Answer to Question #133654 in Real Analysis for M Shibambo

Question

2.1 Richard R Skemp states that “mathematics is not a collection of facts which can be demonstrated and verified in the physical world, but a structure of closely related concepts, arrived at by a process of pure thought”. Do you agree with the statement? Write a paragraph to reflect on Skemp’s statement. In your argument consider how concepts and logical relationships are constructed internally and exist in the mind as part of a network of ideas.

Answer 1

As an argument, we can consider the main features inherent in mathematics, a high degree of abstractness, a logical evidence base and universality of application. In mathematics, they often operate with concepts and methods that have no analogues in the physical world. Methods of mathematics and techniques are applied in various fields in some cases without much understanding of the essence of the process. The use of formal logic and the accuracy of the derivation of proofs is another argument.