This article is devoted to the actual problem of modern education, i.e. the formation of professional competencies through the ability of mathematics teachers and students of pedagogical specialties to solve the problems of the Mathematical Olympiad. The purpose of the Olympiad is to conduct an independent examination of the formation of professional competencies of students, future teachers of mathematics, improving the quality of education through stimulating their cognitive activity and revealing creative potential, as well as identifying, stimulating and supporting mathematics teachers with high methodological and subject knowledge and professional competencies necessary for students to achieve the results of higher education.  The main objectives of the Olympiad are: creation of organizational and methodological conditions for the implementation of competence-oriented pedagogical education, assistance in improving the quality of training graduates of the educational program of the future mathematics teacher, development of intellectual capabilities and professional qualities of mathematics teachers, formation of new competencies based on personal self-education and identification of the best representatives of the profession. One of the leading materials on mathematical education or republican teaching methods, associated with the memories of specialists, has been replenished with a brief history of the Olympiad for ten years. At the end of the article, an example of tasks of a mathematical olympiad for the development of research abilities of teachers and students of mathematics is given.