Black holes are the most prudish objects in the Universe. Fortunately, an elusive idea that emerged on a pedestrian crossing revealed some of their mysteries. Announced by Penrose in barely a couple of pages 57 years ago, that idea was worth the 2020 Nobel Prize in Physics.
In this Colloquium Penrose’s contribution (‘a singularity theorem’) and its relevance will be discussed. After expounding the historical context, the main ideas behind the theorem will be analyzed. The impact of the theorem will be assessed, taking into account their physical significance. Finally, an overview of Penrose's broad legacy for mathematical physics and relativity will be given. Examples will be used for illustrative purposes.
