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Mathematical Geology and the Progress of Geological Sciences

A review of the geological sciences reveals the fact that there was a passage from axiomatic approach in the 18th century to purely inductive adjustment in the following periods. At present mathematical geology again offers the axiomatic approach. The restoration of axiomatic idea is due to maturation of geological sciences. There are three different approaches to mathematical geology. The more mature the geological ideas in the problem are, the more the mathematic tool is determined by the geological meaning of the problem. Less mature geological problems make it necessary to introduce more routine mathematical means with restricted foundation to form geology. Some problems in geology and mathematics have been investigated and shown to be of importance for both sciences as well as for development of mathematical geology.