Next, he moved to New York to work as an engineer and then started at Koch Industries in 1970, in sales in the equipment-manufacturing division. By then, Fred had died, and ownership of the family holdings had passed to his sons in a uniquely structured transaction, one that made philanthropy not merely a nicety but a business obligation.

Before his death, Fred Koch had set up his estate so that his business holdings would be transferred to his sons at a low tax rate. A portion of their inheritance was in the form of stock that spun off an annual dividend that had to be donated to charity every year. His aim was to have his sons avoid inheritance taxes that would force them to sell the company. But it also meant that the sons had to sacrifice their dividends. “So for 20 years, I had to give away all that income,” says Koch, “and I sort of got into it.” The dividend-donation obligation expired in 1986, but Koch continued to donate a great deal of money out of habit.

In time, his family’s business became the largest private concern in the U.S., if not the world. “My joke is that we’re the biggest company you’ve never heard of,” Koch says.

Almost never. Koch Industries has had numerous legal scraps over the years. In 2000, the company was indicted on 97 counts of environmental violations at a refinery in Texas. (After George W. Bush took office, 90 of the counts were dropped, and the company pleaded guilty to one count of falsifying a document.)

But what really grabbed headlines was a massive fight that set brother against brother, with David and his older brother Charles forming an alliance against his twin brother, Bill, and the eldest brother, Fred, who had been disinherited by their father. Though Bill’s efforts to gain control of the company failed, the soap opera of sheer nastiness dragged on for more than 20 years. Bill claimed, among other things, that the company was mismanaged, that he was cheated out of $1 billion, and that Koch Industries had stolen $170 million from oil producers in the 1980s. Though the litigation eventually ended, it left many major businesspeople with a sour taste about the family. To East Coast elites, it seemed more People’s Court than Masterpiece Theater.

Charles and David retained control of the company, with Charles becoming C.E.O. and David executive vice president. David, who winces at the memory of all the drama, remarks that he doesn’t have much to say about it except that “it happened, and it was very unfortunate, and it was resolved.”

He is, however, glad to record the unlikely coda to the ferocious family feud. A few weeks after his first child, David Jr., was enrolled in preschool in Palm Beach, Julia picked him up there and saw he had his arm around another boy. “That’s my best friend, William,” David Jr. said. The other child turned out to be William Koch Jr. A reconciliation between the boys’ fathers followed, and when Bill remarried in 2005, his twin brother, David, was his best man.

David Koch is passionate about cancer research, which is not surprising given that the disease has become one of the major factors in his life. Peter Scardino, chairman of the department of surgery at Memorial Sloan-Kettering Cancer Center in New York, another recipient of Koch’s largesse, likens Koch’s involvement to the input of an informed patient who has learned the details of his disease but knows to defer to his doctors. “What you get from David is not ‘I’ll fund this if it’s good for me,’ but ‘How is this different from what someone else is doing?’ ”

When Koch’s cancer was first revealed, it fell hard on him. “When I found out about it, my numbers were really bad. I thought I was going to live maybe a year. It’s horrifying,” Koch recalls. His blood counts are now back to normal, and he is feeling great. He says, “I found out about 16 years ago, and I look pretty healthy still, don’t I?” But he is anything but sanguine about his prospects. Indeed, he married Julia after successful surgery, but then the cancer came back. “Eventually the therapies I’m being treated with will cease to work, and then I’ll need another treatment,” he says. “I’ve been busy funding prostate-cancer research at many different institutions around the country. A number of them are showing great promise in clinical trials, so I’m optimistic that in a few years, when my treatment starts to fail, I’ll have additional things ready to keep me going.”

So he must give and give more. Most of his donations have been made directly: In addition to the $125 million he gave to M.I.T. for a cancer center, he donated $18 million to the M.D. Anderson Cancer Center in Houston to establish the David Koch Center for Applied Research in Genitourinary Cancers and $40 million to Sloan-Kettering—just a fraction for prostate research, Scardino points out—as well as making gifts to other institutions over the years.

The harsh fact is that he is in a race against time. Koch married Julia in 1996, when he was 56. The youngest of their children is a toddler. “A lot of people have nine lives; I have about 90,” Koch says.