EN

The article presents the results of research on milestones (significant events, critical points, and crystallizing experiments) in the course of life of outstanding mathematicians and mathematically talented adolescents. The work covers the period of approximately the last 80 years. Four distinct group of mathematicians had received their education and pursued their scientific careers at that time: - The late, distinguished professors of mathematics, - Distinguished professors of mathematics who are still alive, - PhD students and doctors of mathematical faculties, - Laureates of mathematical olympiads. The author's intention was to indicate the milestones - key events and moments in their history determined by the author (or those indicated by those interested) to reach the highest position and recognition in the field of mathematics. Those are, for example, important experiences in a person's life that played a huge role in choosing mathematics as a direction for further development or reasserted that mathematics is the right choice. The considerations were based on a holistic, humanistic approach and a biographical approach from the perspective of Charlotte Bühler (1999). The techniques that have been used include document analysis and narrative interviews. According to the recommendations of Ch. Bühler results were presented graphically on the timelines. The information that is interesting and at the same time important from the point of view of mathematical education and the development of mathematical abilities is that some milestones are timeless. It is crucial to properly support children in developing their talents from an early age. Each of the respondents told about the people that were significant in his or her life. However, one can observe the fact that scientific authorities are becoming less and less important. The respondents from the group of distinguished PhDs and PhD students (apart from only one researched) did not mention scientific authorities who directed their mind towards mathematics, when speaking about the milestones in their lives. Trips abroad and scientific internships were much more important. Another important issue is the age of starting a scientific career. The starting point was the date of the first, signifcant publication, as mentioned by the researcher himself. Among the late, distinguished professors and outstanding professors living, it happened when they were between 20 and 30 years old. Unfortunately, no PhD student or fresh PhD graduate mentioned the outstanding work published at that time. Cognitive psychology tells us, however, that young people, due to the stages of intellectual development, can carry out the greatest mathematical discoveries.