How mathematical ideas grow, Mathematics

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HOW MATHEMATICAL IDEAS GROW :  In this section we shall consider three aspects of the nature of mathematical ideas, namely, that they progress from concrete to abstract, from particular to general, and they form hierarchical structures. You may say that these three aspects can be seen in all human pursuit of knowledge. We shall examine them in the context of mathematics, and try and see how basic, crucial and important they are to mathematics.

 


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