The article presents a few aspects of the most important of the unsolved problems of mathematics, the Riemann hypothesis, in the context of the most recent results. The so- called Lehmer\'s phenomenon discovered half a century ago and recently studied very intensively, as well as Newman\'s hypothesis concerning the de Bruijn-Newman\'s constant that is connected with it, seem to suggest that unexpectedly controversial elements sneak into mathematics, and they can be seen even on the level of the language used in (...) it. This probably results from the fact that even the best tools that mathematicians at the moment have at their disposal and by means of which they try in vain to verify the Riemann hypothesis are - for fundamental reasons - inadequate. (shrink)