As he prepared to retire, "60 Minutes" and correspondent Scott Pelley hoped he would overrule that custom and talk with us about the decisions that have changed our times.
It was Stevens who forced a showdown with President Bush over the prisoners at Guantanamo Bay, and Stevens who tried to stop the court from deciding the presidential election of 2000.
At the end of his last term, Justice Stevens ruled on our request and, in a series of interviews, opened a rare window into the nation's highest court.
Full Segment: John Paul Stevens
Extra: Stevens on the Death Penalty
Extra: Stevens on Gay Marriage
Extra: The Supreme Court Robing Room
We met Stevens at the Supreme Court this past summer as he prepared to retire at the age of 90. He was appointed by President Ford, but as a moderate Republican he ultimately became the leader of the court's liberal wing.
With nearly 35 years at the court, he is the third longest serving justice ever, and with history like that it's hard to know where to start.
But we picked the landmark case of 2000, which he thinks is one of the court's greatest blunders.
When asked what the court should have done with Bush v. Gore, Stevens told Pelley, "It should've denied the stay, period."
"And therefore let the recount go on in Florida?" Pelley asked.
"That's right," Stevens said.
Bush versus Gore: a month after Election Day, Florida was recounting ballots; Bush was ahead, but the recount might go either way.
So the Bush campaign asked the court for a stay, to stop the recount, on the grounds that the recount would cause irreparable harm to the nation. The night before the court heard the request, Stevens ran into another justice at a party.
"And I remember both of us saying to one another, 'Well, I guess we're gonna have to meet tomorrow on this, but that'll take us about ten minutes,' because it had obviously no merit to it. Because in order to get a stay in any situation, the applicant has to prove irreparable injury and there just obviously wasn't any irreparable injury to allowing a recount to go through because the worst that happens is you get a more accurate count of the votes. But much to our surprise, on the next day, the majority did decide to grant a stay," Stevens remembered.
Ultimately, the majority ruled that the recount wouldn't be fair because recount procedures were inconsistent across the state and couldn't be fixed before Florida's deadline.
"There were many people in this country who felt that the Supreme Court stole that election for President Bush. That was the accusation that was made," Pelley pointed out.
"It's unfortunate that that kind of accusation was made and that's one of the consequences of the decision that I think made it an unwise decision for the court to get involved in that particular issue," Stevens said.
Asked if the court's decision was a partisan one, Stevens said, "I wouldn't really say that. I don't question the good faith of the people, the justices with whom I disagreed. But I think they were profoundly wrong."
Between interviews, Stevens slipped the "60 Minutes" team into places the public never sees. In his chambers, we saw a shrine to the legends of Chicago sports and a picture of him swearing in the vice president.
It turned out he was wearing the same suit seen in the picture and he still had the oath in his pocket. "In fact, I didn't plan to bring this with me," Stevens said.
In a sense, Stevens was born into a world of crime and justice, the Chicago of the 1920s. He was a rich kid; his father built the largest hotel in the world. But it was the time of Al Capone and when Stevens was living in Chicago at the age of 12, gangsters came in and robbed the family at gunpoint.
"And we were all lined up and they threatened to kill, to shoot everybody with a sub-machine gun," he remembered.
As they faced a machine gun, a neighbor just happened to come to the door and the men fled.