Introduction

The title of this paper is a paraphrase of that of an article (``Probably guilty: Bad mathematics means rough justice''), appeared in New Scientist in October 2009[3], whose incipit induced me to write a `defense of Columbo',²that finally turned into a sui generis introduction to probabilistic reasoning [5].

Indeed, as I wrote in [5], ``I can give firm witness that scientific practice is plenty of mistakes of the kind reported [in the cited New Scientist article], that happen even in fields the general public would hardly suspect, like frontier physics, whose protagonists are supposed to have a skill in mathematics superior to police officers and lawyers.'' In fact, although it might sound amazing, the `bad mathematics' that induces a judge to form a wrong opinion about somebody's guilt or innocence is the same that, for example, in April of this year made media and general public believe that particle physicists strongly believed (although not yet certain) Fermilab had made ``the most significant discovery in physics in half a century''[2] - how else should normal people interpret a statement such as ``this result has a 99.7 percent chance of being correct''[1]?

Although I am quite used to fake claims of this kind, some of which are discussed in [6], and I have no interest in analyzing each individual case, the reason I want to return here to this subject, focusing on the Fermilab case, is twofold. First, due to the modern fast communication on the internet, I was involved in discussions about the issue `discovery or not?' and realized that even people with university background in mathematics or physics were induced to think that it was most likely a discovery, or at least that Fermilab physicists were convinced this was the case. Second, a few days after the CDF announcement, I had to lecture PhD students in Perugia[7] and therefore I amused myself to collect related news and comments on the internet, because I expected that claim would have been a hot topic, as it turned out to be the case. Finally very recent interactions with students and young researchers in Lecce [8] convinced me to resume the paper draft started on the train Rome to Perugia.