Higher educational attainment (EA) is negatively associated with schizophrenia (SZ). However, recent studies found a positive genetic correlation between EA and SZ. We investigate possible causes of this counterintuitive finding using genome-wide association study results for EA and SZ (N = 443,581) and a replication cohort (1169 controls; 1067 cases) with deeply phenotyped SZ patients. We find strong genetic dependence between EA and SZ that cannot be explained by chance, linkage disequilibrium, or assortative mating. Instead, several genes seem to have pleiotropic effects on EA and SZ, but without a clear pattern of sign concordance. Using EA as a proxy phenotype, we isolate FOXO6 and SLITRK1 as novel candidate genes for SZ. Our results reveal that current SZ diagnoses aggregate over at least two disease subtypes: one part resembles high intelligence and bipolar disorder (BIP), while the other part is a cognitive disorder that is independent of BIP.