Long answer:
First of all, the concept of "the highest requirement for mathematics" is actually too general. Without undergraduate mathematics major, there are few things that cannot be done. Engineers and even data scientists are mostly not from mathematics majors, but they also use many very advanced mathematical achievements (it doesn't matter if they don't know much).
Cryptography is not pure, and it is definitely not the only computer discipline closely related to mathematics. On the other hand, learning the mathematics required by computer vision is different from that required by cryptography. And these are just learning.
In the research, if you study mathematics more than the mathematics related to the subject, the best result is just to kill the chicken with an ox knife, and you are lucky (just applying this theory, it is also quite appropriate). The subject of mathematics is large and wide, which may not be helpful to your research topic.
However, people who have a good foundation in mathematics are more likely to make new breakthroughs in interdisciplinary research. But trying to "read widely" mathematics for computer research is really not worth the candle.
If you are not an undergraduate in mathematics, instead of making up advanced mathematics, abstract algebra, partial differential equations and topology, you should think about how to write proof questions, which is what you need most in your research: rigor. On this basis, we should learn many mathematical disciplines used in applied mathematics: discrete, linear generation, statistics, randomness, algorithm, scientific calculation, numerical analysis and so on.
Finally, if we can use the same general concept to talk about the direction of computer science that needs mathematics, I think it should be theory, including algorithm research, parallel computing, data structure, cryptography, machine learning, computational number theory, and many other things that I have guessed in Chinese for a while and still don't know how to say.