Yes user interfaces are patentable.

Yes, some ideas can be patentable, but not all ideas. Some ideas might be better protected by trademark or copyright protection, while others might not be protectable at all. For example, this blog post explores the basics of what differentiates patentable and non-patentable ideas and gives suggestions on how to determine whether a given idea might be patentable:

patentsdemystified.com/are-ideas-patentable/

your teeth are pretty

As an abstract idea, a theorem would not be patentable.

Old enough to invent something patentable.