The article concerns various proposals that have been made with the aim of improving the currently standard 18-column periodic table. We begin with a review of 8-, 18- and 32-column formats of the periodic table. This is followed by an examination of a possible, although rather impractical, 50-column table and how it could be used to consider the changes to the periodic table that have been predicted by Pyykkö in the domain of superheavy elements. Other topics reviewed include attempts to derive the Madelung rule as well as an analysis of what this rule actually provides. Finally, the notion of an 'optimal' periodic table is discussed in the context of recent work by philosophers of science who have examined the nature of classifications in general, as well as the notion of natural kinds. The article takes an unapologetically philosophical approach rather than focusing on specific data concerning the elements. Nevertheless, some pragmatic issues and educational aspects of the periodic table are also examined. This article is part of the theme issue 'Mendeleev and the periodic table'.
Keywords: Mendeleev; chemical education; group 3 of periodic table; history of chemistry; periodic table.