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Unveiling numerical trends among either atomic or equivalent weights thatsomehow preserved resemblances among elements was frequent in the 1860s.Standing out from the crowd, Meyer and Mendeleev went beyond numericalrelationships, certainly motivated by a pedagogical aim. Both were after asystem synthesizing the chemical knowledge of their times in an appealing wayto be presented to chemistry students. Is it still the periodic system aimingat that? Is it really a map of the current chemistry landscape? Solving thesequestions entails addressing others such as: what is the periodic system? If itis about chemical elements, do we really know what a chemical element is? Isthe system unique? How was and how is currently built up? Is it actually usedto conduct chemical research? A suitable tool for chemical predictions? Or isit just a mnemotechnic for fancy trends? Does it have a limit, or multipleones, instead? Let us try to address these questions and let us begin byanalysing the concept of chemical element.

Challenges for the periodic systems of elements: chemical, historical and mathematical perspectives