The educational literature often includes debate over the nature and nurture of mathematical giftedness. The varied schools of thought reflect discrepancies between views, which are to a large extent functions of philosophical, political, and economic considerations. To address this debate, in the context of the current ZDM Special Issue, I attempt to analyze research and practices linked to mathematical giftedness in the Soviet Union in 1960–1980. I also look at the continuation of these Soviet-era practices, and to their influence on practices internationally. Particular attention is paid to the literature devoted to reaching a deeper understanding of the phenomenon of mathematical giftedness and of ways of nurturing this giftedness. The analysis starts with the discussion of domain-specific and domain-general characteristics of mathematical giftedness that have to be taken into account in educational environments for the mathematically gifted. It continues with a review of practices in special mathematical schools and classes in the Soviet Union, and a comparison to similar settings around the world in the twenty-first century. There is also an overview of enrichment mathematical activities, with a focus on mathematical circles, mathematical competitions and Olympiads, accompanied by a description of specificities of the mathematical content employed for the promotion of mathematical giftedness. Finally, the paper focuses on the question of what characterizes an excellent teacher of mathematically gifted students and on new educational technologies that are changing the education of these students worldwide. Following this analysis, I suggest some open questions for future research on the education of mathematically gifted students.

教育文献经常包括关于数学天赋的性质和培养的辩论。不同的思想流派反映了观点之间的差异，这在很大程度上是哲学、政治和经济考虑的功能。为了解决这一争论，在当前 ZDM 特刊的背景下，我试图分析与 1960-1980 年苏联数学天赋相关的研究和实践。我还研究了这些苏联时代实践的延续，以及它们对国际实践的影响。特别关注致力于深入了解数学天赋现象以及培养这种天赋的方法的文献。分析从讨论数学天才的特定领域和领域一般特征开始，这些特征在数学天才的教育环境中必须考虑在内。它继续回顾了苏联特殊数学学校和班级的实践，并与 21 世纪世界各地的类似环境进行了比较。还概述了丰富的数学活动，重点是数学圈、数学竞赛和奥林匹克竞赛，并描述了用于促进数学天赋的数学内容的特殊性。最后，这篇论文的重点是什么是数学天才学生的优秀教师的特点，以及正在改变全球这些学生教育的新教育技术。在此分析之后，我为未来数学天才学生的教育研究提出了一些开放性问题。