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# Mario Pieri

Mario Pieri (22 June 1860 - 1 March 1913) 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.

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.

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 undefined terms, point and motion to develop axioms for geometry. Guiseppe Peano had used three, and Moritz Pasch four.

The research into the foundations of geometry lead 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 in 1915 by S. Kwietniewski. A young Alfred Tarski encountered the text and carried forward Pieri's program, as recounted by Smith.

See also

* Pieri's formula

References

* Hubert C. Kennedy (1974) "Mario Pieri", Dictionary of Scientific Biography.

* E.A. Marchisotto & J.T. Smith (2007) The Legacy of Mario Pieri in Geometry and Arithmetic, Birkhäuser.

* O'Connor, John J.; Robertson, Edmund F., "Mario Pieri", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Pieri.html .

* James T. Smith (2010) "Definitions and Nondefinability in Geometry", American Mathematical Monthly 117:475–89.

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