Pretense theory construes mathematical sentences as prescribed to be imagined true, so that mathematics is a sort of make-believe. Using Kendall Walton's incisive theory of fiction as a springboard, the philosophies of mathematics of Mario Bunge and Mary Leng are exposited as representative of a pretense theoretical approach. This approach is defended against objections based on the obvious truth of mathematics and the disanalogy of mathematics to fiction. A pretense theoretical approach is found to be especially plausible for set theory, which may be taken as a foundation for all of mathematics.