Traditionally, there have been two uses of set theory. In the first decades of this century it became apparent that every mathematical object could be represented as a set, and therefore that set theory could be used as a foundational system. According to Gödel’s second incompleteness theorem no formal system can exhaustively describe the whole mathematical universe, and therefore the point is no longer actually to prove properties of sets, but rather to calibrate them in a scale of increasingly strong logical axioms. The author, analysing some recent applications of set theory to algebra and topology, shows that set theory has been used to crystallize some intuitions for which other frameworks would be too rigid, and to elaborate them with the help of its specific tools, including strong axioms. This role is distinct from the previous ones in that all strong axioms are subsequently eliminated from the picture, so that the final results have no link with set-theoretical hypotheses. When the use of the additional axiom proves to be necessary, this gives rise to the second use of set theory. But if, on the contrary, the set-theoretical axiom can be eliminated, then the additional principle gives only a sort of plausibility before one discovers the final proof. From this point of view, the stronger the axiom is, the more powerful it is likely to be in terms of applications. The author believes that this new role of set theory could help to revitalize the interest in set theory in the future.