Koch, who is not related to former New York mayor Ed Koch (Ed’s last name is pronounced kotch, while the billionaire’s is coke), may be familiar mostly to readers of Palm Beach Post social columns, Dan’s Papers in the Hamptons, and Chemical & Engineering News. He would pass unnoticed on any street in New York, even though he’s the second-richest man in the city, behind billionaire Mayor Michael Bloomberg. He is a fit-looking man, stands about 6 feet 6 inches tall, and has the kind of raucous laugh and aw-heck manner one finds in tourists right off the bus, even though he’s been a Manhattan resident for decades. “He’s one of those people who has pretty much remained in character,” says William Brody, president of Johns Hopkins. “There are people I’ve gone to school with, and you see them now, and they’re a different person from what they were. Then there are other people who, in spite of their success, are still kind of the same person and have the same values.”

Low-key as he may be, Koch is in fact the ninth-richest man in the U.S. He is $8 billion richer than that other Manhattan megabillionaire, George Soros, and could buy out his Park Avenue neighbor, financier Stephen Schwarzman, two times over, with a few billion bucks to spare. As well as the Park Avenue apartment, Koch has homes in Aspen; Southampton, New York; and Palm Beach, Florida. At his memorabilia-strewn office on Madison Avenue, there are samples from the impressive compendium of notable consumer products—everything from Dixie cups to Lycra spandex to Stainmaster spill-resistant carpet and Quilted Northern toilet paper—that makes his family’s company, Koch Industries, the biggest private concern in America. Its web of holdings is surprisingly low profile, despite its vast oil and gas interests, $110 billion in revenue, and 80,000 employees around the world.

Koch is in the traditional mold of the Midwestern or Texas mogul who achieves fame and glory in the big city. “I had more social standing than I could possibly handle,” he says, though he acknowledges that his recent gift, more than any other he’s made, has changed the game for him in his adopted hometown. He now makes more appearances in New York’s social columns, and this year his wife debuted on Vanity Fair’s international best-dressed list.

For as long as anyone can remember, the New York City Opera and the New York City Ballet have been the fine-arts version of squabbling children in a poorly designed suburban tract house. They jointly inhabit the elegant but aging State Theater, opened in Manhattan at the time of the 1964 World’s Fair for exclusive use by the ballet. It was designed to muffle the sound that dancers’ pointe shoes make as they move across the stage. When the opera settled into the building soon afterward, it was as if a thin layer of acoustical gauze had been taped over the mouths of the tenors, baritones, and mezzo-sopranos.

This year, the theater’s overseers launched a $200 million capital campaign, taking baby steps toward upgrading the outmoded physical plant and rectifying the theater’s structural issues. A consultant was hired, and some thought was given to the pricing of that most significant of modern-day philanthropy inducers—the naming gift.

In March, Schwarzman, chief executive of the Blackstone Group, gave $100 million to the New York Public Library for a long-planned reorganization of its midtown flagship. In return, he’ll have his name etched into the pillars at the front of the library’s main building on Fifth Avenue.

Schwarzman’s gift made it all the more routine and ordinary for the theater to rename itself after a single generous soul. Representatives of the State Theater approached Koch, a friend of Schwarzman’s, and told him of the pressing needs and the kind of money that would set things straight and—done. Koch agreed to donate $100 million, the exact sum that Schwarzman had given to the library. Thus was born the David H. Koch Theater.

Koch, in his office, explains the gift this way: “I could afford it.” He adds, “I probably go to the State Theater more than any other theater in the world.” Besides, he says, “I love the whole aspect of it—gorgeous music, fabulous sets,” he says. “And, of course, there are beautiful girls.”

However, it’s clear that a little image rehab wasn’t a terrible thing for Koch. Until this gift, his charity choices had kept him from the stratosphere of New York society, and he still must surely rank among the more vocally right-wing members of the overwhelmingly Democratic New York scene. He and his brother Charles, Koch Industries’ C.E.O., have bankrolled conservative causes for decades, and their father was a founding member of the John Birch Society, though he later distanced himself from the group. While it’s not unheard of in New York society to lean somewhat to the right—the Forbes family is no slouch in this regard—in Koch’s case, there’s perhaps a whiff of too much ardency in his family’s politics.

Some conspicuous contributions to the arts helps balance the scales. “My brother and I support the free market, and we believe strongly in the capitalistic system,” Koch explains. “A lot of people have criticized us for that. I’d like to be known in the future as someone who’s not just a wealthy, successful businessman but someone who really cared about the well-being of others—did his darnedest to be charitable and help others.”

Guilt, and a belated urge to gain entrance through the pearly gates, has been a dominant motive for charity since the first days of giving. “In many ways, it was tainted money,” notes Theodore Berger, a 35-year veteran of the New York arts scene who was the longtime executive director of the New York Foundation for the Arts. Indeed, one major penny-stock figure from the 1980s and 1990s who pleaded guilty to defrauding investors, Randolph Pace, was noted for his charitable giving and, through the late 1990s, his name was still emblazoned on a brass plaque at a major Manhattan religious institution.