Peirce's realism is a sophisticated realism inherited from the Avicennian Scotistic tradition, which may be briefly characterized by its opposition to metaphysical realism (Platonism) and various forms of nominalism. In this chapter, I consider how Peirce's realism fits his approach to mathematics, which is often presented as a somewhat incoherent mixture of Platonistic and conceptualistic elements. Without denying these, I claim that Peirce's subtle position not only helps to clear up some of these so-called inconsistencies but offers many insights for contemporary ways of dealing with the mathematical aspects of the problem of universals;