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, structure, space, models, and change. History On ...

who is known for his work on

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, but ...

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 one o ...

, 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 Salvatore Pincherle (March 11, 1853 – July 10, 1936) was an Italian mathematician. He contributed significantly to (and arguably helped to found) the field of functional analysis, established the Italian Mathematical Union (Italian: "''Unio ...

. Obtaining a scholarship, Pieri transferred to ''

Scuola Normale Superiore The Scuola Normale Superiore in Pisa (commonly known in Italy as "la Normale") is a public university in Pisa and Florence, Tuscany, Italy, currently attended by about 600 undergraduate and postgraduate (PhD) students. It was founded in 1810 wi ...

'' 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 cit ...

. 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. ...

Turin Turin ( , Piedmontese language, 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 ...

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, pro ...

, 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 impo ...

. 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 Corrado Segre (20 August 1863 – 18 May 1924) was an Italian mathematician who is remembered today as a major contributor to the early development of algebraic geometry. Early life Corrado's parents were Abramo Segre and Estella De Ben ...

, 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 stand ...

at Turin. He contributed to the

Formulario mathematico ''Formulario Mathematico'' (Latino sine flexione: ''Formulary for Mathematics'') is a book There are many editions. Here are two: * (French) Published 1901 by Gauthier-Villars, Paris. 230p.OpenLibrary OL15255022Windependent axioms: :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 The World Congress of Philosophy (originally known as the International Congress of Philosophy) is a global meeting of philosophers held every five years under the auspices of the International Federation of Philosophical Societies (FISP). First or ...

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. S ...

. 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 he ...

. The ideas were also advanced by

Alessandro Padoa Alessandro Padoa (14 October 1868 – 25 November 1937) 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 ...

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 ...

point Point or points may refer to: Places * Point, Lewis, a peninsula in the Outer Hebrides, Scotland * Point, Texas, a city in Rains County, Texas, United States * Point, the NE tip and a ferry terminal of Lismore, Inner Hebrides, Scotland * 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 Moritz Pasch (8 November 1843, Breslau, Prussia (now Wrocław, Poland) – 20 September 1930, Bad Homburg, Germany) was a German mathematician of Jewish ancestry specializing in the foundations of geometry. He completed his Ph.D. at the Univer ...

. 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 Poles,, ; singular masculine: ''Polak'', singular feminine: ''Polka'' or Polish people, are a West Slavic nation and ethnic group, w ...

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 a ...

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 Lester is an ancient Anglo-Saxon surname and given name. Notable people and characters with the name include: People Given name * Lester Bangs (1948–1982), American music critic * Lester W. Bentley (1908–1972), American artist from Wisc ...

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 e ...

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 Sant'Andrea di Compito (also ''Sant'Andrea di Cómpito'') is a frazione of Capannori in the province of Lucca region of Tuscany in Italy. The settlement styles itself ''The Village of Camellias'' as it is home to an exceptional collection of ancie ...

, 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 The Italian Mathematical Union ( it, Unione Matematica Italiana) is a mathematical 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 Pr ...

in 1980 under the title ''Opere sui fondamenti della matematica'' (Edizioni Cremonese, Bologna).

Personal Life

For several years before his death, Pieri resided in

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.

References

* E.A.C, Marchisotto, (2022) "H.S.M. Coxeter’s Theory of Accessibility: From Mario Pieri to Marvin Greenberg", ''

Results in Mathematics ''Results in Mathematics/Resultate der Mathematik'' is a peer-reviewed scientific journal that covers all aspects of pure and applied mathematics and is published by Birkhäuser. It was established in 1978 and the editor-in-chief is Catalin Bad ...

'' (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 History (derived ) is the systematic study and the documentation of the human activity. The time period of event before the invention of writing systems is considered prehistory. "History" is an umbrella term comprising past events as well ...

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 consi ...

. *

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, ...

(1903) ''

The Principles of Mathematics ''The Principles of Mathematics'' (''PoM'') is a 1903 book by Bertrand Russell, in which the author presented his famous paradox and argued his thesis that mathematics and logic are identical. The book presents a view of the foundations of ...

'',

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 A university press is an academic publishing hou ...

. {{DEFAULTSORT:Pieri, Mario Geometers Italian logicians 19th-century Italian mathematicians 20th-century Italian mathematicians 1860 births 1913 deaths

Biography

Personal Life

See also

References