There is a puzzle associated with the setting up of the Union. After Pincherle had written to all Italian mathematicians seeking their support for a Union in a letter written on 31 March 1922, he received about 180 positive replies. A list of those interested in supporting the Union was drawn up, and later a second longer list appeared. The puzzle is that despite widespread support, many leading Italian mathematicians do not appear on either list and clearly did not support the initiative. It is reasonable to ask why.
The reason must be the way that mathematics was supported in Italy at the time. Many local, yet highly prestigious, societies were already long established. For example the Mathematical Circle of Palermo had been in existence for almost 40 years and published a prestigious journal. Many universities ran mathematical seminars which operated along the lines of a mathematical society, even to the extent of publishing proceedings which were distributed both nationally and internationally. Another reason was that in some sense Italy already had a national mathematical society. The Mathesis Società Italiana di Matematica had been founded in the 19th century as a national society for school level mathematics. It published a journal, the Periodico di Matematiche, which was edited by Enriques. Moreover this Society had decided in 1908 to extend its coverage of mathematics to include not only school mathematics but also university level mathematics and mathematical research.
The case we have just made to show why many leading Italian mathematicians did not initially support the creation of a Union is so strong that we need now to turn the question round and ask why there was a case for a Union and, in particular, why Pincherle was such an enthusiastic campaigner for the Union. The reason is that the arguments in the previous paragraph show that there was no strong academic case for the foundation of a Union but there was a strong political case.
After World War I, there was a move to establish an International Research Council which would incorporate International Unions in a wide range of subjects. These International Unions would in turn operate with committees in the various countries worldwide and it was proposed that these national committees would be set up by the various National Academies of Science and National Research Councils. The International Mathematical Union was created in 1920 and, in Italy, the Accademia dei Lincei was the responsible National Academy. Volterra was vice-president of the Accademia dei Lincei and he pressed the Academy to set up a Mathematical Union. As a result Pincherle became responsible for setting up the Unione Matematica Italiana and became both President and Secretary.
In 1924 Pincherle was elected President of the International Mathematical Union and Italian Mathematical Union organised the International Congress of Mathematicians in Bologna in 1928. This proved an extremely difficult task since, at that time, the mathematical community was divided over whether German mathematicians should be allowed to participate. At one point, six month before the Congress, there was an attempt by the Italian National Research Council to close down the Unione Matematica Italiana but by this time it was an independent legally constituted body and was able to argue successfully that the National Research Council did not have authority to close it down.
The political situation in Italy with the rise of fascism was the cause of many problems of the Italian Mathematical Union, including the ones mentioned above. By 1934 the government had passed a law which meant that the President, Vice-President and council members of the Italian Mathematical Union had to be approved by the Minister of Education. Exactly what happen in elections for these offices in 1935 is unclear. It does appear that Giulio Vivanti and Volterra received the most votes in the election, yet Luigi Fantappiè and Guido Fubini (who also stood for election but received fewer votes) were appointed. By 1941 the situation was even more extreme with the government passing a decree that the President and Vice-President of the Union were nominated by the Minister of Education and even then had to swear allegiance to the fascist regime before they could serve.
In  Pucci shows how most mathematicians during this period were prepared to support the fascist regime, many with a degree of enthusiasm. One notable exception was Volterra who lost his university position because he refused to swear allegiance to the fascist regime.
We mentioned the Bollettino dell'Unione Matematica Italiana above which began publication before the foundation of the Union. From the start of its publication the bulletin had two sections, one for short communications and the other to report on papers published in other journals, letters, news, book reviews etc. A section on the history of mathematics was added in 1939 and at the same time it began publishing articles on mathematical education. The present bulletin has two sections, one for research papers and one for expository articles.
List of References (4 books/articles)
Other Web site Union Web-site (in Italian)