One Saturday in August, Rhonda Roland Shearer, the widow of the paleontologist Stephen Jay Gould, was on her way back from the park with her daughter and two grandsons. They made a stop, as they often do, at the fire station on Sixth and Houston, so that the boys could check out the fire trucks. Joey Graffagnino showed the kids around the truck while Shearer chatted with another firefighter, Bobby Beddia. Shearer said recently, “He mentioned that he was very lucky, because he was fifty-three, so this year he got to experience living in his ‘birth year.’ ”

Shearer, an artist who has done some work with fractal geometry and runs a group called Art Science Research Laboratory, asked Beddia what he meant. He explained that he was born in 1953 (in September), so his age matched the last two digits of the year in which he was born: a once-in-a-lifetime occurrence. “He had this glow that I recognized from seeing the faces of mathematicians when they’ve discovered a beautiful idea,” Shearer said. “I told him, ‘You should really contact a mathematician to work out a proof.’ As I was saying that, I was secretly planning to explore it myself and surprise him.”

Shearer and her family went to lunch. A few hours later, she got a call from a friend: a seven-alarm fire had broken out in the vacant Deutsche Bank Building, near Ground Zero, and two firemen—Graffagnino and Beddia—had been killed. Shearer decided to continue investigating Beddia’s observation, as a tribute. She called her friend Richard Brandt, a retired N.Y.U. physicist. He pointed out something that would be obvious to mathematicians: the “birth year” can happen only in an even-numbered year—in Beddia’s case, the year beginning in 2006, or, in Brandt’s case, 1982, the year when he turned forty-one (since he was born in ’41). “It’s simple, but the originality is to recognize that it’s happening,” Brandt said the other day.

Shearer told the story to Barry Cipra, a freelance math writer in Minnesota. “When I described it to my wife, she immediately thought of the champagne birthday—when you reach the age of the day of the month you were born,” Cipra said. “But nobody I’ve run this by has ever heard of this notion. What’s sort of great about it is that it will happen to everybody if you live long enough. If you were born in 2000, it happens instantaneously. The people who were born at the end of the century have to take care of themselves.”

Cipra wrote a short paper on the idea, which he calls the “Beddian year.” “It struck me that, at any given moment, the world consists of two types of people: those who have reached their ‘Beddian’ age, and those who haven’t,” Cipra writes. “I got to wondering which group is larger.” That question is really demographic—it depends on generational shifts—but he boils it down to a respectably difficult math problem: “What is the range of ages of people who currently (in 2007) are pre-Beddian?” A hint: they don’t fall into a single age group. For example, in 2008, Shearer, born in ’54, and her grandson Fionn, born in ’04, will share the same Beddian year. (He’ll be four, and she’ll be fifty-four.)

It took Cipra the better part of a week to come up with the complete answer—one that describes, for any given year, the ranges of people who are pre-Beddian. For those who can make sense of it:

Beddia Theorem: In any odd-numbered year, there are exactly 50 pre-Beddian ages. In any even-numbered year, there are exactly 49 pre-Beddian ages. Moreover, with three exceptions, these ages consist of two separate spans. The exceptions are 1998 (or any year ending in ’98), for which the pre-Beddian ages comprise the single span 0-48, 1999 (or any year ending in ’99), for which they comprise the single span 0-49, and 2000 (or any year ending in ’00), for which they comprise the single span 1-49.

The other night at the fire station, some friends of Beddia’s confirmed that he was a numbers guy: he liked poker and golf; when he played roulette, he always played twenty-four—the number of his engine company. “Let me tell you what this means,” Lieutenant Ray O’Hanlon said, slipping off his boots. “It means that if you were talking to Bobby in a bar, and suddenly it came up ‘How old are you?’ and Bobby says, ‘I’m the same age as the year I was born’—now you have to talk to him more. That was Bobby.” O’Hanlon continued, “Trust me, it wasn’t a math quandary. It was a . . . would a pickup line be the wrong answer?” ♦