Richard R skemp states "mathematics is not a collection of facts which can be demonstrated and verified in the physical world , but a structure of closely related concept , arrived by a process of pure thought .

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The principal characteristics of algebra, a significant degree of complexity, and the logical scientific evidence or universality of application could be considered as an argument. It often operates in maths without any equivalent concepts and methods throughout the real world. In some cases, computational processes and approaches are applied in different fields without a great understanding of the essence of the process. Another argument is the use of formal logic as well as the accuracy of evidence extracting.

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