does pursuing a research career in artificial intelligence requires deep understanding of higher mathematics? I'm currently enrolled in an undergrad computer science program. so far a Ph.D. in computer science is what I'm interested in doing in the future.
my question is.
 since there is applied math that includes calculus, linear algebra(without proofs), differential equations, intro probability...
and higher-level math such as abstract algebra, topology, differential geometry, linear algebra(with proofs), real analysis.
does being a successful AI researcher requires fluency with applied mathematics or a deep understanding of the more rigorous proof oriented abstract mathematics.
I believe it depends on the sort of research you want to do. 

If your goal is to better understand machine learning models, then you'd benefit from a solid mathematics background. Mathematics is necessary to understand how models work, intuit potential improvements, and prove various properties about the models. Researchers that rely on a foundational understanding of machine learning models are typically trying to push the state of the art regarding existing problems; they want to solve problems more efficiently, with more accuracy, with less data, with more explainability, etc., than the current best solutions.

If your goal is to apply existing models to solve novel problems, then it won't be as necessary for you to have a strong math background. It will be more important for you to have a general understanding of how different models work and when you'd pick one over another. Researchers that don't rely on mathematics as heavily will often attempt to push our understanding of what machines are capable of, rather than trying to make the machine better at a known problem.

This is my understanding from my experiences in the field. Hopefully it helps.