Mario Pieri
Encyclopedia
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 Pincherle
. Obtaining a scholarship, Pieri transferred to Scuola Normale Superiore in Pisa
. There he took his degree in 1884 and worked first at a technical secondary school in Pisa.
When the opportunity to teach projective geometry
at the military academy in Turin
arose, Pieri moved there. By 1888 he was assisting in instructing that subject also at the University of Turin
. In 1891 he became libero docente at the university, giving elective courses. Pieri continued teaching in Turin until 1900 when he won a competition for the position of extraordinary professor at University of Catania
on the island of Sicily
. In 1908 he moved to University of Parma
, and in 1911 fell ill. Pieri died in Andrea di Compito (Capannori
), not far from Lucca.
Von Staudt's Geometrie der Lage(1847) was a much admired text on projective geometry. In 1889 Pieri translated it as Geometria di Posizione, a publication that included a study of the life and work of von Staudt written by Corrado Segre
, the initiator of the project.
Pieri also came under the influence of Giuseppe Peano
at Turin. He contributed to the Formulario mathematico
, and Peano placed nine of Pieri's papers for publication with the Academy of Sciences of Turin between 1895 and 1912. They shared a passion for reducing geometric ideas to their logical form and expressing these ideas symbolically.
In 1898 Pieri wrote I principii della geometria di posizione composti in un sistema logico-deduttivo. According to J.T. Smith (2010) it is
Pieri was invited to address the International Congress of Philosophy in 1900 in Paris
. Since this was also the year he moved from Turin to Sicily, he declined to attend but sent a paper "Sur la Géométrie envisagée comme un système purement logique" which was delivered by Louis Couturat
. The ideas were also advanced by Alessandro Padoa
at both that Congress and the International Congress of Mathematicians
also held in Paris that year.
In 1900 Pieri wrote Monographia del punto e del moto, which Smith calls the Point and Motion memoire. It is noteworthy as using only two primitive notion
s, point and motion to develop axioms for geometry. Alessandro Padoa shared in this expression of Peano's logico-geometrical program that reduced the number of primitive notions from the four used by Moritz Pasch
.
The research into the foundations of geometry led to another formulation in 1908 in a Point and Sphere memoire. Smith (2010) describes it as
This memoire was translated into Polish
in 1915 by S. Kwietniewski. A young Alfred Tarski
encountered the text and carried forward Pieri's program, as recounted by Smith.
In 2002 Avellone, Brigaglia & Zappulla gave a modern evaluation of Pieri's contribution to geometry:
Giuseppe Peano wrote this tribute to Pieri upon his death:
Mario Pieri's collected works were published by the Italian Mathematical Union
in 1980 under the title Opere sui fondamenti della matematica (Edizioni Cremonese, Bologna).
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....
who is known for his work on foundations of geometry.
Pieri was born in Lucca
Lucca
Lucca is a city and comune in Tuscany, central Italy, situated on the river Serchio in a fertile plainnear the Tyrrhenian Sea. It is the capital city of the Province of Lucca...
, Italy, the son of Pellegrino Pieri and Ermina Luporini. Pellegrino was a lawyer. Pieri began his higher education at University of Bologna
University of Bologna
The Alma Mater Studiorum - University of Bologna is the oldest continually operating university in the world, the word 'universitas' being first used by this institution at its foundation. The true date of its founding is uncertain, but believed by most accounts to have been 1088...
where he drew the attention of Salvatore Pincherle
Salvatore Pincherle
Salvatore Pincherle was an Italian mathematician. He contributed significantly to the field of functional analysis, established the Italian Mathematical Union , and was president of the Third International Congress of Mathematicians...
. Obtaining a scholarship, Pieri transferred to Scuola Normale Superiore in Pisa
Pisa
Pisa is a city in Tuscany, Central Italy, on the right bank of the mouth of the River Arno on the Tyrrhenian Sea. It is the capital city of the Province of Pisa...
. There he took his degree in 1884 and worked first at a technical secondary school in Pisa.
When the opportunity to teach projective geometry
Projective geometry
In mathematics, projective geometry is the study of geometric properties that are invariant under projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts...
at the military academy in Turin
Turin
Turin is a city and major business and cultural centre in northern Italy, capital of the Piedmont region, located mainly on the left bank of the Po River and surrounded by the Alpine arch. The population of the city proper is 909,193 while the population of the urban area is estimated by Eurostat...
arose, Pieri moved there. By 1888 he was assisting in instructing that subject also 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...
. In 1891 he became libero docente at the university, giving elective courses. Pieri continued teaching in Turin until 1900 when he won a competition for the position of extraordinary professor at University of Catania
University of Catania
The University of Catania is a university located in Catania, Italy, and founded in 1434. It is the oldest university in Sicily, the 13th oldest in Italy and the 29th oldest university in the world...
on the island of Sicily
Sicily
Sicily is a region of Italy, and is the largest island in the Mediterranean Sea. Along with the surrounding minor islands, it constitutes an autonomous region of Italy, the Regione Autonoma Siciliana Sicily has a rich and unique culture, especially with regard to the arts, music, literature,...
