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, a Romance ethnic group related to or simply a citizen of the Italian Republic or Italian Kingdom ** Italian language, a Romance languag ...

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, mathematical structure, structure, space, Mathematica ...

who is remembered today as a major contributor to

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

and one of the founders of

finite geometry A finite geometry is any geometry, geometric system that has only a finite set, finite number of point (geometry), points. The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry based ...

Life and career

He was born and studied in

Turin Turin ( , ; ; , then ) 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 from 1861 to 1865. The city is main ...

. Corrado Segre, 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

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

, 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 (''p ...

based on

vector space In mathematics and physics, a vector space (also called a linear space) is a set (mathematics), set whose elements, often called vector (mathematics and physics), ''vectors'', can be added together and multiplied ("scaled") by numbers called sc ...

s over a

finite field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field (mathematics), field that contains a finite number of Element (mathematics), elements. As with any field, a finite field is a Set (mathematics), s ...

. 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 at a single point, but there are some pairs of lines (namely, parallel lines) that d ...

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 of mathematics (projective geometry, technical drawing, etc.), it is given a more precise definition, which may inc ...

s are exactly the irreducible conics. In 1959 he authored a survey "Le geometrie di Galois" on

Galois geometry Galois geometry (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:

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 geom ...

. 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) 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 publishing house of the University of Oxford. It is the largest university press in the world. Its first book was printed in Oxford in 1478, with the Press officially granted the legal right to print books ...

In 1938 he lost his professorship at the

University of Bologna The University of Bologna (, abbreviated Unibo) is a Public university, public research university in Bologna, Italy. Teaching began around 1088, with the university becoming organised as guilds of students () by the late 12th century. It is the ...

, 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, upon assuming office as Prime Minister of Italy, Prime Minister, became the dictator of Fascist Italy from the March on Rome in 1922 un ...

's government. He spent the next 8 years in

Great Britain Great Britain is an island in the North Atlantic Ocean off the north-west coast of continental Europe, consisting of the countries England, Scotland, and Wales. With an area of , it is the largest of the British Isles, the List of European ...

(mostly at the

University of Manchester The University of Manchester is a public university, public research university in Manchester, England. The main campus is south of Manchester city centre, Manchester City Centre on Wilmslow Road, Oxford Road. The University of Manchester is c ...

), 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 spelled as e-book or eBook, is a book publication made available in electronic form, consisting of text, images, or both, readable on the flat-panel display of computers or other electronic devices. A ...

)).. * (also available with , (softcover reprint) and (

)). * *. * *.

Notes

References

*. *. *. *
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