<p>Platonism in the philosophy of mathematics faces metaphysical, metasemantic, and epistemological challenges. For all of these reasons, many philosophers and mathematicians have been attracted to anti-platonist theories. Three types of antiplatonist theories are especially prominent: pluralist platonism, fictionalism, and conventionalism. Some influential anti-platonist philosophers, including Balaguer and, more recently, Field, have argued that, despite appearances, the different versions of anti-platonism do not significantly differ from each other; I disagree. The goal of this paper is to survey and assess the relative merits of the three main versions of anti-platonism while provisionally assuming each version succeeds on its own terms. Despite the obvious philosophical similarities between the theories, I argue that pluralist platonist theories inherit the metaphysical challenges for platonism and fictionalist theories inherit the metasemantic challenges for plationism, while conventionalist theories inherit neither. My ultimate conclusion is that, though similar in several important respects, there are important philosophical differences separating these three versions of anti-platonism.</p>