Guido Castelnuovo
Encyclopedia
Guido Castelnuovo was an Italian
mathematician
. His father, Enrico Castelnuovo
, was a novelist and campaigner for the unification of Italy. Castelnuovo is best known for his contributions to the field of algebraic geometry
, though his contributions to the study of statistics and probability are also significant.
.
After attending a grammar school at Foscarini in Venice, he went to Padua
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. 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.
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
.
had risen to power and in 1938 a large number of anti-semitic law
s 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.
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.
Castelnuovo was strongly influenced by Corrado Segre
. In this period he published high-quality work on algebra
ic curve
s. 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:
He also taught courses on algebraic function
s 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.
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. His father, Enrico Castelnuovo
Enrico Castelnuovo
----Enrico Castelnuovo was an Italian writer who had an active role in the Italian unification movement.He was the father of Guido Castelnuovo.- Literary works :* Il quaderno della zia, 1872...
, was a novelist and campaigner for the unification of Italy. Castelnuovo is best known for his contributions to the field of algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
, though his contributions to the study of statistics and probability are also significant.
Early life
Castelnuovo was born in VeniceVenice
Venice is a city in northern Italy which is renowned for the beauty of its setting, its architecture and its artworks. It is the capital of the Veneto region...
.
After attending a grammar school at Foscarini in Venice, he went to Padua
Padua
Padua is a city and comune in the Veneto, northern Italy. It is the capital of the province of Padua and the economic and communications hub of the area. Padua's population is 212,500 . The city is sometimes included, with Venice and Treviso, in the Padua-Treviso-Venice Metropolitan Area, having...
where he graduated in 1886. At the University of Padua
University of Padua
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. It is among the earliest universities of the world and the second...
he was taught by Giuseppe Veronese
Giuseppe Veronese
Giuseppe Veronese was an Italian mathematician. He was born in Chioggia, near Venice.Although his work was severely criticised as unsound by Peano, he is now recognised as having priority on many ideas that have since become parts of transfinite numbers and model theory, and as one of the...
. He also achieved minor fame due to winning the university salsa dancing competition. After his graduation, he sent one of his papers to Corrado Segre
Corrado Segre
Corrado Segre was an Italian mathematician who is remembered today as a major contributor to the early development of algebraic geometry....
, whose replies he found remarkably helpful. It marked the beginning of a long period of collaboration.
Career
Castelnuovo spent one year in RomeRome
Rome is the capital of Italy and the country's largest and most populated city and comune, with over 2.7 million residents in . The city is located in the central-western portion of the Italian Peninsula, on the Tiber River within the Lazio region of Italy.Rome's history spans two and a half...
to research advanced geometry. After that he was appointed as an assistant of Enrico D'Ovidio at the University of Turin
University of Turin
The University of Turin is a university in the city of Turin in the Piedmont region of north-western Italy...
, where he was strongly influenced by Corrado Segre. Here he worked with Alexander von Brill
Alexander von Brill
Alexander Wilhelm von Brill was a German mathematician.Born in Darmstadt, Hesse, he attended University of Giessen where he earned his doctorate under supervision of Alfred Clebsch. He held a chair at the University of Tübingen, where Max Planck was among his students.-External links:...
and Max Noether
Max Noether
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".-Biography:...
. 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
Luigi Cremona
Luigi 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...
, his former teacher, and took over his job when the later died in 1903. He also founded the University of Rome
University of Rome La Sapienza
The Sapienza University of Rome, officially Sapienza – Università di Roma, formerly known as Università degli studi di Roma "La Sapienza", is a coeducational, autonomous state university in Rome, Italy...
's School of Statistics and Actuarial Sciences (1927). He influenced a younger generation of Italian mathematicians and statisticians, including Corrado Gini
Corrado Gini
Corrado Gini was an Italian statistician, demographer and sociologist who developed the Gini coefficient, a measure of the income inequality in a society. Gini was also a leading fascist theorist and ideologue who wrote The Scientific Basis of Fascism in 1927...
and Francesco Paolo Cantelli
Francesco Paolo Cantelli
Francesco Paolo Cantelli was an Italian mathematician. He was the founder of the Istituto Italiano degli Attuari for the applications of mathematics and probability to economics....
.
Retirement and World War II
Castelnuovo retired from teaching in 1935. It was a period of great political difficulty in Italy. In 1922 Benito MussoliniBenito Mussolini
Benito Amilcare Andrea Mussolini was an Italian politician who led the National Fascist Party and is credited with being one of the key figures in the creation of Fascism....
had risen to power and in 1938 a large number of anti-semitic law
Law
Law is a system of rules and guidelines which are enforced through social institutions to govern behavior, wherever possible. It shapes politics, economics and society in numerous ways and serves as a social mediator of relations between people. Contract law regulates everything from buying a bus...
s were declared, which excluded him, like other Jews, from public work. With the rise of Nazism
Nazism
Nazism, the common short form name of National Socialism was the ideology and practice of the Nazi Party and of Nazi Germany...
