In 1996, Leslie Gordon, a biologist and a pediatrics resident at a hospital in Rhode Island, gave birth to a son, Sam. For a few months, Sam seemed healthy. But Gordon and her husband, a pediatric emergency physician named Scott Berns, soon started to feel that something was wrong. Sam's skin looked tight, shiny, and veiny. He lost hair and was hardly putting on any weight. Doctors couldn't explain why. "It was driving me crazy," Gordon said. "They'd say, 'Oh, he's small, but you guys are small, too.' " One evening, a colleague of Berns's, Monica Kleinman, came over for dinner and looked across the table at Sam. "Something just clicked in my mind," Kleinman told me. She'd seen features like Sam's in a textbook. A few days later, she told Berns that Sam might have a rare, fatal condition called progeria. "It was one of the hardest things I've ever had to do," Kleinman said. A specialist in New York confirmed the diagnosis. "Within a week, it was clear that there was nothing out there," Gordon told me. "No research. No treatments. No hope."

Progeria, which derives from the Greek for "early old age," was first described in the late nineteenth century. It is a disease of rapid, brutal aging that is thought to afflict fewer than one in every four million babies. By the time children with progeria enter their teen-age years, their bodies have effectively aged eight or nine decades. They have a distinctive appearance: small, wizened, and bald, with wrinkled skin, rigid arteries, stiff joints, and weak bones. Many die of heart attacks before their fifteenth birthday. There are estimated to be about twenty people living with the condition in the U.S. and several hundred in the world.

After Sam's diagnosis, Gordon withdrew from her residency and began to study progeria full time. She and Berns started a nonprofit, the Progeria Research Foundation, and recruited her sister, Audrey, to serve as its executive director. Gordon organized a meeting of several dozen scientists from various fields: genetics, orthopedics, immunology. "I scoured the earth for anyone who knew anything that might theoretically be useful for progeria," she said. She also assembled an international registry of dozens of progeria patients; Sam became friends with many of them. Berns, for his part, spent a year in the federal government, working as a senior adviser to the Secretary of Transportation as part of a White House Fellowship. At a work event one evening, he met Francis Collins, then the director of the National Human Genome Research Institute, which was sequencing a complete human genome for the first time. Berns told Collins about the diagnosis, not knowing whether he would recognize the condition. In fact, Collins had once cared for a patient diagnosed as having progeria.

Collins invited the family to his home. When they visited, he tossed a Frisbee with Sam, who was now four, in the back yard. He told them that he'd try to identify the genetic culprit. "That really epitomizes who Francis is," Gordon told me. "Here he is, in charge of the entire Human Genome Project, and at the same time he's looking for a gene for one kid." Collins soon tasked Maria Eriksson, a postdoc from Sweden who had recently joined his institute, to search for genes that might cause progeria. "Don't spend more than a year on this," he told her. "If it doesn't work out, we'll find something else for you to work on."

Eriksson studied the DNA of progeria patients along with that of their parents, thinking that the condition must be a recessive trait -- one that shows up in a child only when both parents have a particular genetic variation. Then, on a Saturday in 2002, about a year into her work, she called Collins. "I think I'm seeing something interesting," she told him. Children with progeria had a mutation that their parents didn't, she said. The condition didn't seem to be hereditary at all but, rather, to arise from a spontaneous mutation present at birth, a C replaced by a T on chromosome 1. The human genome contains billions of letters, enough to fill hundreds of books; the disease was apparently caused by the equivalent of a single typo.

Gordon and Collins held a press conference. "This discovery is likely to shed light on the normal process of aging," Collins announced. "It reverberates well beyond its application to progeria." In healthy cells, a protein called lamin A helps to shape and stabilize the nucleus. But the mutation produced an abnormal, toxic version of the protein called progerin, which warped the nucleus. At first, when cells affected by progeria divide, "they don't look so bad," Collins told me. "But, after seven or eight passes, they look really, really bad. The nuclei are totally messed up."

Meanwhile, Sam grew older. He developed heart disease at a young age, saw numerous doctors, and took a slew of medications. When he was a teen-ager, members of the Dave Matthews Band, which he loved, heard about his condition and invited him backstage. In high school, he played the snare drum in marching band; with its harness, the instrument weighed forty pounds, nearly as much as he did. (An engineer helped design a special apparatus so he could wear it.) He went to Disney World and, because his bones were so weak, cracked two ribs just sitting on a ride. He excelled in school and said that he wanted to be an inventor, "like Albert Einstein and Steve Jobs, combined."

Sam became the subject of an HBO documentary called "Life According to Sam," which was released in 2013. "I kind of deal with death a lot different than other people," he says in the movie. "I asked my mom about one of my friends, Ory, and my mom said, 'Oh, he passed away.' I'm, like, 'Oh, what about Stuart?' She's, like, 'Well, he passed away.' 'What about Ronnie?' 'He died, and Mierko died.' " A few months before his own death, at seventeen, he gave a TEDX talk that has been viewed more than a hundred million times. His life was a happy one, he told the audience, with the authority of someone preparing to depart it. Focus on what you can control, he said. Surround yourself with good people. Keep moving forward. And never miss a party if you can help it.

Kaylee Halko was born in 2003, in a small town in Ohio. She, too, had progeria. But her experience was different from Sam's in a crucial way: she was seven years younger. When Kaylee was four, the Progeria Research Foundation helped launch the first-ever clinical trial of a potential progeria drug, and she enrolled. Young patients took lonafarnib, which had originally been investigated as a cancer treatment. They gained weight, their hearing improved, and their arteries became more pliable. Lonafarnib interfered with a sort of chemical anchor that helps the lamin A protein target the nucleus. The drug didn't eliminate the abnormal protein, but it seemed to reduce the damage: children taking it ultimately lived two and a half years longer.

