The key word here is preference, which is subjective by definition. Just because certain notations are considered outdated does not mean there is no situation i

The key word here is preference, which is subjective by definition. Just because certain notations are considered outdated does not mean there is no situation in which they can have merit. To wit, my preferred method for understanding tensors is without indices, and matrix notation is primarily useful for computers, not humans (in that regard I prefer the coordinate-free perspective). In fact, the insistence that linear algebra must be understood entirely using matrices and rows and columns is a red flag in my book! I'm not saying that notation is irrelevant, I'm saying it's a matter of perspective. Of course there are notational breakthroughs throughout history. But what makes a breakthrough depends on what problems you're trying to solve, which is largely why computer scientists like indices and algebraic geometers like commutative diagrams. Each is as unwelcome in the wrong domain as roman numerals are in algebra.