A Conspiracy Theory
September 8, 2017
1:03 PM
The rule of thumb is that if you catch yourself believing in or inventing a conspiracy theory, you are probably deluding yourself. Notwithstanding, here's mine.
Below, a "quantum group" means "the quantized universal enveloping algebra of a semi-simple Lie algebra, as an object that supports a solution of the Yang-Baxter equation that can be used to create knot invariants".
Theory. Perhaps with the exception of Drinfel'd, nobody genuinely understands quantum groups, why they exist, and even more so, why they must be there from a topological perspective.
Some know they don't understand, but are afraid to admit it.
Many pretend to understand, but they really just quote.
Many think they understand, but they are deluding themselves. They have become comfortable with quantum groups, and stopped asking "why" questions. Are quantum groups as clear to them as differential forms are to me?  
Some have even written "introduction to quantum groups" books and articles, in which they state the facts but add little understanding. Often these books serve as fig leafs for others, "it's well known, it's in that thick book". But very few have really read those thick books, and those thick books don't deliver.
Why isn't anybody doing anything?