|Intro||Italian mathematician and logician, a contributor to the school of Giuseppe Peano|
|Birth||14 October 1868, Venice, Province of Venice, Veneto, Italy|
|Death||25 November 1937, Genoa, Metropolitan City of Genoa, Liguria, Italy (aged 69 years)|
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 is truly independent of the other primitive notions. There is an analogous problem in axiomatic theories, namely deciding whether a given axiom is independent of the other axioms.
The following description of Padoa's career is included in a biography of Peano:
- He attended secondary school in Venice, engineering school in Padua, and the University of Turin, from which he received a degree in mathematics in 1895. Although he was never a student of Peano, he was an ardent disciple and, from 1896 on, a collaborator and friend. He taught in secondary schools in Pinerolo, Rome, Cagliari, and (from 1909) at the Technical Institute in Genoa. He also held positions at the Normal School in Aquila and the Naval School in Genoa, and, beginning in 1898, he gave a series of lectures at the Universities of Brussels, Pavia, Berne, Padua, Cagliari, and Geneva. He gave papers at congresses of philosophy and mathematics in Paris, Cambridge, Livorno, Parma, Padua, and Bologna. In 1934 he was awarded the ministerial prize in mathematics by the Accademia dei Lincei (Rome).
The congresses in Paris in 1900 were particularly notable. Padoa's addresses at these congresses have been well remembered for their clear and unconfused exposition of the modern axiomatic method in mathematics. In fact, he is said to be "the first … to get all the ideas concerning defined and undefined concepts completely straight".
At the International Congress of Philosophy Padoa spoke on "Logical Introduction to Any Deductive Theory". He says
Padoa went on to say:
Padoa spoke at the 1900 International Congress of Mathematicians with his title "A New System of Definitions for Euclidean Geometry". At the outset he discusses the various selections of primitive notions in geometry at the time:
Padoa completed his address by suggesting and demonstrating his own development of geometric concepts. In particular, he showed how he and Pieri define a line in terms of