Corrado Segre
Encyclopedia
Corrado Segre was an Italian mathematician
who is remembered today as a major contributor to the early development of algebraic geometry
.
Segre developed his entire career at the University of Turin
, first as a student of Enrico D'Ovidio. In 1883 he published a dissertation on quadric
s in projective space
and was named as assistant to professors in algebra and analytic geometry
. In 1885 he also assisted in descriptive geometry
. He began to instruct in projective geometry, as stand-in for Giuseppe Bruno, from 1885 to 88. Then for 36 years he had the chair in higher geometry following D'Ovidio. Segre and Giuseppe Peano
made Turin known in geometry. As Avellone (2002) wrote:
The Erlangen program
of Felix Klein
appealed early on to Segre, and he became a promulgator. First, in 1885 he published an article on conics in the plane where he demonstrated how group theory facilitated the study. As Hawkins says (page 252) "the totality of all conics in the plane is identified with P5(C)". The group of its projectivities is then the group that permutes conics. About Segre, Hawkins writes
The inspiring Geometrie der Lage (1847) of Karl Georg Christian von Staudt
provided Segre with another project. He encouraged Mario Pieri
to make a translation, Geometria di Posizione (1889), while Segre composed a biographical sketch of von Staudt that was included in the publication.
Segre also expanded algebraic geometry by consideration of multicomplex numbers, in particular the bicomplex numbers. Segre's 1892 contribution to Mathematische Annalen
shows him extending the work of William Rowan Hamilton
and William Kingdon Clifford
on biquaternions. But Segre was unaware of earlier study of tessarines that had anticipated his bicomplex numbers.
In English, the best known work of Segre is an inspirational essay meant for Italian students, translated by J.W. Young in 1904. The vision and care of this paper in the Bulletin of the American Mathematical Society
have made it a favorite.
In a 1926 memorial article, H.F. Baker called Segre the "father of" the Italian school of algebraic geometry
.
The 1912 article "Higher-dimensional Space" (Mehr-dimensional Raume) for Encyklopädie der mathematischen Wissenschaften
spanned 200 pages. In admiration, Baker (1926) wrote and Coolidge (1927) reiterated
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....
who is remembered today as a major contributor to the early development 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...
.
Segre developed his entire career 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...
, first as a student of Enrico D'Ovidio. In 1883 he published a dissertation on quadric
Quadric
In mathematics, a quadric, or quadric surface, is any D-dimensional hypersurface in -dimensional space defined as the locus of zeros of a quadratic polynomial...
s in projective space
Projective space
In mathematics a projective space is a set of elements similar to the set P of lines through the origin of a vector space V. The cases when V=R2 or V=R3 are the projective line and the projective plane, respectively....
and was named as assistant to professors in algebra and analytic geometry
Analytic geometry
Analytic geometry, or analytical geometry has two different meanings in mathematics. The modern and advanced meaning refers to the geometry of analytic varieties...
. In 1885 he also assisted in descriptive geometry
Descriptive geometry
Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions, by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art...
. He began to instruct in projective geometry, as stand-in for Giuseppe Bruno, from 1885 to 88. Then for 36 years he had the chair in higher geometry following D'Ovidio. Segre and Giuseppe Peano
Giuseppe Peano
Giuseppe Peano was an Italian mathematician, whose work was of philosophical value. 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...
made Turin known in geometry. As Avellone (2002) wrote:
- ... in the mid 1880's, these two very young researchers, Segre and Peano, both of them only just past twenty and both working at the University of Turin, were developing very advanced points of view on fundamental geometrical issues. Although their positions were quite different from one another, they were in some way more complementary than opposed. So it must come as no surprise that Turin was the cradle of some of the most interesting studies on such issues.
The Erlangen program
Erlangen program
An influential research program and manifesto was published in 1872 by Felix Klein, under the title Vergleichende Betrachtungen über neuere geometrische Forschungen...
of Felix Klein
Felix Klein
Christian Felix Klein was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory...
appealed early on to Segre, and he became a promulgator. First, in 1885 he published an article on conics in the plane where he demonstrated how group theory facilitated the study. As Hawkins says (page 252) "the totality of all conics in the plane is identified with P5(C)". The group of its projectivities is then the group that permutes conics. About Segre, Hawkins writes
- ...shortly after he assumed the chair of projective geometry in Turin in 1888, he decided it would be worthwhile to have an Italian translation of the Erlangen Program because he felt its contents were not well enough known among young Italian geometers. ... Segre convinced one of the students at Turin, Gino FanoGino FanoGino Fano was an Italian mathematician. He was born in Mantua, Italy and died in Verona, Italy.Fano worked on projective and algebraic geometry; the Fano plane, Fano fibration, Fano surface, and Fano varieties are named for him....
, to make a translation which was published in Annali di Mathematische in 1890. Fano's translation thus became the first of many translations of the Erlangen Program.
The inspiring Geometrie der Lage (1847) of Karl Georg Christian von Staudt
Karl Georg Christian von Staudt
Karl Georg Christian von Staudt was a German mathematician born in the Free Imperial City of Rothenburg, which is now called Rothenburg ob der Tauber in Germany. From 1814 he studied in Gymnasium in Ausbach. He attended the University of Göttingen from 1818 to 1822 where he studied with Gauss who...
provided Segre with another project. He encouraged Mario Pieri
Mario Pieri
Mario Pieri was an Italian mathematician who is known for his work on foundations of geometry.Pieri was born in Lucca, Italy, the son of Pellegrino Pieri and Ermina Luporini. Pellegrino was a lawyer. Pieri began his higher education at University of Bologna where he drew the attention of Salvatore...
to make a translation, Geometria di Posizione (1889), while Segre composed a biographical sketch of von Staudt that was included in the publication.
Segre also expanded algebraic geometry by consideration of multicomplex numbers, in particular the bicomplex numbers. Segre's 1892 contribution to Mathematische Annalen
Mathematische Annalen
Mathematische Annalen is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann...
shows him extending the work of William Rowan Hamilton
William Rowan Hamilton
Sir William Rowan Hamilton was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques...
and William Kingdon Clifford
William Kingdon Clifford
William Kingdon Clifford FRS was an English mathematician and philosopher. Building on the work of Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honour, with interesting applications in contemporary mathematical physics...
on biquaternions. But Segre was unaware of earlier study of tessarines that had anticipated his bicomplex numbers.
In English, the best known work of Segre is an inspirational essay meant for Italian students, translated by J.W. Young in 1904. The vision and care of this paper in the Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
The Bulletin of the American Mathematical Society is a quarterly mathematical journal published by the American Mathematical Society...
have made it a favorite.
In a 1926 memorial article, H.F. Baker called Segre the "father of" the Italian school of algebraic geometry
Italian school of algebraic geometry
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...
.
The 1912 article "Higher-dimensional Space" (Mehr-dimensional Raume) for Encyklopädie der mathematischen Wissenschaften
Klein's encyclopedia
In mathematics, Klein’s encyclopedia refers to a German mathematical encyclopedia published in six volumes from 1898 to 1933. Felix Klein and Wilhelm Meyer were organizers of the encyclopedia. Its title in English is "Encyclopedia of mathematical sciences including their applications", which is...
spanned 200 pages. In admiration, Baker (1926) wrote and Coolidge (1927) reiterated
- For completeness of detail, breadth of view, and generous recognition of the work of a host of other writers, this must remain for many years a monument of the comprehensiveness of the man.