Popularising mathematics requires a preliminary reflection on language and terms, the choice of which results from underlying dynamics. The aim of this article is to start an overall analysis of the conditions influencing this linguistic choice.

What may be defined as the "standard model" of the public communication of science began to develop in the second half of the nineteenth century, gained a clear structure (especially in an Anglo-Saxon context) in the first three decades of the twentieth century and dominated until the nineties. Roughly speaking, the model tends to describe science as a compact social (and epistemic) corpus, largely separated from the rest of society by a type of semipermeable membrane. That is, information and actions can flow freely from science to the rest of society (through the application of technologies and the spread of scientific culture, for instance), but much more limitedly in the opposite direction (through science politics or the influence of sociocultural events on science itself).

"I consider Leopardi's poetry and pessimism to be the best expression of what a scientist's credo should be". This quotation is from Bertrand Russell, no less. With these very emblematic words, the greatest man of letters, the supreme icon of the Italian Parnasse, the author of such collections of poems as Canti (Poems) and Operette Morali (The Moral Essays) and philosophical thoughts as Zibaldone (Miscellany) has been associated to the world of science. This relationship, very intense and to a certain extent new, was greatly emphasised on the occasion of the poet's birth bicentenary. During the celebration in 1996, an exhibition with the name of Giacomo and Science was organized in his birthplace to underline the close connection between the poet and the scientific culture of his epoch. This point has also been stressed recently.

There is no use denying it: whenever a scientist gets a piece of news in a newspaper or on television concerning his own field of research, eight times out of ten he feels irritated. The reason does not solely depend on the fact that, in his opinion, the news given to the public is often rather inaccurate or centred on secondary aspects, sometimes even distorted. There is actually something more? Something deeper that the scientist can hardly grasp.

"We can only appeal to society, considering that governments and parties have fallen constantly short of expectations since the late eighties. The public must know that without research there is no innovation, and without innovation there is no state-of-theart. The lack of research is a handicap for the development of the country". The words of Silvio Garattini, director of Milan's Mario Negri Institute, reveal rage and passion. This is how he explained the reasons why more than one year ago 1,500 Italian scientists made an unprecedented, resolute and unmediated appeal to the general public to back research in Italy.

It is often said that a new era is beginning, one that is founded on knowledge, thus envisaging a new society, founded on information. Meanwhile, technological innovation already characterises our daily lives and our vision of the world: no past generation saw their surroundings change so quickly and deeply as we do.

Ever since Galileo's time, scientists have been interested in how to create a perfect language capable of supporting communication at a horizontal level i.e. within the scientific community, and at a vertical level, i.e. between scientists and the public. Special attention will be spent on the mathematicians' role, especially Giuseppe Peano's. The Italian mathematician played a leading role in the creation of a perfect language, both at a horizontal and a vertical level. On the one hand, there is his successful attempt to introduce a standard logical and symbolic system of notation, which became essential for communication among mathematicians. On the other hand, there is the complete failure of his ambitious Latino sine flexione (Latin without inflection), a perfect language which died with its creator.

Theatrical action can bring out the value of the exhibits of a museum, while creating a new way of experiencing the exhibitions. Theatrical actions link education and entertainment, consequently becoming a highly effective didactic instrument. The advantages of theatre are briefly outlined, considering it as an interpretative technique to communicate science from the point of view of the goals pursued by museums, of epistemology and of theatrical research.

The aim of this project is to communicate the basic laws of particle physics with Feynman diagrams - visual tools which represent elementary particle processes. They were originally developed as a code to be used by physicists and are still used today for calculations and elaborations of theoretical nature. The technical and mathematical rules of Feynman diagrams are obviously the exclusive concern of physicists, but on a pictorial level they can help to popularize many concepts, ranging from matter and the antimatter; the creation, destruction and transformation of particles; the role of "virtual" particles in interactions; the conservation laws, symmetries, etc.