazzo Corsini on the Via della Lungara in Rome, Italy.

A **senator for life** is a member of the senate or equivalent upper chamber of a legislature who has life tenure. As of 2018, six Italian Senators out of 320, three out of the 47 Burundian Senators and all members of the British House of Lords have lifetime tenure. Several South American countries once granted lifetime membership to former presidents but have since abolished the practice.

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 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.

**Giuseppe Peano** was an Italian mathematician and glottologist. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much notation. The standard axiomatization of the natural numbers is named the Peano axioms in his honor. As part of this effort, he made key contributions to the modern rigorous and systematic treatment of the method of mathematical induction. He spent most of his career teaching mathematics at the University of Turin. He also wrote an international auxiliary language, Latino sine flexione, which is a simplified version of Classical Latin. Most of his books and papers are in Latin sine flexione, others are in Italian.

**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.

**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.

In mathematics, **Max Noether's theorem** in algebraic geometry may refer to at least six results of Max Noether. Noether's theorem usually refers to a result derived from work of his daughter Emmy Noether.

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.

In mathematics, the **Castelnuovo–de Franchis theorem** is a classical result on complex algebraic surfaces. Let *X* be such a surface, projective and non-singular, and let

**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.

The **Faculty of Mathematics and Computer Science** is one of twelve faculties at the University of Heidelberg. It comprises the Institute of Mathematics, the Institute of Applied Mathematics, the School of Applied Sciences, and the Institute of Computer Science. The faculty maintains close relationships to the Interdisciplinary Center for Scientific Computing (IWR) and the Mathematics Center Heidelberg (MATCH). The first chair of mathematics was entrusted to the physician Jacob Curio in the year 1547.

**Guido Zappa** was an Italian mathematician and a noted group theorist: his other main research interests were geometry and also the history of mathematics. Zappa was particularly known for some examples of algebraic curves that strongly influenced the ideas of Francesco Severi.

**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.

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.

**Pia Maria Nalli** was an Italian mathematician known for her work on the summability of Fourier series, on Morera's theorem for analytic functions of several variables and for finding the solution to the Fredholm integral equation of the third kind for the first time. Her research interests ranged from algebraic geometry to functional analysis and tensor analysis; she was a speaker at the 1928 International Congress of Mathematicians.

**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.

- "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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