Othello is a tragedy by William Shakespeare, considered one of his great works and a classic of literature. In Brave New World, however, it is not known or appreciated. The new world has eliminated literature, art and history in order to enforce a conditioned 'happiness' that does not involve truth and beauty.
A similar line is taken in another famous dystopian novel, Nineteen Eighty-Four by George Orwell (1949). In Nineteen Eighty-Four, the culture of the old world is converted into Newspeak. Newspeak is a simplified, dull, even culture-less and unimaginative language. By reducing literature such as Shakespeare's plays into Newspeak, the meaning and art are lost, and in a sense Shakespeare stops existing. In Brave New World, the world controller has recognised that Othello cannot exist in the new world because no one would understand it in its pure form; if modified, it would no longer be Othello. In this way, literature and art are not simply banned, they are made completely irrelevant.
Comparing the dystopias of Nineteen Eighty-Four and Brave New World, social critic Neil Postman wrote:
"What Orwell feared were those who would ban books. What Huxley feared was that there would be no reason to ban a book, for there would be no one who wanted to read one. Orwell feared those who would deprive us of information. Huxley feared those who would give us so much that we would be reduced to passivity and egoism. Orwell feared that the truth would be concealed from us. Huxley feared the truth would be drowned in a sea of irrelevance." (Read more at Wikipedia)
The growth of the Internet and modern mass communication suggests Huxley was closer to the truth.