Gino Fano (5 January 18718 November 1952) was an Italian

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 ...

, best known as the founder 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 Traditionally, a finite verb (from la, fīnītus, past particip ...

. 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 language, Lombard and la, Mantua) is a city and ''comune'' in Lombardy, Italy, and capital of the Province of Mantua, province of the same name. In 2016, Mantua was designated as the Italian Capital of Culture ...

, 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. His work in the foundations of geometry predates the similar, but more popular, work of David Hilbert 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 ca ...

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 profes ...

and electrical engineer Robert Fano 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 planes:

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 ''Encyclopedi ...

. The first (SS. 221–88) was a comparison of analytic geometry and synthetic geometry 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 group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...

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