Both Jerome and Vincent are determined. Jerome will do almost anything to make his dream come true and go into space. Vincent has always won in swimming as he is a perfect swimmer. But when he gets the bronze medal instead oof the gold, he will remember his loss for the rest of his life.
2) Was Jerome mentally ill?
There is a big difference between being mentally ill and depressed. In my opinion, Jerome was not at all mentally ill but he was certainly depressed and suicidal. This maybe partly because he was physically ill and could not do, what he loved and use to be good at, anymore. He could no longer swim. Swimming was his passion, his life, without it and without the best results (i.e. Gold medal ALL THE TIME) he became depressed and had no more motivations.
3) Compare Anton and Vincent, the two brothers. How was Vincent able to beat Anton at swimming despite Vincent's weak heart?
Although Anton's heart was stronger than Vincent's, Anton kept some of his strength for the swim back. Vincent didn't. He gave 150% and left none for when he had to come back. He gave 10% talent but 90% effort. On the other hand, Anton relied on his talent.
If you would like to watch the movie, here is a link: http://online-movie-db.info/watch.php?vid=Gattaca
Or just watch the trailer: http://www.youtube.com/watch?feature=player_embedded&v=m_nkVmRSpfE
