Sometimes the reasons are historical or due to the fact that certain mathematical objects weren't yet developed at the time, or just not known to the mathematician.

As an example take James Maxwell, when he worked on what are now called Maxwell's equations, he didn't use vector notation, and they were a bit less than 2 dozen equations, now they're more commonly taught with vector notation and are written more concisely as four equations, going even further using tensors you can group them into two equations only.