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I have a different opinion about mathematics and its aspects. First we should know about history of mathematical concepts - why they come to be. Second we should be able to ‘generalize’ or apply these concepts to further understand and solve problems - (this is very much) how to use these concepts as tools. Third we should think with more precision - we must learn to observe and be more exact in admitting conditions. {This is the basic of set theories: what is ‘in’ and what is ‘not’; what are the constraints of tools, we use to solve problems!}

All others like theories, operations, logics, models, patterns,… are techniques.

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