Critics of the box-office hit, based on a biography of the same name, have accused the filmmakers of leaving out significant details of his life.
But in an interview with correspondent Mike Wallace of the CBS News program 60 Minutes, Nash, who suffers from schizophrenia, his wife, Alicia, and son Johnny deny these allegations, which have made this Academy Award contender controversial in recent weeks.
This is the first time Nash has spoken out since the movie was released.
He tells Wallace he began hearing voices when he was in his thirties. "I thought of the voices as . . . something a little different from aliens. I thought of them more like angels . . . "It's really my subconscious talking, it was really that…I know that now," says Nash.
Was he anti-Semitic?
"I did have strange ideas during certain periods of time," Nash concedes. Typical, he says, of the paranoid rantings of schizophrenics.
But, says Wallace, Nash is not anti-Semitic, and never has been. "Everyone with whom I talked who knows John, everyone say no. He . . . doesn't feel that way about Jews at all," Wallace says.
Nash's wife Alicia adds, "I've never heard him say anything like that."
What about the charges that Nash is homosexual? Alicia Nash says no. "I've known him since I was 20 and that's just not true…I should know," she says.
Nash denies it, too, but won't discuss it. "I've learned that it's better that I don't talk about it," he tells Wallace.
If, as critics have charged, Nash ignored a son born of a long-ago relationship, he says he is close to him now and has given John David Stier a share of the royalties from "A Beautiful Mind."
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While Nash's mental illness diminished through the 1970s and 1980s, his son, Johnny, showed increasing signs of the same illness. Nash believes his concern for Johnny may have led to his own partial recovery but also makes a poignant yet macabre analogy: "It's possible. It's almost as if a demon might have passed from one host to another."
Johnny Nash says simply, "He was a good father. Yes," in answering a Wallace question.
He's also a PhD mathematician, and says he wanted to follow in his father's footsteps. "That was always my life's (dream). . . I still felt that I could equal him . . . I haven't done so yet, but I'm trying to."
The New York Times said in its Saturday editions that some in the film industry say Nash is actually the victim of a whisper campaign whose aim is to scuttle the movie's Oscar hopes. It's a phenomenon they say has become increasingly common in the intense competition for Academy Awards.
"This may not be the worst year in Oscar history, but it's pretty low," Pete Hammond, a film historian and consultant for American Movie Classics, is quoted by the Times as saying. "To accuse the subject of a film of being anti-Semitic when you know that a lot of the people who will be voting on the Oscars are Jewish, well, that's really down and dirty."
The Times reports that the film's backers say the whisper campaigns, which reach a peak during Oscar balloting, are fueled by the Internet, by a fascination with tabloid-type scandals and by the rise of private Oscar strategists hired by the studios.
But even in that context, the campaign against "A Beautiful Mind" has struck many in Hollywood as particularly brutal, the Times adds.
"It's getting nastier," Mr. Hammond said. "It's like a political campaign now. You get these so-called Oscar consultants who go out there thinking, What kind of dirt can we dig up?"
Mrs. Nash says tells Wallace the allegations about her husband are "undoubtedly" being spread by supporters of other films.
Nash was born on June 13, 1928, in Bluefield, W.Va.; it became apparent when he was young that he was a genius. He studied mathematics, and became a brilliant Princeton mathematician in the 1950s. He then began to suffer from schizophrenia.
He suffered terribly on and off for years. In 1994, while in remission, he was awarded the Nobel Prize in economics for work he had done more than 40 years earlier while studying at Princeton.
Nash is still a working mathematician at Princeton.
The film has been nominated for a number of Academy Awards including Best Picture. Russell Crowe, who plays Nash, and Jennifer Connolly, who plays Alicia, also were nominated for Best Actor and Best Supporting Actress awards respectively.