From the past, we know how much "serendipity" has played a pivotal role in scientific discoveries. The definition of serendipity implies the finding of one thing while looking for something else. The most known example of this is the discovery of penicillin. Fleming was studying "Staphylococcus influenzae" when one of his culture plates became contaminated and developed a mold that created a bacteria-free circle. Then he found within the mold, a substance that proved to be very active against the vast majority of bacteria infecting human beings. Serendipity had a key role in the discovery of a wide panel of psychotropic drugs as well, including aniline purple, lysergic acid diethylamide, meprobamate, chlorpromazine, and imipramine. Actually, many recent studies support a step back in current strategies that could lead to new discoveries in science. This change should seriously consider the idea that to further focus research project milestones that are already too focused could be a mistake. How can you observe something that others did not realize before you? Probably, one pivotal requirement is that you pay a high level of attention on what is occurring all around you. But this is not entirely enough, since, specifically talking about scientific discoveries, you should have your mind sufficiently unbiased from mainstream infrastructures, which normally make you extremely focused on a particular endpoint without paying attention to potential "unexpected discoveries". Research in medicine should probably come back to the age of innocence and avoid the age of mainstream reports that do not contribute to real advances in the curing of human diseases. Max Planck said "Science progresses not because scientists change their minds, but rather because scientists attached to erroneous views die, and are replaced", and Otto Warburg used the same words when he realized the lack of acceptance of his ideas. This editorial proposes a series of examples showing, in a practical way, how unfocused research may contribute to very important discoveries in science.