A polymer of an embodiment includes a recurring unit containing at least one bivalent group selected from among a formula (1), a formula (2), a formula (3), and a formula (4). Z1 indicates carbon having an R1 group, nitrogen, or the like. Z2 indicates oxygen, sulfur, selenium, nitrogen having an R2 group, or the like. The R1 and R2 groups indicate hydrogen, a substituted or unsubstituted alkyl group, a substituted or unsubstituted aryl group, a substituted or unsubstituted heteroaryl group, or the like, X indicates oxygen, sulfur, selenium, or the like.