Do people typically seperate their backend and frontend into seperate classes?

I hope I'm using those words correctly here.

So, I'm making a basic math app with javafx that the user can interact with, click some buttons, and then get a polynomial equation of their choice solved.

So in my mind there are 2 big parts to this. The UI, or the stuff the user sees, and the calculations for solving the polynomials. Each of these big parts can be broken into smaller tasks, but those are the biggest ones. I also could write another class to handle changes in the UI, but I'm not sure if that's necessary.

Anyways, it would be a lot easier for me to leave everything in 1 class and 1 file. Is it worth the hassle to split the classes up?