How important are extracurricular activities as a Mathematics Major?
In the US, and I suspect elsewhere, such things have little bearing on admissions to graduate school. People will look at your academic achievements, mostly, but not entirely, in your major subject. They are looking for evidence of academic success and want to be able to make an easy prediction about your fit into their program. It is a much more important thing for admission to an undergraduate program in the US, but not a graduate program. 

However, evidence of hard work and dedication to a goal can also be evidence of academic success. But the more important thing is the courses you took, your grades, and any writing you have done.