Beniamino Segre (16 February 1903 – 2 October 1977) was an
Italian
Italian(s) may refer to:
* Anything of, from, or related to the people of Italy over the centuries
** Italians, an ethnic group or simply a citizen of the Italian Republic or Italian Kingdom
** Italian language, a Romance language
*** Regional Ita ...
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
who is remembered today as a major contributor to
algebraic geometry
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 ...
and one of the founders of
finite geometry
Finite is the opposite of infinite. It may refer to:
* Finite number (disambiguation)
* Finite set, a set whose cardinality (number of elements) is some natural number
* Finite verb, a verb form that has a subject, usually being inflected or marked ...
.
Life and career
He was born and studied in
Turin
Turin ( , Piedmontese language, Piedmontese: ; it, Torino ) is a city and an important business and cultural centre in Northern Italy. It is the capital city of Piedmont and of the Metropolitan City of Turin, and was the first Italian capital ...
.
Corrado Segre
Corrado Segre (20 August 1863 – 18 May 1924) was an Italian mathematician who is remembered today as a major contributor to the early development of algebraic geometry.
Early life
Corrado's parents were Abramo Segre and Estella De Ben ...
, his uncle, also served as his
doctoral advisor
A doctoral advisor (also dissertation director, dissertation advisor; or doctoral supervisor) is a member of a university faculty whose role is to guide graduate students who are candidates for a doctorate, helping them select coursework, as well ...
.
Among his main contributions to
algebraic geometry
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 ...
are studies of birational invariants of algebraic varieties, singularities and algebraic surfaces. His work was in the style of the old
Italian School, although he also appreciated the greater rigour of modern algebraic geometry.
Segre was a pioneer in
finite geometry
Finite is the opposite of infinite. It may refer to:
* Finite number (disambiguation)
* Finite set, a set whose cardinality (number of elements) is some natural number
* Finite verb, a verb form that has a subject, usually being inflected or marked ...
, in particular
projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, pro ...
based on
vector space
In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', may be added together and multiplied ("scaled") by numbers called '' scalars''. Scalars are often real numbers, but can ...
s over a
finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtr ...
. In a well-known paper he proved the following theorem: In a
Desarguesian plane
In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect in a single point, but there are some pairs of lines (namely, parallel lines) that do ...
of odd order, the
oval
An oval () is a closed curve in a plane which resembles the outline of an egg. The term is not very specific, but in some areas (projective geometry, technical drawing, etc.) it is given a more precise definition, which may include either one or ...
s are exactly the irreducible conics. In 1959 he authored a survey "Le geometrie di Galois" on
Galois geometry
Galois geometry (so named after the 19th-century French mathematician Évariste Galois) is the branch of finite geometry that is concerned with algebraic and analytic geometry over a finite field (or ''Galois field''). More narrowly, ''a'' Ga ...
. According to
J. W. P. Hirschfeld, it "gave a comprehensive list of results and methods, and is to my mind the seminal paper in the subject."
[
Some critics felt that his work was no longer geometry, but today it is recognized as a separate sub-discipline: ]finite geometry
Finite is the opposite of infinite. It may refer to:
* Finite number (disambiguation)
* Finite set, a set whose cardinality (number of elements) is some natural number
* Finite verb, a verb form that has a subject, usually being inflected or marked ...
or combinatorial geometry
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geo ...
. According to Hirschfeld, "He published the most as well as the deepest papers in the subject. His enormous knowledge of classical algebraic geometry enabled him to identify those results which could be applied to finite spaces. His theorem on the characterization of conics (Segre's theorem
In projective geometry, Segre's theorem, named after the Italian mathematician Beniamino Segre, is the statement:
*Any oval in a ''finite pappian'' projective plane of ''odd'' order is a nondegenerate projective conic section.
This statement was ...
) not only stimulated a great deal of research but also made many mathematicians realize that finite spaces were worth studying."[ J. W. P. Hirschfeld (1979) Preface to ''Projective Geometries over Finite Fields'', page vii, ]Clarendon Press
Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print books ...
In 1938 he lost his professorship at the University of Bologna, as a result of the anti-Jewish laws enacted under Benito Mussolini
Benito Amilcare Andrea Mussolini (; 29 July 188328 April 1945) was an Italian politician and journalist who founded and led the National Fascist Party. He was Prime Minister of Italy from the March on Rome in 1922 until his deposition in 194 ...
's government. He spent the next 8 years in Great Britain
Great Britain is an island in the North Atlantic Ocean off the northwest coast of continental Europe. With an area of , it is the largest of the British Isles, the largest European island and the ninth-largest island in the world. It is ...
(mostly at the University of Manchester
, mottoeng = Knowledge, Wisdom, Humanity
, established = 2004 – University of Manchester Predecessor institutions: 1956 – UMIST (as university college; university 1994) 1904 – Victoria University of Manchester 1880 – Victoria Univer ...
), then returned to Italy to resume his academic career.
Selected publications
*.
*
*. The second volume was never published: however an updated and largely expanded English edition was published as: .
*.
*.
*
*.
* (also available with (ebook
An ebook (short for electronic book), also known as an e-book or eBook, is a book publication made available in digital form, consisting of text, images, or both, readable on the flat-panel display of computers or other electronic devices. Alt ...
)).[.
]
* (also available with , (softcover reprint) and (ebook
An ebook (short for electronic book), also known as an e-book or eBook, is a book publication made available in digital form, consisting of text, images, or both, readable on the flat-panel display of computers or other electronic devices. Alt ...
)).
*
*.
*
*.
Notes
References
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*
Sernesi, Edoardo: "''Beniamino Segre (Torino 1903-Frascati 1977)''" (incl. extensive bibliography)
External links
*
{{DEFAULTSORT:Segre, Beniamino
1903 births
1977 deaths
20th-century Italian Jews
Scientists from Turin
20th-century Italian mathematicians
Italian algebraic geometers
Algebraic geometers
Members of the Lincean Academy
Academic staff of the University of Bologna
Italian expatriates in the United Kingdom