Nominalism is one of the most important positions in the contemporary philosophy of mathematics. The goal of this article is to point out various factors that have effected the rapid development of nominalism. In particular, the figures of the Polish precursors of nominalism are presented, that is, Leśniewski, Kotarbiński and Tarski. Consequently, the article of Quine and Goodman entitled Steps Toward a Constructive Nominalism is discussed. The article became the ideological declaration of nominalism and initiated reconstructionist tendencies within it. The presentation is concluded with the attempt of the modal interpretation of mathematics according to Putnam. This interpretation inspired the nominalists to enrich the existing logical apparatus with new methods and tools that are more efficient in the implementation of the strategy indicated by Quine and Godman.