- A lot of math grad school is reading books and papers and trying to understand what's going on. The difficulty is that reading math is not like reading a mystery thriller, and it's not even like reading a history book or a New York Times article.
The main issue is that, by the time you get to the frontiers of math, the words to describe the concepts don't really exist yet. Communicating these ideas is a bit like trying to explain a vacuum cleaner to someone who has never seen one, except you're only allowed to use words that are four letters long or shorter.
What can you say?
"It is a tool that does suck up dust to make what you walk on in a home tidy."
That's certainly better than nothing, but it doesn't tell you everything you might want to know about a vacuum cleaner. Can you use a vacuum cleaner to clean bookshelves? Can you use a vacuum cleaner to clean a cat? Can you use a vacuum cleaner to clean the outdoors?
When I was working on my physics degree, I became acutely aware that I would become fixed in a mindset that was a result of the type of thinking that I was required to practice. There is a reason why physicists and mathematicians are stereotypically loopy and absent-minded. They spend their days immersed in a language that is not commonly spoken, studying ideas that are rarely considered.
I think this is true of a number of fields, but if your background is in the arts, when you start talking in "that language" people tend to think you're pretentious and/or douchey. To be fair, there are a lot of pretentious douches involved in the arts.
I can see that. However, I think the misfortune of those that study the arts is that they cannot apply their craft to the production of new technologies. Whether deserved or not, there's a certain legitimacy granted to those in endeavors that spawn material progress. Also, impostors sink in math.
I don't think it's necessarily true that people who study the arts "cannot apply their craft to the production of new technologies." After all, art is at its core about ideas and exploring them. There is innovation in the arts as there is in all things, though it's not always obvious what those things are, or how they contribute to the production of new technologies.