Alessandro Padoa attended secondary school in Venice, then studied engineering at the University of Padua. He was awarded a mathematics degree from the University of Turin in 1895.
After graduating, Padoa became a secondary school teacher, teaching in Pinerolo, Rome and Cagliari. However, Padoa gave many lectures at universities and lectures at congresses. Beginning in 1898 he gave a series of lectures at the Universities of Brussels, Pavia, Berne, Padua, Cagliari and Genoa. He lectured at congresses in Paris, Cambridge, Livorno, Parma, Padua and Bologna. From 1909 he taught at the Technical Institute in Genoa.
Padua belonged to Peano's school of mathematical logic, popularising this type of work. He gave the important lecture Essay of an algebraic theory of whole numbers, preceded by a logical introduction to any deductive theory at the International Congress of Philosophy in Paris in 1900.
He had discovered an important method in the theory of definition which became even more important when model theory was developed and Tarski proved Padoa's method in 1924. Padoa was the first to present a method to prove that a primative term of a theory cannot be defined within the system using the remaining primative terms. This result was first made public in his lecture at the Paris Congress referred to above. Padoa believed, correctly, that his result was of major importance and wrote in this paper:-
We can now settle completely (and, we believe, for the first time) a question of the greatest logical importance.
Immediately following the Congress of Philosophy in Paris, the Second International Congress of Mathematicians took place. Padoa spoke on A new system of definitions for Euclidean geometry but began with a summary of his lecture at the Philosophy Congress. Charlotte Scott found this one of the most interesting talks at the Congress but wrote:-
Mr Padoa did not get beyond this definition, possibly because he had entered so minutely into the details of the proof of the independance of the seven postulates that he had exhausted his allowance of time.
Halsted also attended the Congress and wrote that Padoa was:-
... among the most interesting personalities present.
In 1934 Padoa was awarded the mathematics prize of the Accademia dei Lincei.
Article by: J J O'Connor and E F Robertson
December 1997