In a brief article published by Science1 last October, British scientists stated that the expression "Public Understanding of Science" (PUS), which was traditionally employed in Anglosaxon societies to refer to the issue of the relationship between science, technology and society, is out-of-date. It should be replaced by "Public Engagement with Science and Technology" (PEST), a new acronym that clearly invites to reconceptualise the relationship between science and the public. The new approach involves the engagement of the public or rather the publics of science, through dialogue, in particular through an open and equal-to-equal discussion between scientists and non-experts that would enable non-experts to become the actual protagonists in the scientific decisions producing social effects.

"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.

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.