Like a man in the first draft of a limerick, Tennys Sandgren is a tennis player from Tennessee. Last winter, after scraping his way onto the list of the top hundred professional players, he secured a spot at the Australian Open. He advanced to the quarter-finals. At a press conference, he responded happily to questions about his unexpected achievement. Then someone asked him about his Twitter feed. Sandgren had tweeted, retweeted, or “liked” disparaging remarks about Muslims and gays; he had highlighted an article suggesting that recent migration into Europe could be described as “Operation European Population Replacement”; he had called Marx’s ideas worse than Hitler’s. He had also promoted the Pizzagate conspiracy theory, which accuses Hillary Clinton of human trafficking. Sandgren told reporters that, though he didn’t support the alt-right, he did find “some of the content interesting.”

This became a small news story. Sandgren then lost his quarter-final, and, at the subsequent press conference, he read a statement condemning the media’s willingness to “turn neighbor against neighbor.” Later that day, he was surprised to receive a supportive message from Glenn Greenwald, the journalist, whom he followed on Twitter. (Sandgren also followed Roger Federer, Peter Thiel, and Paul Joseph Watson, of Infowars.)

Greenwald, a former lawyer who, in 2013, was one of the reporters for a Pulitzer Prize-winning series in the Guardian on Edward Snowden’s disclosures about the National Security Agency, is a longtime critic, from the left, of centrist and liberal policymakers and pundits. During the past two years, he has further exiled himself from the mainstream American left by responding with skepticism and disdain to reports of Russian government interference in the 2016 Presidential election. On Twitter, where he has nearly a million followers, and at the Intercept, the news Web site that he co-founded five years ago, and as a frequent guest on “Democracy Now!,” the daily progressive radio and TV broadcast, Greenwald has argued that the available evidence concerning Russian activity has indicated nothing especially untoward; he has declared that those who claim otherwise are in denial about the ineptitude of the Democrats and of Hillary Clinton, and are sometimes prone to McCarthyite hysteria. These arguments, underpinned by a distaste for banal political opinions and a profound distrust of American institutions—including the C.I.A., the F.B.I., and Rachel Maddow—have put an end to his appearances on MSNBC, where he considers himself now banned, but they have given him a place on Tucker Carlson’s show, on Fox News, and in Tennys Sandgren’s Twitter feed. Greenwald is also a tennis fan—and a regular, sweary player. He recently began working on a documentary about his adolescent fascination with Martina Navratilova.

Sandgren told me that Greenwald’s message had celebrated his success in the tournament, adding, “He knows quite a lot about tennis—enough to know it was the result of my lifetime. And he wanted to encourage me in that particular moment to continue to learn, to continue to grow, and to remember to be kind—to yourself and to your critics.”

Greenwald has experienced his own share of criticism, but is not known for showing kindness to critics. Michael Hayden, the former director of the C.I.A. and the N.S.A., has written that debating him was like looking “the devil in the eye.” Leading American progressives—speaking off the record, and apologizing for what they describe as cowardice—call Greenwald a bully and a troll. One told me that “he makes everything war.” The spouse of one of Greenwald’s friends visualizes him as the angry emoji. On Twitter, he has little use for agree-to-disagree courtesies, or humor: he presses on. More than one tweet has started with “No, you idiot.” He’ll tweet “Go fuck yourself” to a user with twenty or so followers. A few years ago, Greenwald had a Twitter disagreement with Imani Gandy, a legal journalist, who tweets as @AngryBlackLady; another Twitter user, in support of Greenwald, proposed to Gandy that “Obama could rape a nun live on NBC and you’d say we weren’t seeing what we were seeing.” Greenwald replied, “No—she’d say it was justified & noble—that he only did it to teach us about the evils of rape.”

Sandgren thanked Greenwald for his message, and the next day tweeted an apology for an old post in which he’d described his “eyes bleeding” after visiting a gay club. A month later, in February, Sandgren played in Brazil, at the Rio Open. Greenwald lives in Rio de Janeiro with his husband, David Miranda, their two sons, and two dozen dogs, former strays; Sandgren offered Greenwald and his children tickets, and they all met at the venue. Video of one match shows Greenwald, in the front row, applauding every point with dad-outing gusto. He and Sandgren subsequently formed what Greenwald called a “very intense” friendship.

Sandgren described their trade in tennis and politics. “Glenn asks me what it’s like to return Ivo Karlović’s serve—a six-foot-eleven guy—and then I ask him what’s going on in the political world,” he said. “Maybe he respects the fact that I’m very interested in learning.” Greenwald has sent him YouTube links to speeches he has made. Since meeting Greenwald, Sandgren has also watched Oliver Stone’s film “Snowden,” in which Greenwald is played by Zachary Quinto, the actor best known for his role in the “Star Trek” movies. Sandgren recalled thinking, “They got Spock to play Glenn? That’s fitting: very interested in factual information, truth and reason and logic. And, if he does get a little frustrated or angry, then look out.”

Greenwald told me about his friendship with Sandgren during one of several recent conversations at his home. We sat in a high-ceilinged room with a baby grand piano; the space echoed with the sound of dogs barking—and with the sound of Greenwald responding to the barking by shouting, “The fuck?”

Greenwald, who is fifty-one, and was brought up in Florida, has lived largely in Rio for thirteen years. For most of that time, he and Miranda, a city-council member, rented a home on a hillside above the city, surrounded by forest and monkeys. Last year, they moved to a more residential neighborhood. The house is in a baronial-modernist style, and built around a forty-foot-tall boulder that feels like the work of a sculptor tackling Freudian themes: it exists partly indoors and partly out. Greenwald has a pool, and his street is gated. A thousand feet away is the crush of Rocinha, Brazil’s largest favela, from which Greenwald often hears gunfire.

He seemed happy. He was wearing shorts and flip-flops; he has a soft handshake and an easy, teasing manner that he knows will likely confound people who expect the sustained contentiousness that he employs online and on TV. (On cable news shows, Greenwald draws his lower lip over his bottom teeth, blinks slowly, and seems able to state his position on the Espionage Act of 1917 while inhaling.) Greenwald, though untroubled about being thought relentless, told me that he was “actually trying to become less acerbic, less gratuitously combative” in public debates. He recently became attached to the idea of mindfulness, and he keeps a Buddha and a metal infinity loop on a shelf behind the sofa; a room upstairs is used only for meditation. He has turned to religious and mystical reading, and has reflected that, in middle age, one’s mood “is more about integrating with the world.”