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Background: In the previous authorsВ’ publications it was shown that modeling of fundamental properties of mathematics within the teaching process is very efficient. A group of fundamental properties consists of several so-called dualistic properties, which are inherent in all the branches of mathematics in all periods of its history. The purpose of this article is to bring to light some up-to-date factors, which generate a new appearance of the dualistic properties as well as their gradual modification. Methods: ...

Background: Originality is the main specific feature of mathematical Olympiad problems. Formulating these problems requires a special kind of creativity and only a few people have this ability. They are called problem composers, and Rosen Nikolaev is one of them. H? creates mathematical tasks every day. More than 14 of them have been selected for the The National Student Olympiad in Mathematic and more than 40 for the Bulgarian Mathematical Olympiad. Such specialists are unique, not only because of their special a...