The phone rang last year as soon as the Senate confirmed Elena Kagan as the Supreme Court’s newest justice.

Chief Justice John G. Roberts Jr. said he wanted to be the first to congratulate and welcome Kagan to the court, she recalled at a recent event at the Aspen Institute. And Roberts told her one other thing: that the two were going to be serving together for the next 25 years.

“Only 25?” Kagan responded.

The potential of a lifetime of duels involving the liberal Kagan and conservative Roberts — the two youngest justices — is one of the intriguing storylines to emerge from Kagan’s first year on the court. A first term provides a limited perspective, but as the court opens its new session early next month, Kagan’s performance last year offered clear signals about a woman who came to the bench as something of a mystery.

The first justice in more than 40 years who had never been a judge, Kagan established herself quickly as a forceful and insightful questioner on a court filled with strong personalities.

While Kagan’s writings as an academic did not suggest a strong legal philosophy, her opinions and dissents from the bench have shown a conversational, confident writer, at times as sarcastic and cutting as a veteran.

And liberals who worried that she would not shore up the court’s left flank have so far found their concerns unfounded. The man she replaced, Justice John Paul Stevens, said he can think of only a couple of cases where she voted differently than he would have. And the senior liberal justice, Ruth Bader Ginsburg, seems especially taken with her. “She has already shown her talent as an incisive questioner at oral argument and a writer of eminently readable opinions,” Ginsburg said in a speech this summer.

Richard Lazarus, a Harvard law professor who closely follows the court, said the “most striking thing about the term, especially since she had never been a judge, was that she hit the ground running and seemed to fit right in at the court.”

Certainly, Kagan has reached out to her new colleagues: She’s been skeet-shooting with Antonin Scalia, to the opera with Ginsburg, to dinner with Sonia Sotomayor, shared the stage at a Harvard Law School reunion with Anthony M. Kennedy and this summer showed up at a New York University law school conference in Buenos Aires with Clarence Thomas and his wife, Virginia.

Beyond the court, the never-married Kagan moves in a social circle of old friends from law school and her stint in the Clinton White House.

“She doesn’t go to Washington parties where’s she’s invited as ‘Justice’ Elena Kagan,” said her friend Ron Klain, who served as chief of staff to Vice Presidents Biden and Gore.

On the other hand, Klain said, she “has not stopped coming to social events with friends, as she always has, before she was a justice.” Recently, that included Klain’s birthday party, where a jeans-wearing Kagan was unknown to about a third of the guests, he estimates.

At 51, Kagan is the youngest of the justices and at times displays a less-formal demeanor and style. During the court’s arguments over the sale of violent video games, she casually mentioned the “iconic” game Mortal Kombat, “which I’m sure half of the clerks who work for us spent considerable amounts of time in their adolescence playing.”

Before Kagan, one would have looked in vain through hundreds of years of Supreme Court opinions for the phrase “loosey-goosey.”

As the junior justice, she was assigned to write opinions in her share of forgettable cases — she told those in the courtroom one day that her summary of a decision would be best followed by a person who had a law degree and several cups of coffee. But she made her views clear elsewhere.

In two cases, she wrote powerful dissents that displayed a strong opposition to government efforts that aid religion and a lengthy defense of campaign finance laws enacted to remove corruption from politics.

In both, she represented the liberal side of the court. She received plaudits for her crisp writing and uncompromising language, and a few questions about whether she was too brash for a rookie.

Kagan declined an interview request for this story, but she told her questioner at the Aspen event that she viewed writing opinions the same way she approached teaching as a law professor.

The goal is to “figure out how to communicate complicated ideas to people who know a lot less than you do about a certain subject,” Kagan said, adding she looks for “vivid ways of explaining that will stick with people.”

So she fills her opinions and dissents with examples and comparisons. “Imagine two states, each plagued by a corrupt political system,” she wrote in her campaign finance dissent.

She also was tough and sarcastic in her dissents; Cornell law professor Michael Dorf called it “channeling her inner-Scalia,” referring to the senior justice’s famously acid-tipped pen. Dorf thought it was at times the wrong tone for Kagan in her first year. “It struck me as her saying, ‘Hey, I can be one of the boys.’ ” he said. But he acknowledges that others disagree.

For instance, in the campaign finance dissent, she said her colleagues on the other side thought that they had found a smoking gun. “But the only smoke here is the majority’s, and it is the kind that goes with mirrors,” Kagan wrote.

When her interviewer at Aspen read that line, the audience laughed and applauded. Kagan said: “You know, listening to that, I’m not sure I would have written it that way again.”

The majority view in that case was written by Roberts. And when Kagan chose to summarize her dissent from the bench — a rare move even rarer for a rookie — their point-by-point arguments resembled the opening round between two people identified early in their careers for their potential.

Roberts and Kagan are something of a pair: ideological opposites who possess similar Ivy League educations and intellects; potential coalition builders on a splintered court and writers who seem to strive to explain their jurisprudence to those beyond the walls of the Supreme Court.

“I think it fair to say that they are doppelgangers of a sort,” said former acting solicitor general Neal Katyal, who was Kagan’s deputy and has argued before Roberts.

He calls them “two of the most hard-working people in a town of hard workers. They take the job, and themselves and each other, very seriously.”

Roberts has publicly praised Kagan and Kagan routinely says the chief justice, who as a lawyer argued frequently before the court, “may have been the best oral advocate in the history of the Supreme Court.”

Her friend Klain said that while her ability to turn a phrase may remind some people of Scalia, her opinions read more like those of Roberts: “crisp and clear, with a well-articulated argument for the opinion’s point of view.”

“I think we will see them going at it for quite some time,” Dorf said, not with “personal nastiness” but “intellectual grappling.”

Lazarus said it is “in her blood” for Kagan to want to be a leader on the court.

Kagan said that the most valuable preparation for being on the court was the year she spent as solicitor general, which is the government’s chief lawyer before the court.

“You’re not deciding the cases but you’re focused all the time on the Supreme Court,” she said at the Aspen Institute gathering. “Your job is to try to figure out how to persuade nine Supreme Court justices to take a particular position. And now my job is to figure out how to persuade eight.”

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