I wish I'd read "Is Maths Real" first before commenting here! Oh well...anyone with more insights? Sometimes I feel once the principles/axioms are laid out, a giant puzzle is untangled within that logical system, and I wonder how much is really practical math vs academic sandbox?

E.g. this quote "You need a new idea, a good definition, a statement that you think you’ll be able to exploit. Only then can your work start."

Why is such an idea necessary in the first place, is the context missing here?

"By learning about the objects, by manipulating them and using them in mathematical arguments, they ultimately become your friend."