Greenland sharks are among nature’s least elegant inventions. Lumpish, with stunted pectoral fins that they use for ponderously slow swimming in cold and dark Arctic waters, they have blunt snouts and gaping mouths that give them an unfortunate, dull-witted appearance. Many live with worm-like parasites that dangle repulsively from their corneas. They belong, appropriately enough, to the family Squalidae, and appear as willing to gorge on fresh halibut as on rotting polar-bear carcasses. Once widely hunted for their liver oil, today they are considered bycatch. For some fishermen, a biologist recently told me, netting a Greenland shark is about as welcome as stepping in dog poop.

And yet the species has an undeniable magnetism. It is among the world’s largest predatory sharks, growing up to eighteen feet in length, but also among its most elusive. Its life history is a black box, one that researchers have spent decades trying in vain to peer inside. Where do Greenland sharks mate? What is their global range and population structure? And, most enticing of all, how long do they live? A study begun in the nineteen-thirties suggested that the species’ lifespan might well be extraordinary, based on the slow growth rate of a single shark that a scientist was lucky enough to catch twice. Verifying this, however, proved nearly impossible. To determine age in other sharks, biologists count the growth rings on their fin spines and vertebrae. But Greenland sharks have no hard tissues in their bodies; even their vertebrae are soft. The longevity question seemed unanswerable.

The mystery might have lingered were it not for the work of three Danish scientists—a physicist named Jan Heinemeier and two marine biologists, John Fleng Steffensen and Julius Nielsen. Nine years ago, Heinemeier and four of his colleagues published a paper on lens crystallines, a class of proteins found in the human eye. Like all organic molecules, crystallines contain carbon, including trace amounts of the radioactive isotope carbon-14. Unlike other proteins, which undergo constant recycling and replenishment, crystallines remain stable throughout a person’s life; they are envelopes sealed at birth, their contents an artifact from the womb. And, if crystallines are the envelopes, then carbon-14 is the postmark. The isotope has always occurred naturally on Earth, formed wherever incoming cosmic rays strike the atmosphere, but some of the current supply also comes from nuclear-weapons tests. The level fluctuates from year to year, and that means that every given time period has its own carbon-14 signature. (There was a particularly huge spike, called the bomb pulse, in the nuke-happy heyday of the fifties and sixties.) Experimenting on cadavers’ lenses, Heinemeier found that he could measure how much carbon-14 they contained and use it to determine the deceased’s date of birth.

Heinemeier’s paper made no mention of Greenland sharks. He and his co-authors did note, however, that their lens technique might be useful in the field of forensics. Not long after the study was published, Heinemeier received a request from police in Germany. They needed his help cracking an unusual case. In the city of Wenden, near Cologne, a teen-ager had opened his family’s freezer in search of a snack and discovered the bodies of three infant girls, wrapped in plastic. The investigators suspected the boy’s mother of having killed the children, but she denied it. While the victims’ ages were obvious—all were clearly newborns—the police had no way of knowing when the murders had taken place. Heinemeir analyzed the infants’ lenses and came up with remarkably precise estimates. Two, he found, had been born in the second half of the nineteen-eighties, the third between 2003 and 2007. Although one of the murders fell outside Germany’s two-decade statute of limitations on manslaughter, the others were prosecutable. The mother was ultimately sentenced to four years in prison.

In 2009, Heinemeier received another request, this time from Steffensen, who had recently travelled to Greenland and confronted the longevity puzzle. Was there a way, Steffensen asked, to use the sharks’ soft vertebrae for carbon dating? Heinemeier told him about his recent breakthrough in the murder case and suggested that Steffensen return to Greenland and bring back some lenses. But there was a problem. Though sharks do possess crystallines in their eyes, acquiring enough samples for a rigorous study was an expensive and logistically tricky proposition; at first, Steffensen managed to get just two. Hearing this at one of Steffensen’s lectures, Nielsen, a young biology student, proposed a solution. He had spent the summer in Greenland, working on research vessels for the Greenland Institute of Natural Resources, and it occurred to him that the trawlers’ unwanted bycatch was a biological goldmine. Over the next five years, as Nielsen completed a master’s and then a doctorate at the University of Copenhagen, he and a group of research trawlers and local fishermen harvested eyes from twenty-eight Greenland sharks.

Nielsen and his collaborators published their results in August of last year. Using Heinemeier’s method, they found that the smallest of the sharks they caught—those around seven feet long—were born after the bomb pulse, while the largest animals were born well before it. With the help of a mathematical model that linked size with age, they estimated that one sixteen-foot female was at least two hundred and seventy-two years old, and possibly as much as five hundred and twelve years old. Because it is difficult to establish background carbon-14 levels in the ocean, and because Nielsen and his colleagues didn’t know which part of the ocean the sharks had been born in, the figure was inexact. Still, it firmly established Greenland sharks as the longest-living vertebrates on Earth. In theory, the biggest ones could be nearly six centuries old.

The question now is how the sharks do it. Increasingly, scientists are searching the natural world for the genetic and behavioral mechanisms that endow creatures with their special abilities—that make elephants virtually immune to cancer, say, or axolotls capable of regenerating a lost limb. There may be Greenland sharks alive today that were born before Christopher Columbus; the species is not even thought to reach sexual maturity until around a hundred and fifty years of age. Why? The answer likely has to do with a very slow metabolism and the cold waters that they inhabit. But for now, Nielsen said, it’s yet another mystery. “I’m just the messenger on this,” he told me. “I have no idea.”