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I'm a curious fellow. Another topic here on the forums or rather a detour in this topic (the metric vs imperial topic, to be exact) stirred up that curiosity. What is mathematics anyway? So, I began looking around. First stop was ye ol' Wikipedia. Now Wikipedia can be a great source of information but it can be a wild ride sometimes (too often, in fact). Here is what is driving me up the walls (from Wikipedia's article on mathematical structure): "In mathematics, a structure on a set, or more generally a type, consists of additional mathematical objects that..:" So, to understand structure, I should know what a set is but wait no, a set apparently is only part of something bigger, a type so I should look that up first, or should I look at mathematical objects first, to understand better what a type is? So what I did was, as soon as I came across anything to the likes of "based on [new concept here]", or "a sub-set of [new concept here]" etc, I followed those links hoping to get to an even more fundamental er, fundament that would explain a certain idea or term. Soon I came across the article on mathematical objects https://en.wikipedia.org/wiki/Mathematical_object Now we are rushing towards the realm of philosophy. Still I feel there are even more fundamental terms I should understand before really understanding mathematical objects. Looking around, it is true that often you will find say an explaination of A that requires a prior explaination of B, which itself refers to A for prior explaination, or to C which in turn refers back to A. Circular explainations are tricky. Most of the time, it seems, they ultimately fail to explain but one can not rule out that at the very base, there are in fact some A that can only exist if B exists and vice versa, the two are not the same but one can not exist without the other, and together they do form a unit (in lack of a better word) of foundation which all other ideas rest upon. If anyone here have ever dived into the depth of mathematics, here's a question: Where would one want to start to learn about mathematics in it's purest form if one wants to start at the very start, where the foundations have no further foundations underneath?