My comment about euclid's elements was not intended to be taken literally - only figuratively, and perhaps with some humor (ie, instead of reading lots of texts, go back to a basic text and understand it well)
I meant that the foundations of what it means to do math can be found in as elementary a text as the Elements. Most importantly it shows how an abstract world (what we feel as space around us) can be modeled as Geometry with a set of axioms, along with a way to demonstrate statements without doubt. Just understanding this very deeply (in your bones) with a lot of problems would make you a better mathematician than if you read all the books listed above, at least in my view. Other areas of mathematics model different kinds of abstract worlds, but the activity is largely similar.
The problem I see is the focus on gathering knowledge without properly assimilating it (ie reading a lot of books). By assimilating I mean, being able to explain how something is constructed from the very basic first principles of how the conceptual structure was built.
I meant that the foundations of what it means to do math can be found in as elementary a text as the Elements. Most importantly it shows how an abstract world (what we feel as space around us) can be modeled as Geometry with a set of axioms, along with a way to demonstrate statements without doubt. Just understanding this very deeply (in your bones) with a lot of problems would make you a better mathematician than if you read all the books listed above, at least in my view. Other areas of mathematics model different kinds of abstract worlds, but the activity is largely similar.
The problem I see is the focus on gathering knowledge without properly assimilating it (ie reading a lot of books). By assimilating I mean, being able to explain how something is constructed from the very basic first principles of how the conceptual structure was built.