Gino Fano (5 January 18718 November 1952) 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 ...

, best known as the founder of finite geometry. He was born to a wealthy

Jewish Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""The ...

family in

Mantua Mantua ( ; it, Mantova ; Lombard and la, Mantua) is a city and '' comune'' in Lombardy, Italy, and capital of the province of the same name. In 2016, Mantua was designated as the Italian Capital of Culture. In 2017, it was named as the Eur ...

, in

Italy Italy ( it, Italia ), officially the Italian Republic, ) or the Republic of Italy, is a country in Southern Europe. It is located in the middle of the Mediterranean Sea, and its territory largely coincides with the homonymous geographical ...

and died in

Verona Verona ( , ; vec, Verona or ) is a city on the Adige River in Veneto, Italy, with 258,031 inhabitants. It is one of the seven provincial capitals of the region. It is the largest city municipality in the region and the second largest in nor ...

, also in Italy. Fano made various contributions on projective and

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 ...

. His work in the

foundations of geometry Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries. These are fundamental to the study and of historical importance, bu ...

predates the similar, but more popular, work of

David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many ...

by about a decade. He was the father of

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...

Ugo Fano Ugo Fano (July 28, 1912 – February 13, 2001) was an Italian American physicist, notable for contributions to theoretical physics. Biography Ugo Fano was born into a wealthy Jewish family in Turin, Italy. His father was Gino Fano, a professo ...

and electrical engineer

Robert Fano Roberto Mario "Robert" Fano (11 November 1917 – 13 July 2016) was an Italian-American computer scientist and professor of electrical engineering and computer science at the Massachusetts Institute of Technology. He became a student and worki ...

and uncle to physicist and mathematician Giulio Racah.

Mathematical work

Fano was an early writer in the area of finite projective spaces. In his article on proving the independence of his set of axioms for projective ''n''-space, among other things, he considered the consequences of having a fourth harmonic point be equal to its conjugate. This leads to a configuration of seven points and seven lines contained in a finite three-dimensional space with 15 points, 35 lines and 15 planes, in which each line contained only three points. All the planes in this space consist of seven points and seven lines and are now known as

Fano plane In finite geometry, the Fano plane (after Gino Fano) is a finite projective plane with the smallest possible number of points and lines: 7 points and 7 lines, with 3 points on every line and 3 lines through every point. These points and lines ...

Fano went on to describe finite projective spaces of arbitrary dimension and prime orders. In 1907 Gino Fano contributed two articles to Part III of

Klein's encyclopedia Felix Klein's ''Encyclopedia of Mathematical Sciences'' is a German mathematical encyclopedia published in six volumes from 1898 to 1933. Klein and Wilhelm Franz Meyer were organizers of the encyclopedia. Its full title in English is ''Encyclope ...

. The first (SS. 221–88) was a comparison of

analytic geometry In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and enginee ...

and

synthetic geometry Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is the study of geometry without the use of coordinates or formulae. It relies on the axiomatic method and the tools directly related to them, that is, compass ...

through their historic development in the 19th century. The second (SS. 282–388) was on continuous groups in geometry and

group theory In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen ...

as a unifying principle in geometry.

Notes

References

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External links

* * {{DEFAULTSORT:Fano, Gino 1871 births 1952 deaths Scientists from Mantua 19th-century Italian mathematicians 20th-century Italian mathematicians Algebraic geometers Italian algebraic geometers 20th-century Italian Jews