I have just come across "Foundations of Mathematics". Wikipedia describes it as
Foundations of mathematics can be conceived as the study of the basic mathematical concepts (number, geometrical figure, set, function, etc.) and how they form hierarchies of more complex structures and concepts, especially the fundamentally important structures that form the language of mathematics (formulas, theories and their models giving a meaning to formulas, definitions, proofs, algorithms, etc.) also called metamathematical concepts, with an eye to the philosophical aspects and the unity of mathematics.
Now this seems a bit strange to me. If foundations of mathematics really do deal with the study of basic mathematical concepts shouldn't they be taught to us as the first thing ? Also in theory wouldn't this mean that someone who has a good grasp of foundations of mathematics will have a very good understanding of mathematics as a whole ?
If that is true then why isn't foundation of mathematics taught at a earlier stage in life and more often ?
I apologize for the over simplification, but I am not an ace mathematician. Hence I want some insight into what foundations of mathematics are.