G. Vailati was born in Crema on 24th April 1863 of nobleman Vincenzo and Teresa Albergoni. He attended the secondary school (liceo) in Lodi at "Collegio S. Francesco" kept by Barnabiti Fathers.
He passed his exams brilliantly and then he went to Turin University where he took a degree in pure Mathematics and one in Engineering. In 1888 he came back to Crema where he joined some municipal commissions. In that period he devoted himself to the study of modern languages and also he showed a keen interest in music, especially Bach and Wagner.
In 1892 he was again in Turin as Peano's assistant in the course in Infinitesimal Analysis. In the academic year 1895-96 he was assistant Professor (Lecturer) in the course of Projective Geometry; from 1896 to 1898 he was Volterra's assistant in the course in History of Mechanics , held on the model of famous courses held in Vienna by E. Mach, who was to become one of Vailati's correspondents. The opening lectures of Vailati's courses were about the "Importance of the researches into history of sciences" (1896), the "Deductive method as instrument of research" (1897) and "Some observations on the questions of words in the history of science and culture" (1898). In those writings Vailati emphasised the epistemological limits of the classic positivism and the importance of the language in the historical evolution of philosophical and scientific thought.
During those years he was engaged in Peano's team's researches into logic-mathematics, which led to several publications on the "Rivista di matematica " and he also took part in the realization of the famous "Formulario Mathematico ".
In Turin lively environment, Vailati enlarged his cultural interests, being in touch with C. Lombroso, G. Mosca, P. Jannacone, P. Ricci and G.C. Ferrari; he also frequented the Political Economy Laboratory, founded by Cognetti de Martiis, where he met Luigi Einaudi, who was to become his friend.
During the Psychology Meeting in Munich in 1896, he met M. Calderoni with whom he shared the aim to spread in Italy the pragmatism, as an epistemological doctrine which studies how strictly the validity of linguistic statements and, particularly, of scientific ones can be verified.
In 1899 he decided to leave the University and began to teach in high school. He got a teaching post at Liceo of Siracusa; in Sicily he was in frequent contact with the philosopher F. Brentano, to whom he dedicated his communication during the International Congress of Psychology in Paris in 1900. In the summer of 1902 he stayed in Austria, host of Brentano's family.
In Agoust 1903 he was in Cambridge with Calderoni and in Harrow where he met Lady Victoria Welby. The Accademia dei Lincei proposed Vailati as editor of the national edition of Torricelli works, so the Minister of Education transferred him from Como to the "Istituto Tecnico G. Galilei" in Florence. In the tuscan city Vailati began to contribute to the review "Leonardo" with a brief writing about the new Russell's definition of mathematics. Vailati shared Prezzolini and Papini's ( the young editors of "Leonardo") ideas about the provincialism of Italian environment ; however his scientific conception of pragmatism was far away from Papini and Prezzolini's activism and "magic pragmatism".
In November 1905 the Minister of Education called on Vailati to take part in the Royal Committee having to deal with the secondary school reform. Vailati thoroughly engaged himsefl in the new task: he travelled in several european countries to know their school systems; he organized the work on the drafting of mathematical "curricula" and he suggested ingenious solutions about different subjects. For the love of teaching he asked , in autumn 1908, to go back to "Istituto Galileo" in Florence, however binding himself to be present at Committee meetings. Unfortunately in December 1908 he fell ill . He returned to Rome, hoping to recover, but here his illness worsened. He died on 14th May 1909, forty-six years old.
After Vailati's death , some friend of his opened a subscription to publish all Vailati's writings ( about 200, already published in several reviews) in only one tome. The subscribers were more than 250. Amongst the foreign intellectuals, who helped this editorial enterprise, we remember B. Russell, F. Brentano, P. Duhem, E. Mach and V.Lady Welby.