There is evidence for genetic overlap between cognitive abilities and schizophrenia (SCZ), and genome-wide association studies (GWAS) demonstrate that both SCZ and general cognitive abilities have a strong polygenic component with many single-nucleotide polymorphisms (SNPs) each with a small effect. Here we investigated the shared genetic architecture between SCZ and educational attainment, which is regarded as a "proxy phenotype" for cognitive abilities, but may also reflect other traits. We applied a conditional false discovery rate (condFDR) method to GWAS of SCZ (n = 82 315), college completion ("College," n = 95 427), and years of education ("EduYears," n = 101 069). Variants associated with College or EduYears showed enrichment of association with SCZ, demonstrating polygenic overlap. This was confirmed by an increased replication rate in SCZ. By applying a condFDR threshold <0.01, we identified 18 genomic loci associated with SCZ after conditioning on College and 15 loci associated with SCZ after conditioning on EduYears. Ten of these loci overlapped. Using conjunctional FDR, we identified 10 loci shared between SCZ and College, and 29 loci shared between SCZ and EduYears. The majority of these loci had effects in opposite directions. Our results provide evidence for polygenic overlap between SCZ and educational attainment, and identify novel pleiotropic loci. Other studies have reported genetic overlap between SCZ and cognition, or SCZ and educational attainment, with negative correlation. Importantly, our methods enable identification of bi-directional effects, which highlight the complex relationship between SCZ and educational attainment, and support polygenic mechanisms underlying both cognitive dysfunction and creativity in SCZ.