Earlier quoted context omitted.
Using matrices to perform the calculations is an optimization over doing a bunch of for loops. This vectorization results in faster code within higher level languages and on certain hardware platforms (SIMD). It's nothing to do with "slicker notation", although having written gradient descent with for loops and matrix operations, the vectorized version is simpler and cleaner to read in my opinion.
He's not complaining about using vectorization in code. The problem is papers and even explanations targeted at non-experts, often use obfuscated math in place of clear explanations. I've complained about this before here: https://news.ycombinator.com/item?id=13953530 Mathematical notation is basically a programming language. A programming language with weird symbols you can't type to search for, single letter variab…
It's about the level of abstraction. And yeah if you don't understand the notation or syntax at the level of abstraction you're studying, it will be very hard.
(FWIW I find Scala code quite hard to understand sometimes, but I also find the more I know about the language, the more comprehensible it gets).