Abstract
The focus of attention of public organizations and international rankings on ensuring access of the population to high-quality education in the exact sciences emphasizes their role in the economic and technical development of countries. Observing the situation in the education system of the post-Soviet republics, we are convinced that the school is losing its purpose to teach, provide basic education, develop the potential and talents of young people. The authors see the possibility of overcoming the crisis of the modern educational system in strengthening mathematical education at school as a fundamental factor in the effective mastery of students in the disciplines of the mathematical and natural science cycle. Emphasizing the importance of Olympiads for the development of thinking, the purpose of the article is defined - to study the possibilities of Olympiad problems in mathematics for the formation and development of creative mathematical thinking of students. The study determined that the main tool for the development of mathematical creativity is a problem. The degree of creativity is assessed in the process of setting and demonstrating strategies for solving different types of problems based on the parameters: fluency, flexibility and originality. Internal (giftedness, genetics) and external (quality education, creative environment, Olympiad activities) factors in the development of mathematical creativity are identified.