In 1995, the South African rugby team reached the World Cup finals, where they faced the New Zealand All Blacks on June 24, 1995, at Ellis Park in Johannesburg. Even before the game began, Carlin said, Mandela had already succeeded in bringing two warring populations together peacefully.
"The great thing was, on the morning of the World Cup, the vast majority of the population, white and black, was united," Carlin said. "That was an extraordinary situation."
In an interview for ESPN's documentary series, "30 for 30," Springbok forward Balie Stewart said, "We were all very aware that this was going to change our lives forever. It did change my life forever."
Although Carlin watched the game from the South African Embassy in Washington, D.C., he said, he could feel the incredible energy from the stadium that day. The moment when Mandela walked out on the field before the game to shake the players' hands, wearing a Springbok green jersey in front of a mostly white crowd, was "extraordinary," he said.
"They started chanting 'Nel-son, Nel-son,'" he said. "Black people watching on TV were blown away."
In a stunning victory, Springbok player Joel Stransky kicked the winning drop goal in extra time, making the final score 15-12, South Africa over New Zealand. It was at that moment, Carlin said, that the threat of an uprising was "banished once and for all."
"There was no happier moment in Mandela's political life ... or more joyful, more euphoric than that rugby cup in 1995," Carlin said. "It was the day his dreams came true."
Even if the team had lost, Carlin still believed that Mandela had already reached a significant milestone in bringing his country together for something.
"It would have been a shared disappointment," Carlin said. "A nation building, uniting for a common cause."
Carlin's book about Mandela's legacy later became the inspiration for the 2009 film "Invictus." South African-born Anthony Peckham, who penned the screenplay for the film, said it was "a privilege" to write it and when he first read Carlin's book proposal, he was moved to tears.
"We were told all our lives that this man was the most dangerous man on the planet and then you start learning about him," Peckham said, "And he was dangerous but for none of the reasons that these fools gave you… he was dangerous because he was powerful."
"These fools" Peckham referred to were the white government officials in power at the time, which he said controlled Mandela's image in the media.
"It was literally an act of terrorism to show a picture of Mandela," Peckham said. "We were told he was the devil incarnate... and he wanted to throw us all into the sea."
Peckham left South Africa in 1981 at the height of the apartheid, which he called "the dark days." He said he remembered getting up at 5 a.m. in his San Francisco home to watch the news coverage of Mandela's release from prison in 1990.
"I looked at all of this from afar as someone who left the country long ago until I got [Carlin's] story," he said. "I felt as if the story had found me... it felt somewhat ordained and I've never had that feeling on project and I'm certain I will never have it again."
The major events depicted in the movie happened just as he wrote them, Peckham said, and there was little he had to embellish.
"We worked hard to try to keep things on a human level, and to show how tiring it was and how lonely it was," he said. "So that it wasn't all choirs and trumpets and happiness...we very consciously kept it as real as we could."
One of those scenes taken from real life was when the South African leader faced a stadium full of his people and placed a Springbok baseball cap on his head. Peckham said it was the equivalent of 'putting on a Ku Klux Klan hood, and saying we can't survive without these people."
"He put on the clothing of his enemy and showed his people, people he was in the process of guiding into democracy and freedom, he was showing them physically and symbolically," that they had to be willing to accept the people who had oppressed them, he said.
But one of the most iconic scenes in the film -- when Mandela, played by Morgan Freeman, gives team captain Francois Pienaar, played by Matt Damon, a piece of paper with the Victorian poem "Invictus" written on it -- never actually happened.
"That particular poem was important to Mandela while he was in prison," he explained. "He did read it, it did inspire him."
Given that, Peckham said he still found the scene appropriate, "It's a film about inspiration in a way. And so an inspirational poem didn't seem out of place."
Although writing the story was "terrifying" because he was "afraid of not doing it justice," Peckham's fears were absolved when he talked with Mandela's daughter at the film's premiere.
"I met Lindsay at the premiere, and I said to her 'I hope none of this offends you.' She said, 'No, no...you've taken my father's legacy and made it eternal, thank you, thank you, thank you,' and I thought 'OK, I really am done.'"
Peckham also heard from one of Freeman's producers that Mandela was pleased with the film. He said the producer told him that while watching it with Freeman, "Mandela kept grabbing Morgan and saying 'I know that man, and I know that man,' and giggling."
Freeman told Parade Magazine in a 2009 interview that he had felt "destined" to play Mandela. The Academy-award winning actor met the South African leader for the first time in the early '90s after he was released from prison.
"He told me he wanted me to play him in a movie someday," Freeman explained. "I said, 'Then I need access to you, and I need to be able to hold your hand.' And he said, 'We'll do that.' ... I was sort of the chosen one, as it were."
Carlin told ABC News that when he sat down with Freeman to discuss his book's becoming a movie, he was shocked at how much the actor knew about the political and social issues in South Africa.
"I said to him, it's about an event that details the essence of Nelson Mandela's genius and the essence of the South African miracle," Carlin said in talking with Freeman. "Then he said, 'Oh, you mean the rugby game?' I was completely flummoxed and astonished that he made that leap."
While the rugby finals were a pinnacle moment for Mandela and the nation of South Africa, Carlin said, it wasn't the cure-all to ending violence in the country, but it was a catalyst towards rebuilding.
"I think Mandela is a political genius in the same way that Mozart was a musical genius," he said. "A natural-born talent for political leadership."