The questions means at least two things: Do we only see the same maths over and over again? If so, why?
My maths background is as a modeller. You will see from my papers
that I have worked on many different areas of applied/industrial/applicable maths: I turn physical/financial processes into some math model for the obvious reasons. I have complained for decades about the state of modelling in finance. I see the same model over and over again, with little variation. When there is variation it is not generally liked by the majority of the community. And obviously I've complained about the accuracy of these models as well.
What maths do we see? Martingales, Monte Carlo simulations, and the same linear diffusion equation, with the occasional trivial integral equation. Ad nauseam.
Am I right that the type of maths is limited? If so, why is it limited? Does it matter?
I have my own views on this.
In The Money Formula
David Orrell and I compare and contrast quant finance with mathematical biology. The latter should be an inspiration for quants. But sadly very, very few quants know enough mathematics to appreciate the possibilities of modelling. (I can only think of a couple who do!)