I think it was invented, because numbers don't exist. They are a placeholder we use for a certain amount. They're not exactly one thing, if they were, shape-shifting could exist, because numbers would be everywhere. They're sort of a principle.
The idea of a placeholder makes sense.
Objects counted any other way would still be just as numerical. The numerical quality itself perhaps comes with objects being physical. There might be 1 x 10^80 atoms in the physical universe ... it's an intrinsic quality/principle of the universe, we might say?
Yes, and I just got a message from one of the authors on the explanation:
"2013 is the smallest number that needs at least six squares to make."
That means that 2013 is the smallest number that *requires* at least six squares to produce. Yes, there are smaller numbers that can be made with six squares. But all of those numbers can also be made with five or fewer squares