Giuseppe Veronese
Encyclopedia
Giuseppe Veronese was an Italian
mathematician
. He was born in Chioggia
, near Venice
.
Although his work was severely criticised as unsound by Peano
, he is now recognised as having priority on many ideas that have since become parts of transfinite number
s and model theory
, and as one of the respected authorities of the time, his work served to focus Peano and others on the need for greater rigor.
He is particularly noted for his hypothesis of relative continuity which was the foundation for his development of the first non-archimedean
linear
continuum.
Veronese produced several significant monographs. The most famous appeared in 1891, Fondamenti di geometria a più dimensioni e a più specie di unità rettilinee esposti in forma elementare, normally referred to as Fondamenti di geometria to distinguish it from Veronese' other works also styled Fondamenti. It was this work that was most severely criticised by both Peano and Cantor
, however Levi-Civita
described it as masterful and Hilbert
as profound.
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
mathematician
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....
. He was born in Chioggia
Chioggia
Chioggia is a coastal town and comune of the province of Venice in the Veneto region of northern Italy.-Geography:...
, near Venice
Venice
Venice is a city in northern Italy which is renowned for the beauty of its setting, its architecture and its artworks. It is the capital of the Veneto region...
.
Although his work was severely criticised as unsound by 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...
, he is now recognised as having priority on many ideas that have since become parts of transfinite number
Transfinite number
Transfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the word infinite in connection with these...
s and model theory
Model theory
In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....
, and as one of the respected authorities of the time, his work served to focus Peano and others on the need for greater rigor.
He is particularly noted for his hypothesis of relative continuity which was the foundation for his development of the first non-archimedean
Archimedean
Archimedean means of or pertaining to or named in honor of the Greek mathematician Archimedes. These are most commonly:* Archimedean property* Archimedean absolute value* Archimedean solid* Archimedean point* Archimedean tiling* Archimedean spiral...
linear
Linear
In mathematics, a linear map or function f is a function which satisfies the following two properties:* Additivity : f = f + f...
continuum.
Veronese produced several significant monographs. The most famous appeared in 1891, Fondamenti di geometria a più dimensioni e a più specie di unità rettilinee esposti in forma elementare, normally referred to as Fondamenti di geometria to distinguish it from Veronese' other works also styled Fondamenti. It was this work that was most severely criticised by both Peano and Cantor
Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor was a German mathematician, best known as the inventor of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets,...
, however Levi-Civita
Tullio Levi-Civita
Tullio Levi-Civita, FRS was an Italian mathematician, most famous for his work on absolute differential calculus and its applications to the theory of relativity, but who also made significant contributions in other areas. He was a pupil of Gregorio Ricci-Curbastro, the inventor of tensor calculus...
described it as masterful and Hilbert
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
as profound.
External links
- Fondamenti di geometria, full text in Italian, as image files.
- Peano's dismissal of Veronese' work.
- 'Generic points' attributed to Veronese.
- Biography & Bibliography by P. Cantù