Sometimes I think mathematicians are amazingly creative. Leonhard Euler's solution to the Konigsberg Bridge problem is elegant. Cantor's proof that the set of irrational numbers is uncountably infinite is elegant. Much of ancient Greek solid geometry in elegant.
Other times I think mathematicians aren't creative at all. I offer as one example the symbology of vertical lines. We use vertical lines to mean entirely different things depending on the context; do we lack so much creativity that we couldn't come up with different symbols?
| | . A pair of vertical lines.
That symbol is used 4 entirely different ways that I know of, and there's plenty of math I haven't even heard of. Perhaps it's even used other ways as well.
In a case like |x|, the vertical lines mean "absolute value" of a number, be that number real or imaginary.
In a case like |z| it represents the magnitude of vector z.
It could also represent the determinant of a matrix, det A:
| 3 5 7|
| 2 4 6|
| 1 4 9|
or |A| for short.
Lastly, at least in my experience, it represents the cardinality of a set--that is, how many items are in the set. |1, 3, 5, 7, 9, 11|=6, or |Z+| = אo, which means that the set of positive integers (Z+) is countably infinite, symbolized by "aleph-naught".
Maybe, instead of worrying that mathematicians aren't creative, I should celebrate the efficiency of using the same symbol so many different ways. That's a much more positive way to look at things. Yes, that's what I think I'll do.