Just finished the book, but can't help talking about both the movie and the book, since I saw the movie first. Which in fact brings us to the interesting question of movies based on books, and which one should you read/ see first. But we'll leave that topic for another day.
Frankly in this case, I think the movie had very little in common with the book. The movie though brilliantly made and acted in, is a very limited and simplified account when it comes to covering John's life. It covers mainly the schizophrenia, which I thought it did beautifully. I specially like the idea of starting out from a patient's viewpoint and how real everything is to them. However there's a lot more to him in the biography of course, a third of it doesn't even begin about his illness.
The book is a much more detailed and researched bit. In fact I would say too detailed - too many names and facts. Perhaps that inevitable with a bio, however it does diminish the enjoyment for someone who's not familiar with the mathematical circles. It does a fair job of sketching his mathematical achievements, the person himself, warts and all, the hint of the illness always lingering in the background, and the final interesting background of the Nobel itself which perhaps was the main reason that we've heard of him at all. Overall an interesting read, but could've been more interesting with less names, and more well ideas..
I loved the name though. The beauty implied is very different from the one portrayed in the movie, and thats interesting. After all beauty does lie in the eye of the beholder.