They've met the transvestites and transsexuals, sat with them on bright drapes and cushions, and heard about sex work. They've inspected the lifesaving beauty salon, where the transvestites get reminders about condoms while flowers are woven into their hair. Now they're on their way to call on female sex workers, who will greet them with heartbreaking personal stories and an ear-breaking drum troupe. But just for the moment they are stuck in traffic. So Bill and Melinda Gates are talking about their favorite subject: the world's biggest challenge and what can be done.

The challenge is global health inequity. Only a fraction of the billions spent on medical research targets illnesses that affect poor countries, even though these same illnesses account for 90 percent of the world's disease burden. Each year some 10 million children die before their fifth birthday — that's almost as though the population of two Marylands were wiped out annually — and around three-quarters could be saved by basic medicines that already exist. Fixing the twin injustices of skewed research dollars and haphazard deployment is the mission of the foundation set up by Bill Gates and his wife, Melinda (who is a director of The Washington Post Co).

Until just a few years ago, history's most generous philanthropist was John D. Rockefeller, whose dominance of the oil industry in the late 19th century made him the Bill Gates of his time. But the Gateses have already given $28.8 billion, four times as much as Rockefeller measured in inflation-adjusted dollars, and whereas Rockefeller was two months shy of his 70th birthday when he made his first blockbuster donation, the Gateses have taken to philanthropy while still comparatively young. Yet it's not just the giving that's important. "We don't sit there and say, 'Hey, we gave away $9 billion,' " Bill Gates remarks in another conversation later. "We ask, 'How are we doing against malaria?' "

It's a question that engages the couple on multiple levels. Helping the world's poor is a moral mission, certainly: Gates describes his recent visit to a Bangladeshi project as "a religious experience." Battling disease is a scientific puzzle, equally, and Gates exudes a boyish delight in the new vaccine technologies that the foundation is backing. It's also a business challenge: How do you structure incentives for pharmaceutical companies to research diseases that kill people who have no purchasing power? And finally, most treacherously, the Gateses' philanthropy is a test of their most basic assumption: that brilliant intellects applied to urgent questions can improve the human lot.

Commentators, particularly conservative ones, love to bemoan the post-1960s relativism that is said to dominate our culture: "Truth" is relative; there is no right and wrong. But to listen to Gates is to realize how overblown this is. The people who have made the most impact on our society as inventors and creators of wealth believe passionately in truth and falsity, right answers and wrong answers, and in the Enlightenment faith that reason brings progress. Scientists necessarily believe in truth and reason, but so, too, do business leaders. Management — some would say, the science of management — is based on smart analysis of organizational psychology and consumer data. The Gateses revere Alfred P. Sloan Jr., the legendary boss of General Motors, who coined the anti-relativist injunction to "manage with the force of facts."

The Enlightenment rationalists were tested by revolutions and romanticism, then later by Freud's speculations on the irrational drivers of human conduct, and still later by modern economics, which explains why even rational individual behavior can sometimes lead to irrational societal outcomes. But if you visit health projects in India, you see how the Gateses have signed up for their very own test of the rationalist credo. It's one thing to finance health projects in villages. It's another to expect that villagers will make rational use of them.

Last Tuesday, Melinda Gates asked a slum dweller in Delhi what she had learned from local health workers, and the answer was "nothing." "The biggest challenge is the mind-set of the people," sighed the Indian doctor leading the tour. It's the same story in Uttar Pradesh, a bit east of Delhi, where the organizers of an immunization drive battle to reach villagers who don't want to be vaccinated, and even at the AIDS counseling centers in Chennai, where the challenge is to get the prostitutes to act rationally on medical advice. Sitting on those cushions with the Gateses, a transsexual with a blouse stretched over her broad back explained her confused feelings. She is lonely, she said simply. "It's out of love that you don't use condoms."

The Gateses are not the first people to fight global diseases — the Rockefeller Foundation battled malaria and tuberculosis years ago — and it's natural to ask whether they can succeed where others have not. But for every depressing moment during visits to health projects, there are a few uplifting ones.

At the slum in Delhi, a nurse estimates that the proportion of women who spurn medical advice has fallen from around nine in 10 to one in 10 since "link workers" were recruited from the community to change people's attitudes. In Uttar Pradesh the vaccine strategists marvel at how new syringes, designed to jam after one use so they don't spread viruses from patient to patient, have cut the incidence of painful abscesses and so boosted compliance.

Sometimes medicine is as elegant as computing: You invent a brilliant vaccine, and one shot protects a patient for the rest of his life. Most of the time medical advances are murkier, and yet the Enlightenment faith remains justified.

Though it never triumphed against malaria, the Rockefeller Foundation made great strides against hookworm and sponsored the creation of a vaccine for yellow fever that saved millions of lives. The Gates Foundation has already backed vaccination drives that have saved more than a million lives since 2000. With the advantages of modern science and huge financial resources, it will one day claim successes that go beyond even that.

Sebastian Mallaby is a member of The Washington Post's editorial page staff.