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mathematics

Why is Mathematics Difficult?

It is the languages that are difficult, not the ideas.

A curious revelation of logic, mathematics and physics is that the concepts themselves are never really all that difficult and can usually be quite rapidly grasped if the method of education is sufficiently powerful. The difficulty lies in acquiring an aptitude to intuitively understand and leverage the relationships between the symbols that are used to represent artefacts, entities and systems. As a consequence, education in the topics of higher mathematics is complicated by the breadth and depth of cognitive investment in wrapping one’s mind around the syntax and grammar of whichever technical language is in play.

These languages are of course procedurally acquired and build upon themselves in cumulative, iterative ways. I have recently been abseiling back down this rabbit hole and it is beginning to dawn upon me that the ways in which we define and explain mathematics may be quite unnecessarily intricate. The artefacts, entities and systems of interest are generally quite complex but the ways in which we teach (and learn) them may be generating redundant inertia and inhibition to many students.

What, I wonder, is it about psychology and culture that predisposes us quite unwittingly towards a tribal value system of information and complexity that asserts value as a measure of the limited number of people who fully comprehend a topic? Is it possible that we are almost entirely unaware, beyond whatever analytical or practical utility these information systems bring, that they optimally self-propagate through the reproduction of an exclusivity and functional occlusion as partial indecipherability that generates radiating diversity of incomplete and indefinitely-extensible definitions?

In short, are there better ways to teach and learn logic, mathematics and physics?

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