This study investigated characteristics of five IMO winners and influences from their formal and informal educational experiences. In particular, this study provides in-depth understanding of former Korean IMO winners' characteristics and environmental influences. Also, implications including education for parents of the gifted, professional development for pre- and in-service teachers, and changes in schools to accommodate the needs of exceptional students are discussed. Mathematical giftedness is in the focus of educational research for decades. One important contribution was made by Krutetskii (1976) who outlined five elements of gifted "readiness for an activity"--positive attitudes, characteristic traits, positive mental state, knowledge, and ability--to understand characteristics of the mathematically gifted. Efforts have been made to understand various influential factors on their talent development. One of the recent examples of such studies important for designing this study was conducted by Muratori et al. (2006). They conducted an in-depth study of two successful mathematicians' development and careers. A flexible school system, parents, and mentors were revealed as highly influential for their talent development. This study employed the case study design and aspects of ethnographical methodology. Partially structured interviews were conducted them, parents of three Olympians, and a professor who led the Korean IMO teams. The grounded theory was employed for data analysis. Results of the study confirmed Krutetskii's (1976) findings of characteristics of the mathematically gifted. Various combinations of "readiness for an activity" were found in each Olympian. In terms of formal education, deficiencies in supporting and encouraging the mathematically gifted within various aspects of Korean compulsory education were found. Among aspects of informal education, parents' support and participation in competitions were found to be the most influential in identifying students' interest, in guiding students talent development, and in keeping them on the right track. Also, distinctive educational practices such as group tutoring institutions, called Ha-Gwon, and weekly mathematics workbooks were acknowledged while the influence from mentors and peers was minimal. Findings and contributions of this investigation may be of help for teachers and parents of mathematically gifted students assisting them in building environment that will develop students' talent to the fullest. [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.]