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After a brief outline of the topic of non-language thinking in mathematics the central phenomenological tool in this concern is established, i.e. the eidetic method. The special form of eidetic method in mathematical proving is implicit variation and this procedure entails three rules that are established in a simple geometrical example. Then the difficulties and the merits of analogical thinking in mathematics are discussed in different aspects. On the background of a new phenomenological understanding of the performance of non-language thinking in mathematics the well-known theses of B. L. van der Waerden that mathematical thinking to a great extent proceeds without the use of language is discussed in a new light.

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