You need basic background of almost all of the engineering mathematics, except for differential equations (for traditional machine learning).
Broadly speaking, following are the math topics you need to be familiar with for learning data science:
- Linear algebra
- Probability theory
- Multivariable Calculus
- Multivariate Statistics
- Optimization: Linear programming and convex optimization
Once you understand the key concepts in these subjects, I guarantee that you can then comprehend almost any research papers or tools related to machine learning. If you want to be a good machine learning researcher or engineer, there is no escape from mathematics. If you want jobs where people just implement ML methods, then you can probably escape but only until you encounter a dataset for which traditional methods fails. Then, nothing but good understanding of mathematics can save you.