First off, I have no interest in being a mathematician. Math was always and continues to be quite difficult for me.
So, as an outsider to advanced math, it blows my mind that there are people who’s entire job title is mathematician. How does that work? What does a mathematician do?
Speaking from a pure maths’ perspective here: Frankly, a little bit. I think at the university research level, the academically inclined professors might be a bit tired to be sidelined with the applied ones, especially when the latter are applauded for their industrial cooperation (read research investments) and appliances (read private ownership over publicly funded research). My study mates and I joked about applied math being dirty, but in reality it is more the absence of creativity and rigor that is the problem with applied math in my opinion.
To me, math is all about answering cool questions, sometimes posing even cooler questions in the process. Maybe an appropriate analogy would be whether an artist judges those that make commercials. Exploratory work can take a life of their own that is usually not possible when the format of the answer is predefined. That being said, I do not really judge, I only think that the different expressions are (usually) quite distinct in direction and content. I did not do math for money, though I rely on my mathematical skills for income.
This is such a neat window into a whole different world for me, thank you for writing all this out!
It does sound very much like artists and the whole conversation of who’s selling out and who is being true to the art.
It seems to me that we definitely need both types in this world, ones like you who are curious and just want to explode the edges of what we understand for the sake of discovery, and ones who are willing to apply their mathematic knowledge to narrowly defined problems.