Intelligence can have an extremely high heritability, but also be malleable; a paradox that has been the source of continuous controversy. Here we attempt to clarify the issue, and advance a frequently overlooked solution to the paradox: Intelligence is a trait with unusual properties that create a large reservoir of hidden gene–environment (GE) networks, allowing for the contribution of high genetic and environmental influences on individual differences in IQ. GE interplay is difficult to specify with current methods, and is underestimated in standard metrics of heritability (thus inflating estimates of “genetic” effects). We describe empirical evidence for GE interplay in intelligence, with malleability existing on top of heritability. The evidence covers cognitive gains consequent to adoption/immigration, changes in IQ’s heritability across life span and socioeconomic status, gains in IQ over time consequent to societal development (the Flynn effect), the slowdown of age-related cognitive decline, and the gains in intelligence from early education. The GE solution has novel implications for enduring problems, including our inability to identify intelligence-related genes (also known as IQ’s “missing heritability”), and the loss of initial benefits from early intervention programs (such as “Head Start”). The GE solution can be a powerful guide to future research, and may also aid policies to overcome barriers to the development of intelligence, particularly in impoverished and underprivileged populations.