Then why is paper still the overwhelmingly preferred medium?
Using hypertext it would be trivial to link to an external source describing the specific concept used from linear algebra.
Not providing supporting links is only good for an audience that holds the entirety of mathematical knowledge in their heads (ie mathematicians in academia).
The rest of the world, incl those who have since moved on like the author, don't fit into that category.
Therefore, the work can only be accurately read and understood by the tiny minority of specialists capable of decoding the intent of the work.
Limited reach = limited value to society.
Is the intent of a PHD really to advance the field of mathematics? Or is it just another 'measuring stick' for individuals to prove to others how 'smart' they are?
It’s also one of his more moronic quotes. Certainly on a very abstract, dumbed-down level everything can be explained simply; sure, if you cannot give your parents a rough idea what you’re doing, you might want to look into more examples. But there are plenty of things which require a very extensive basis to be understood thoroughly.
For example, it is very easy to summarise what a (mathematical) group is and for anyone with a basic understanding of abstract maths, it will be understandable. It’s also very simple to find some examples (integers with addition, ℝ/{0} with multiplication etc.) which might be understandable by laypeople, but you will either confuse the latter or only give examples and not the actually important content.
Further, when you have “simply explained” what a group is, can you go on and equally “simply explain“ what a the fundamental representation is and how irreducible representations come about? You just need a certain level of knowledge (e.g., linear algebra) already and not every paper can include a full introduction into representation theory.