Will the great mathematicians in history ever have had fun proposing and solving problems of recreational mathematics? Or, occupied by their high offices, will they have avoided putting themselves to the test with problems created only for the fun of it? Whatever the answer, it is easy to imagine that what would have appeared paltry problems to them could be ‘difficult’ for ordinary people. The Rudi Mathematici, hesitating over their great passions – telling stories about mathematicians and proposing entertaining problems of mathematics – have found the strange compromise of imagining some great mathematical minds at crucial times in their (real) lives, while they propose and solve some questions which in actual fact they probably never really had to tackle. This way, we find Isaac Newton as a precursor of Sherlock Holmes in the attempt to solve (mathematically) a case of murder, or see an irritated John Von Neumann stealing sweets from Ed Teller, while the Earth risks blowing up; not to mention the strange way with which Vilfredo Pareto, Paul Erdős, G. H. Hardy, Leonardo and others treated the intriguing questions of the world of numbers.