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In mathematics we witness a certain tension between intuitive and non-intuitive elements or between intuitive and rigorous approach. Some philosophizing mathematicians remind us of the intuitive as a necessary background of all productive mathematical work, while others prefer to steer clear of anything „merely intuitive“ since they view it as something leading us to mistakes and paradoxes. The aim of this paper is to point out the variety of the intuitive in mathematical praxis and appeal for its more adequate appreciation both in the didactics and philosophy of mathematics. As a sort of a preliminary semantical map we make use of Reuben Hersh’s list of the distinctive usage of term „intuitive“ in contemporary mathematical discourse.