You have to see modern art in the context of it's history.
At the time Mondrian was painting, Van Gough had been pushing the boundries - everyone thought those swirling colours put on with a trowel were laughable at the time, and then Picasso started abstracting even more. Mondrian was pushing cubism further and further until he had just lines and colours - could he reduce it
that far and still move, affect an audience?
How modern art affects you, whether it appeals to you at all can be very personal - I have never really got Rothko but I think Pollock was a genius.
He doesn't always get it to work but when he does it's fabulous. In the Tate modern there's a couple of his pictures, the first I've tried to like, I really have but I just don't think it works.
The second is fabulous
http://homepage.mac.com/mag16/UniversityWebPag e/vacantPositions/ImagesVacant/summertime.jpg
Look at it and tell me you can't see the dancers!