Why maths?

A great many people dislike mathematics, and often with good reason. Taught poorly, it becomes an endless list of rules to be memorised, with little connection to the real world or to a learner's own intuition.

Yet mathematics is unusual among subjects in being infinitely comprehensible. However abstract an idea may appear, there is always a path leading back to something that can be seen to be true—not a rule held in the memory, but a principle that is genuinely understood. My goal with these articles is to lay out those paths.