I have used quite a bit of advanced math, especially to solve problems in experimental mathematics using data science methods. For instance, solving stochastic integral equations. You can find the techniques I used in my recent book (full title: Applied Stochastic Processes, Chaos Modeling, and Probabilistic Properties of Numeration Systems.)
Some of the material used or created include:
I also read some interesting use of advanced math in data science by Colleen Farrelly. She mentions the following:
Laura Knight mentions measure theory and linear spaces leading to Hilbert space, Lebesque integration and the geometry of multivariate statistics.