Fully developing the talents of all students is a fundamental goal for personal well-being and development and ultimately for global societal innovation and flourishing. However, in this paper we focus on what we believe is an often neglected and underdeveloped population, that of the gifted. We draw from the cognitive aptitude and gifted education research literatures to make the case that solutions to consequential real-world problems can be greatly enhanced by more fully developing the talents of the intellectually gifted population, which we operationalize in this paper as roughly the top 5% of cognitive talent. Should well-supported high achievers choose to solve them, these problems span health, science, economic growth, and areas unforeseen. We draw from longitudinal research on intellectually precocious students and retrospective research on leaders and innovators in society, showing that mathematical, verbal, and spatial aptitudes are linked to societal innovation. We then discuss two remaining fundamental challenges: the identification of disadvantaged and marginalized groups of students who have traditionally been neglected in selection for gifted programming suited to their current developmental needs, and the building of skills beyond academic ones, specifically in the related areas of open-minded thinking and intellectual humility.