Kaylee's parents, Tim and Marla, also had three healthy boys. They tried to insure that Kaylee had as normal an upbringing as possible, despite the obvious challenges that she would face. As a child, she experienced instances of vicious bullying about her appearance. To this day, strangers sometimes stare and point. Others direct conversation solely toward her parents. "They talk to them like I'm not even there," Kaylee said. "They'll look down and say, 'Oh, how old is she?' "

A decade ago, Kaylee started posting short videos on Musical.ly, a social-media platform that eventually merged with TikTok. Her parents found out only after she became internet famous; she currently has half a million followers on TikTok and more than a hundred and fifty thousand on Instagram. I was surprised that, after receiving so much undesired attention, Kaylee would want to be so public online. In the comments, a small number of people sound much like those who bullied her when she was a child. But many are supportive to the point that they go after the haters on her behalf. "Kaylee's condition has allowed me to see, to feel, the good nature of people," Marla told me. "I don't think I would have seen that side of humanity as clearly if it wasn't for Kaylee."

Some of Kaylee's posts simply capture moments in her life: dancing in her living room, going to a concert, watching a sunset at the beach. Others try to give people a sense of what it's like to live with progeria. In one video, viewed more than thirty million times, she snips a single hair from her otherwise bald head. In another, a sombre ballad plays while she has a subtitled conversation with her younger self.

Young Kaylee asks about her life expectancy: "So did we beat the odds?"

Older Kaylee smiles gently. "Yeah, we're 21."

Then young Kaylee poses a question. Older Kaylee rolls her eyes. "No," she answers. "Our boobs did not grow."

Recently, Kaylee filmed a video response to an insensitive comment that someone left on one of her TikToks: "for a second I thought that was my grandma's hands." A screen grab of the remark appears onscreen. For a moment, it looks as though Kaylee, who is wearing a baggy yellow sweatshirt, is preparing to scold or make fun of the commenter. Then it becomes clear that someone else's hands are protruding from the sleeves, gesticulating madly. One of her college-age friends, hidden by the sweatshirt, is pretending that her hands are Kaylee's.

Kaylee tries to do a bit, feigning shock that anyone would think she has "old-lady hands." But her friend's hands move so wildly that she keeps breaking character and giggling. By the end of the video, she is laughing so hard that her eyes are full of tears.

In "Far from the Tree: Parents, Children, and the Search for Identity," the writer Andrew Solomon defines "vertical identities" as traits or norms that are passed from parents to children, and that therefore tend to be shared and celebrated: ethnicity, religion, language, customs. Horizontal identities, in contrast, are not shared. They may flow from spontaneous genetic mutations, personal experience, environmental factors, or sheer chance; they can include disease, disability, neurodivergence, and sexual orientation. "For people who must accept a fixed external reality, the only way forward is to adjust internal reality," Solomon writes. It takes effort to transform such traits from sources of stigma and misunderstanding to objects of tolerance or pride. Often, it takes community -- something that, in the case of progeria, had to be laboriously created. The Progeria Research Foundation is aware of only about a hundred and fifty people worldwide with the condition, and the population that has had it in all of human history probably numbers in the thousands. (Progeria is formally known as Hutchinson-Gilford progeria syndrome; there are other conditions that cause premature aging, but they present differently and arise from different genetic mutations.)

When Gordon created the foundation, she worked to build connections between progeria patients and their families. She now hosts Zoom calls that are attended by a quarter of known progeria patients, who in turn sometimes organize meetups around the world. Through the foundation, Kaylee befriended three others; they called themselves the "P dawgs." In a remarkable coincidence, one lived just a few miles away, so the group often convened in Ohio. "It was special because we could really relate," Kaylee said. "The progressiveness of the disease. The relentlessness of it." Over time, all of the other P dawgs died. Kaylee, who went to church intermittently as a girl, has become increasingly religious, and she told me that she expects to see her friends again. "Death is not something I want to happen," she said. "But it doesn't scare me, either."

Donations to the Progeria Research Foundation -- from individuals, grants, fund-raising events, and campaigns by volunteers -- eventually surpassed two million dollars a year. About a decade ago, Gordon directed some of the organization's funds to a South Korean researcher named Bum-Joon Park, who was studying how the abnormal lamin A protein attaches to the nucleus of a cell. He thought he'd identified a molecule, progerinin, that could block its effect through a different mechanism than lonafarnib. In 2021, his team published a paper showing that progerinin could reduce concentrations of the toxic protein in cells and extend the life spans of mice with progeria. In Phase I safety trials conducted with healthy adults, the drug was well tolerated, and the F.D.A. green-lighted a Phase II trial, which will measure how well it works in progeria patients. Gordon is one of its primary investigators. Monica Kleinman, who first diagnosed Gordon's son as having progeria, is another.

In January, Kaylee travelled to Boston for the start of the trial. On a frigid evening, I met her and her mom at a sports bar near Fenway Park. Kaylee's legs dangled from her chair; a compact wheelchair and a white Labrador were nearby. After I greeted them, the dog nuzzled my leg and sat on my foot.

"Sorry," Kaylee said. "That's Iris. We're still training her." Her voice was quiet and high-pitched, and I had to lean in to hear her over the din of the bar. She ordered chicken tenders from the kids' menu.