| Mathematics is NOT Boring; the teaching of Maths divorced of Real-World Applications is what is Boring. An over-emphasis on Formalism/Abstraction is what is killing people's interest in Maths/Sciences. The Teaching of all Maths/Sciences should always start with a Real-World motivating example and then introduce the Maths as necessary to Solve it. In this context see V. I. Arnold's essay; On Teaching Mathematics - https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html Quote from the above article: * Attempts to create "pure" deductive-axiomatic mathematics have led to the rejection of the scheme used in physics (observation - model - investigation of the model - conclusions - testing by observations) and its substitution by the scheme: definition - theorem - proof. It is impossible to understand an unmotivated definition but this does not stop the criminal algebraists-axiomatisators. * What is a group? Algebraists teach that this is supposedly a set with two operations that satisfy a load of easily-forgettable axioms. This definition provokes a natural protest: why would any sensible person need such pairs of operations? "Oh, curse this maths" - concludes the student (who, possibly, becomes the Minister for Science in the future). * We get a totally different situation if we start off not with the group but with the concept of a transformation (a one-to-one mapping of a set onto itself) as it was historically. A collection of transformations of a set is called a group if along with any two transformations it contains the result of their consecutive application and an inverse transformation along with every transformation. |