, he was forced into hiding. However, during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, he organised and taught secret courses for Jewish students — the latter were not allowed to attend university either.
Final years and death
After the liberation of Rome, Castelnuovo was appointed as a special commissioner of the Consiglio Nazionale delle RicercheConsiglio Nazionale delle Ricerche
The Consiglio Nazionale delle Ricerche or National Research Council, is an Italian public organization set up to support scientific and technological research. Its headquarters are in Rome.-History:The institution was founded in 1923...
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
Accademia dei Lincei
The Accademia dei Lincei, , is an Italian science academy, located at the Palazzo Corsini on the Via della Lungara in Rome, Italy....
until his death and was elected a member of the Académie des Sciences in Paris. On 5 December 1949, he became a life senator
Senator for life
A senator for life is a member of the senate or equivalent upper chamber of a legislature who has life tenure. , 7 Italian Senators out of 322, 4 out of the 47 Burundian Senators and all members of the British House of Lords have lifetime tenure...
of the Italian Republic.
Castelnuovo died at the age of 86 on 27 April 1952 in Rome.
Work
In TurinTurin
Turin is a city and major business and cultural centre in northern Italy, capital of the Piedmont region, located mainly on the left bank of the Po River and surrounded by the Alpine arch. The population of the city proper is 909,193 while the population of the urban area is estimated by Eurostat...
Castelnuovo was strongly influenced by Corrado Segre
Corrado Segre
Corrado Segre was an Italian mathematician who is remembered today as a major contributor to the early development of algebraic geometry....
. In this period he published high-quality work on algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
ic curve
Curve
In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...
s. He also made a major step in reinterpreting the work on linear series by Alexander von Brill
Alexander von Brill
Alexander Wilhelm von Brill was a German mathematician.Born in Darmstadt, Hesse, he attended University of Giessen where he earned his doctorate under supervision of Alfred Clebsch. He held a chair at the University of Tübingen, where Max Planck was among his students.-External links:...
and Max Noether
Max Noether
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".-Biography:...
(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:
He also taught courses on algebraic function
Algebraic function
In mathematics, an algebraic function is informally a function that satisfies a polynomial equation whose coefficients are themselves polynomials with rational coefficients. For example, an algebraic function in one variable x is a solution y for an equationwhere the coefficients ai are polynomial...
s and abelian integrals. Here, he treated, among other things, Riemann surfaces, non-Euclidean geometry
Non-Euclidean geometry
Non-Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate, namely hyperbolic and elliptic geometry. This is one term which, for historical reasons, has a meaning in mathematics which is much...
, differential geometry, interpolation
Interpolation
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points....
and approximation
Approximation
An approximation is a representation of something that is not exact, but still close enough to be useful. Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws.Approximations may be used because...
, and probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
. 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
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
, Le origini del calcolo infinitesimale nell'era moderna.
Castelnuovo's most important work was done in the field of algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
. 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
Federigo Enriques
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....
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
Accademia dei Lincei
The Accademia dei Lincei, , is an Italian science academy, located at the Palazzo Corsini on the Via della Lungara in Rome, Italy....
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
Algebraic surface
In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has complex dimension two and so of dimension four as a smooth manifold.The theory of algebraic surfaces is much more complicated than that...
, having at most isolated singular points
Mathematical singularity
In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability...
, with a general tangent plane turn out to be reducible
Reduction (mathematics)
In mathematics, reduction refers to the rewriting of an expression into a simpler form. For example, the process of rewriting a fraction into one with the smallest whole-number denominator possible is called "reducing a fraction"...
curves, then surface is either ruled surface
Ruled surface
In geometry, a surface S is ruled if through every point of S there is a straight line that lies on S. The most familiar examples are the plane and the curved surface of a cylinder or cone...
and in fact a scroll, or the Veronese surface
Veronese surface
In mathematics, the Veronese surface is an algebraic surface in five-dimensional projective space, and is realized by the Veronese embedding, the embedding of the projective plane given by the complete linear system of conics. It is named after Giuseppe Veronese...
. Kronecker never published it but stated it in a lecture. Castelnuovo proved it. In total, Castelnuovo published over 100 articles, books and memoirs.
See also
- Castelnuovo–Mumford regularityCastelnuovo–Mumford regularityIn algebraic geometry, the Castelnuovo–Mumford regularity of a coherent sheaf F over projective space Pn is the smallest integer r such that it is r-regular, meaning thatH^i=0 \,...
- Castelnuovo theorem
- Castelnuovo–de Franchis theorem
- Italian school of algebraic geometryItalian school of algebraic geometryIn 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...