So if Sakura participates in the theater troupe's practice, it's at least plausible that they may have discovered that she has some kind of natural talent for acting even on the first day. She may not be ready to like, do a professional performance, but they may have been able to tell that she's got something worth developing.
Discovering that kind of thing on her first karate practice seems less certain. Even if she's a physical genius, if she's had no practice she's just gonna be moving randomly. You need to build muscle memory over a long period of time in order to perform a martial art properly.
However, trying to participate in a research-level math lecture and discussions between math phds is just completely absurd. That is going to be incomprehensible mumbo jumbo to even university level math undergrads most likely. Maybe even other mathematicians if it's not within their own field.