The purpose of this study was to describe the development of the Hungarian mathematics education system from the first half of the 20th century to the present day. The study focused on educational programs for mathematically talented students in Hungary, since it is the success of these talented students that has earned Hungary such an impressive international reputation. The study sought to identify the in-school and extracurricular offerings that comprise the current system for mathematically talented students in Hungary and to determine the major changes to the mathematics education system for gifted students in the past twenty years. To answer these questions, the researcher combined analysis of historical documents and current publications with a series of in-depth interviews with current Hungarian secondary school teachers, mathematicians, professors, and other educators. The primary changes within the school system have come as a result of the decentralization of education that took place along at the end of the 1980s, including a decrease in the reliability of financing for schools and the dissolution of the school inspectorate program. While some of these changes paved the way for increased school autonomy and the ability to offer more customized programs for students, they have also sparked concerns about a decreasing overall level of standards and student knowledge in mathematics. In the special mathematics schools, the admissions process has recently been changed to prohibit these schools from requiring separate exams or interviews, and instead students now take the same standardized exam as all other Hungarian 6th grade students, regardless of intended specialization. This new policy raises questions about public sentiment toward and governmental support for such specialized programs. Extracurricular programs such as camps and competitions remain a strong part of the Hungarian tradition, with an increasing number of competitions offered for students each year. New types of competitions in recent years include team competitions, multiple choice competitions, and some exclusively for students who are not in a special mathematics class. The founding of these new competitions reflects a possible shift in the focus and purpose of competitions away from a strictly talent-search model to a more inclusive "enrichment" approach. Following the regime change in 1990, Hungarian students have faced fewer restrictions in traditional fields along with new opportunities in economics and information technology. As a result, mathematics may no longer hold the privileged position it did during the first half of the 20th century. However, it is clear that in Hungary, tradition itself remains a strong motivating factor and continues to stimulate the development of mathematically talented students. The involvement of the mathematical community in the identification and education of young talents helps perpetuate these traditions. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]