. In 1908 he moved to University of Parma
University of Parma
The University of Parma is one of the oldest universities in the world, founded in the 11th century. It is organised in twelve faculties. The University of Parma has currently about 30,000 students.-History:...
, and in 1911 fell ill. Pieri died in Andrea di Compito (Capannori
Capannori
Capannori is a town and comune in the province of Lucca, in northern Tuscany .-Geography:The area is characterized by the number of distinctive towers .-History:...
), not far from Lucca.
Von Staudt's Geometrie der Lage(1847) was a much admired text on projective geometry. In 1889 Pieri translated it as Geometria di Posizione, a publication that included a study of the life and work of von Staudt written by Corrado Segre
Corrado Segre
Corrado Segre was an Italian mathematician who is remembered today as a major contributor to the early development of algebraic geometry....
, the initiator of the project.
Pieri also came under the influence of 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...
at Turin. He contributed to the Formulario mathematico
Formulario mathematico
Formulario Mathematico is a book by Giuseppe Peano which expresses fundamental theorems of mathematics in a symbolic language developed by Peano...
, and Peano placed nine of Pieri's papers for publication with the Academy of Sciences of Turin between 1895 and 1912. They shared a passion for reducing geometric ideas to their logical form and expressing these ideas symbolically.
In 1898 Pieri wrote I principii della geometria di posizione composti in un sistema logico-deduttivo. According to J.T. Smith (2010) it is
- based on nineteen sequentially independent axioms – each independent of the preceding ones – which are introduced one by one as they are needed in the development, thus allowing the reader to determine on which axioms a given theorem depends.
Pieri was invited to address the International Congress of Philosophy in 1900 in Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
. Since this was also the year he moved from Turin to Sicily, he declined to attend but sent a paper "Sur la Géométrie envisagée comme un système purement logique" which was delivered by Louis Couturat
Louis Couturat
Louis Couturat was a French logician, mathematician, philosopher, and linguist.-Life:Born in Ris-Orangis, Essonne, France, he was educated in philosophy and mathematics at the École Normale Supérieure...
. The ideas were also advanced by Alessandro Padoa
Alessandro Padoa
Alessandro Padoa was an Italian mathematician and logician, a contributor to the school of Giuseppe Peano. He is remembered for a method for deciding whether, given some formal theory, a new primitive notion is truly independent of the other primitive notions...
at both that Congress and the International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
also held in Paris that year.
In 1900 Pieri wrote Monographia del punto e del moto, which Smith calls the Point and Motion memoire. It is noteworthy as using only two primitive notion
Primitive notion
In mathematics, logic, and formal systems, a primitive notion is an undefined concept. In particular, a primitive notion is not defined in terms of previously defined concepts, but is only motivated informally, usually by an appeal to intuition and everyday experience. In an axiomatic theory or...
s, point and motion to develop axioms for geometry. Alessandro Padoa shared in this expression of Peano's logico-geometrical program that reduced the number of primitive notions from the four used by Moritz Pasch
Moritz Pasch
Moritz Pasch was a German mathematician specializing in the foundations of geometry. He completed his Ph.D. at the University of Breslau at only 22 years of age...
.
The research into the foundations of geometry led to another formulation in 1908 in a Point and Sphere memoire. Smith (2010) describes it as
- a full axiomatization of Euclidean geometry based solely on the primitive concepts point and equidistance of two points N and P from a third point O, written ON = OP.
This memoire was translated into Polish
Polish language
Polish is a language of the Lechitic subgroup of West Slavic languages, used throughout Poland and by Polish minorities in other countries...
in 1915 by S. Kwietniewski. A young Alfred Tarski
Alfred Tarski
Alfred Tarski was a Polish logician and mathematician. Educated at the University of Warsaw and a member of the Lwow-Warsaw School of Logic and the Warsaw School of Mathematics and philosophy, he emigrated to the USA in 1939, and taught and carried out research in mathematics at the University of...
encountered the text and carried forward Pieri's program, as recounted by Smith.
In 2002 Avellone, Brigaglia & Zappulla gave a modern evaluation of Pieri's contribution to geometry:
- Pieri's work was very influential. B. RussellBertrand RussellBertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
and L. Couturat rightly regarded him as the founder of mathematics as a hypothetical-deductive science. His precision, his rigour, and his analytical clarity are unrivaled by other Italian geometers, perhaps with the exception of Peano.
Giuseppe Peano wrote this tribute to Pieri upon his death:
- Pieri was totally dedicated to science and teaching. He was an untiring worker, honest, and of a singular modesty. When, some twenty years ago, the professors in Italy agitated for higher salaries, Pieri declared that their salaries were already above the work they did and their merit.
- from Hubert C. Kennedy (1980), Peano, page 142, D. Reidel/Kluwer.
Mario Pieri's collected works were published by the Italian Mathematical Union
Italian Mathematical Union
The Italian Mathematical Union is a mathematics society based in Italy. It was founded on December 7, 1922 by Luigi Bianchi, Vito Volterra, and most notably, Salvatore Pincherle, who became the Union's first President...
in 1980 under the title Opere sui fondamenti della matematica (Edizioni Cremonese, Bologna).