Beginner in Dance at 30

I have always had a desire to dance, but since I was very good at mathematics, I was advised to do engineering field. I was taken to where I am doing my phd in engineering but I always have a spark of dance in me where I just want to do dancing. Have gone to ballroom dance classes but not professionally, I am turning 30 and I feel I should start following my dream. I have couple of questions:
is dancing school just teach ballet?

When you say “dancing school”, what exactly do you mean?

You need to look for dance schools that offer classes for adult beginners. Where are you? Do some research and find some dance schools near you that offer adult classes, and take them.

The adult beginner classes that tend to be offered include ballet, tap, jazz, contemporary, and hip hop. You can also continue in ballroom dance if you’d like.

You are too old to be able to become a “professional” in most fields of dance. However, you are in no way too old to start dancing, and to become quite good. You absolutely should pursue this alongside your mathematics studies. Start taking adult beginner dance classes now, and then, once you graduate and get a job in your field, use your income from engineering to fund your dancing. See where it all takes you.