A read of her biography on Wikipedia is pretty long for someone still only 25 years old, and she certainly isn't a product of anyone's manufacture - she is the real deal. Obviously a very determined and talented artist whether you like her or not and very much more of a modern day Bowie than a Madonna - there is far more to her than the single persona for a start, but there is an awful lot more to her than just a pop musician. It would appear that she is an artist who has chosen music currently as her media rather than just being a pop musician, meaning that she is truly an artist in the proper sense of the word.
People like this don't come along very often. She isn't for me personally, but nevertheless I can recognise her extraordinary talent. Whether that makes her a genius depends on whether you would call Bowie or McCartney a genius. If yes, then yes. She seems to have the ability to absorb absolutely any subject and use that knowledge to her advantage, so she is clearly frighteningly intelligent.