Mario Pieri

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Mario Pieri entered the University of Bologna in 1880 and there his talents for mathematics were quickly spotted by Pincherle. Pieri was awarded a scholarship to study at the Scuola Normale Superiore in Pisa and he began his studies there in November 1881. His graduation was on 27 June 1884 and, after graduating, he began teaching at the Technical School in Pisa.

After teaching only a short while in Pisa, Pieri moved to the Military Academy in Turin where he became professor of projective geometry. In 1888 he also was appointed an assistant in projective geometry at the University of Turin. In 1891 Pieri received his doctorate from the University of Turin and he taught projective geometry courses there for several years.

In 1900 Pieri left Turin to take up an appointment at the University of Catania in eastern Sicily, after winning the competition for a chair. In Catania he taught projective geometry and descriptive geometry. After spending eight years in Sicily, Pieri moved to the north of Italy, taking up an appointment in Parma.

Pieri's main area was projective geometry and he is an important member of the Italian School of Geometers. However, after he moved to Turin, Pieri became influenced by Peano at the University and Burali-Forti who was a colleague at the Military Academy. This influence led Pieri to study the foundations of geometry.

In 1895 he set up an axiomatic system for projective geometry with three undefined terms, namely points, lines and segments. He improved on results of Pasch and Peano and then, in 1905, Pieri gave the first axiomatic definition of complex projective geometry which does not build on real projective geometry.

In 1898 Pieri published the memoir The principles of the geometry of position through the Academy of Sciences of Turin. Russell was impressed by this memoir and wrote, in his Principia :-

This is, in my opinion, the best work on the present subject.

Pieri attended both the Congress of Philosophy and the International Congress of Mathematicians in Paris in 1900. At the first of these conferences he lectured on Geometry considered as a purely logical system and certainly impressed Hans Freudenthal who wrote:-

In the field of the philosophy of sciences the Italian phalanx was supreme: Peano, Burali-Forti, Padoa, Pieri absolutely dominated the discussion.

The first Lobachevsky Prize was awarded to Lie in 1897. Pieri submitted an entry for the Lobachevsky Prize on the third time the Prize was offered. He received an 'honourable mention', as did Barbarin, Lemoine and Study, while the Prize went to Hilbert for the 1903 edition of his Die Grundlagen der Geometrie.

In 1911 Pieri became interested the vector calculus through the work of Burali-Forti and Marcolongo. However, around this time his health began to fail and cancer was diagnosed. His mathematical work came to an abrupt end at a time when he was at the height of his creative powers.

Peano in [8] writes:-

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.

Article by: J J O'Connor and E F Robertson

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