Mario Pieri
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Mario Pieri (22 June 1860 – 1 March 1913) 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 ...
who is known for his work on foundations of geometry.


Biography

Pieri was born in
Lucca Lucca ( , ) is a city and ''comune'' in Tuscany, Central Italy, on the Serchio River, in a fertile plain near the Ligurian Sea. The city has a population of about 89,000, while its province has a population of 383,957. Lucca is known as ...
, Italy, the son of Pellegrino Pieri and Ermina Luporini. Pellegrino was a lawyer. Pieri began his higher education at
University of Bologna The University of Bologna ( it, Alma Mater Studiorum – Università di Bologna, UNIBO) is a public research university in Bologna, Italy. Founded in 1088 by an organised guild of students (''studiorum''), it is the oldest university in continuo ...
where he drew the attention of Salvatore Pincherle. Obtaining a scholarship, Pieri transferred to '' Scuola Normale Superiore'' in
Pisa Pisa ( , or ) is a city and ''comune'' in Tuscany, central Italy, straddling the Arno just before it empties into the Ligurian Sea. It is the capital city of the Province of Pisa. Although Pisa is known worldwide for its leaning tower, the ...
. There he took his degree in 1884 and worked first at a technical secondary school in Pisa. When an opportunity arose at the
military academy A military academy or service academy is an educational institution which prepares candidates for service in the officer corps. It normally provides education in a military environment, the exact definition depending on the country concerned. ...
in
Turin Turin ( , Piedmontese: ; it, Torino ) is a city and an important business and cultural centre in Northern Italy. It is the capital city of Piedmont and of the Metropolitan City of Turin, and was the first Italian capital from 1861 to 1865. Th ...
to teach
projective geometry In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, pr ...
, Pieri moved there and, by 1888, he was also an assistant instructor in the same subject at the
University of Turin The University of Turin ( Italian: ''Università degli Studi di Torino'', UNITO) is a public research university in the city of Turin, in the Piedmont region of Italy. It is one of the oldest universities in Europe and continues to play an imp ...
. By 1891, he had become ''libero docente'' at the university, teaching elective courses. Pieri continued to teach in Turin until 1900 when, through competition, he was awarded the position of ''extraordinary professor'' at
University of Catania The University of Catania ( it, Università degli Studi di Catania) is a university located in Catania, Sicily. Founded in 1434, it is the oldest university in Sicily, the 13th oldest in Italy, and the 29th oldest university in the world. With a ...
on the island of
Sicily (man) it, Siciliana (woman) , population_note = , population_blank1_title = , population_blank1 = , demographics_type1 = Ethnicity , demographics1_footnotes = , demographi ...
. 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 Giuseppe Peano (; ; 27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist. 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 sta ...
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''. It progressively introduced
independent axiom An axiom P is independent if there are no other axioms Q such that Q implies P. In many cases independence is desired, either to reach the logical consequence, conclusion of a reduced set of axioms, or to be able to replace an independent axiom to ...
s: :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 () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. ...
. 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 (; 17 January 1868 – 3 August 1914) was a French logician, mathematician, philosopher, and linguist. Couturat was a pioneer of the constructed language Ido. Life and education Born in Ris-Orangis, Essonne, France. In 1887 h ...
. The ideas were also advanced by Alessandro Padoa at both that congress and the
International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...
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 In mathematics, logic, philosophy, and formal systems, a primitive notion is a concept that is not defined in terms of previously-defined concepts. It is often motivated informally, usually by an appeal to intuition and everyday experience. In an ...
s, point and
motion In physics, motion is the phenomenon in which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed and frame of reference to an observer and mea ...
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 :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 may refer to: * Anything from or related to Poland, a country in Europe * Polish language * Poles, people from Poland or of Polish descent * Polish chicken *Polish brothers (Mark Polish and Michael Polish, born 1970), American twin screenwr ...
in 1915 by S. Kwietniewski. A young
Alfred Tarski Alfred Tarski (, born Alfred Teitelbaum;School of Mathematics and Statistics, University of St Andrews ''School of Mathematics and Statistics, University of St Andrews''. January 14, 1901 – October 26, 1983) was a Polish-American logician ...
encountered the text and carried forward Pieri's program.James T. Smith (2010
"Definitions and Nondefinability in Geometry"
(winner of a 2011 Lester R. Ford Award),
American Mathematical Monthly ''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an ...
117:475–89
In 1908 Pieri moved to
University of Parma The University of Parma ( it, Università degli Studi di Parma, UNIPR) is a public university in Parma, Emilia-Romagna, Italy. It is organised in nine departments. As of 2016 the University of Parma has about 26,000 students. History During the ...
, and in 1911 fell ill. Pieri died in Sant'Andrea di Compito, not far from Lucca. In 2002 Avellone, Brigaglia & Zappulla gave a modern evaluation of Pieri's contribution to geometry: :Pieri's work was very influential. B. Russell 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. 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).


Personal Life

For several years before his death, Pieri resided in Sant'Andrea di Compito as a guest of his sister Gemma Pieri Campetti and her husband, Umberto, a lawyer. Pieri was initially buried in a local church before his remains were transferred to the monumental cemetery in Lucca.


See also

*
Pieri's formula In mathematics, Pieri's formula, named after Mario Pieri, describes the product of a Schubert cycle by a special Schubert cycle in the Schubert calculus, or the product of a Schur polynomial by a complete symmetric function. In terms of Schur fu ...


References

* E.A.C, Marchisotto, (2022) "H.S.M. Coxeter’s Theory of Accessibility: From Mario Pieri to Marvin Greenberg", '' Results in Mathematics'' (Special issue in memory of Heinrich Wefelscheid) 77:187 https://doi.org/10.1007/s00025-022-01690-9. * E.A.C. Marchisotto & F. Rodriguez-Consuegra & J.T. Smith (2021) ''The Legacy of Mario Pieri on the Foundations and Philosophy of Mathematics'', Birkhäuser. * E.A.C. Marchisotto & A. Millán Gascia, (2021) "Mario Pieri’s View of the Symbiotic Relationship between the Foundations and the Teaching of Elementary Geometry in the Context of the Early Twentieth Century Proposals for Pedagogical Reform", ''Philosophia Scientiae'' 25(1):157-183. * E.A. Marchisotto, (2010) "Mario Pieri: the man, the mathematician, the teacher", ''La Matematica nella Società e nella Cultura Rivista dell'Unione Matematica Italiana'' 3(3):321-364, 465. * E.A. Marchisotto, (2006) "The Projective Geometry of Mario Pieri: A Legacy of Karl Georg Christian von Staudt",
Historia Mathematica ''Historia Mathematica: International Journal of History of Mathematics'' is an academic journal on the history of mathematics published by Elsevier. It was established by Kenneth O. May in 1971 as the free newsletter ''Notae de Historia Mathemat ...
33(3):277–314. * E.A. Marchisotto, (1995) "In the shadow of giants. The work of Mario Pieri in foundations of mathematics", History and Philosophy of Logic 16:107–119. * * Hubert C. Kennedy (1974) "Mario Pieri",
Dictionary of Scientific Biography The ''Dictionary of Scientific Biography'' is a scholarly reference work that was published from 1970 through 1980 by publisher Charles Scribner's Sons, with main editor the science historian Charles Gillispie, from Princeton University. It con ...
. *
Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ar ...
(1903) '' The Principles of Mathematics'',
Cambridge University Press Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press in the world. It is also the King's Printer. Cambr ...
. {{DEFAULTSORT:Pieri, Mario Geometers Italian logicians 19th-century Italian mathematicians 20th-century Italian mathematicians 1860 births 1913 deaths