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"We didn't have a particularly good science programme at school," she says. "I'll pick up something on the immune system and say to Bill, 'I have just read the following about white blood cells I don't really understand,' and Bill loves to teach and we'll have a long discussion about it . .  It's hard to discuss grants for malarial medicine if I don't understand the life cycle of the mosquito. It's not just about signing the cheques." And in the absence of an HIV vaccine, she can talk microbicides — vaginal creams and gels —  without conceding a blush; she is perfectly at ease discussing with prostitutes about how men pay more for sex without condoms.

The pace of their giving has moved from a dawdle to a sprint, sparked by Bill Gates's visit to Soweto, by Melinda's soaring evangelism and by the death of his mother, Mary, in 1994. A woman of high standards, adored by her son, she once wrote to him that "to whom much is given much is expected", which, says her daughter-in-law, has been the foundation's guiding principle. It has been observed, maybe unfairly, that the generosity bloomed after Microsoft was found guilty in 2001 of abusing its monopoly power to "exterminate" competitors.

The foundation started small in 1997, with requests for money assessed and cheques signed on the kitchen table of the widowed Bill Gates Sr, who had volunteered to help. It was officially launched in 2000, bearing the name of a woman for whom the "deal" of her marriage had been to maintain a low profile. But that was before she was seized with the desire to promote her causes. The mystery girl became the seasoned advocate who argues her case at the highest levels. Sure, she admits, it was easier to be around Seattle with her kids before she began trailblazing, but the city is respectful; she and Bill stand in line for a movie occasionally, take the children to play in public parks. "It was natural that the foundation's title would include my name," she says, "and I don't even remember if there was a discussion.

I wanted to take my involvement slowly . . . but I have become so passionate about the foundation that it didn't feel right any more for me not to speak out." Is being Mrs Gates ever oppressive? She seems perplexed by the idea. "I knew what I was getting into when I married him. One of the nice things about the foundation is that it allows us to walk side by side and say, 'This isn't about Bill, this isn't about Melinda: this is about us as a couple trying to change the world.'"

It is strange, a month after Britain's bitter general election, to hear one's own political leaders hailed as messiahs of compassion but, maybe privately contrasting her own government (which spends half as much on combating malaria in a year as it spends on a day in Iraq), Melinda talks of Tony and Gordon "leading the world" with their G8 priorities and the Commission for Africa. With its propensity to sap optimism as disaster succeeds catastrophe, Africa is not only the crucible of their efforts but also a metaphor for the immensity of the task. They harnessed technology to change the world once; now they believe that the science of the next decade will be "transformative" for the shoeless millions.

The signs are good. They have made progress in developing a safe, cheap drug for visceral leishmaniasis (a malaria-like disease), and a single vaccine for pneumonia that could reduce all African deaths by 15%, as well as the first new drug for sleeping sickness in 50 years. Their view is that, when steeped in science, whose business is achieving the impossible, you cannot be anything other than optimistic. Mozambique is hosting a Gates-sponsored trial for a vaccine against malaria, which kills an African child every 30 seconds. "We are very passionate about science," she enthuses, "because we see what it has done for the developed world over the past century. We say yes, there is this big problem called malaria, and we are working on a vaccine but meanwhile, has any country in Africa tried to apply all the available tools — insecticide-treated bed nets, the right insecticides in the home, the right malarial medicines? No country had tried it." As a result, in May she announced a $35m partnership with the government of Zambia to try just such an experiment. The target is to reach 85% of the population and cut malaria deaths by 75% in three years.

Onto a land of biblical plague, pestilence and sanitation levels, the Gateses plan to shine the white-hot light of science, finding vaccines, creating market incentives for pharmaceutical companies to produce and sell them cheaply, pooling buyers to create the largest markets, underwriting research costs in return for cut-price deals for poor nations. In so doing they have re-energised Third World preventive medicine, which — with no market incentives — had stalled in the 1990s; the goal is deliverable technology, cheap drugs, vaccines you only give once. The holy grail is the HIV vaccine; Gordon Brown's prediction of a breakthrough by 2012 is not shared by the foundation. Nothing better illustrates their business-savvy approach than the creation of the HIV Vaccine Enterprise,  which co-ordinates research and is set to receive $400m in new funds. Scientific research is usually a piecemeal affair, but business knows the importance of co-ordinated management, of accepting failure and moving on.

"Aids is such a huge problem," she says. "We said, 'Okay, people are trying for a vaccine but shouldn't we be working with the scientific community to establish a standard?' So as each scientist goes down their own path, everyone is learning from that. It's not unlike solving a technology problem at Microsoft. When you are building an operating system, you had better be sure everyone's co-ordinated and the code they are writing all fits together."

Melinda Gates is a woman desperate to learn, open enough to admit the lessons the foundation has taken on board; to pick its battles; to understand that organisational and training hold-ups slow progress (in Botswana's Aids programme, it could take eight or nine years to spend the donated $100m). She has also seen that improvements like roads may allow women to reach antenatal services but also bring Aids to remote villages. Until her children are older, her trips are limited to one a year; she visits unannounced and laughs that, while the people are happy with her patronage, they also complain to her they don't have toothbrushes. Sometimes the travelling is heartbreaking.

"You have to let yourself go and be part of it and feel it. But I have to stand back and say yes, it is very painful to leave this orphanage, but it's not just about these 20 children, it's about the 10m orphans in Africa because of Aids. And you bet I've thought about taking a baby home."

She raises an eyebrow at her own former ignorance of the developing world. "We didn't want to know how bad it was in these countries. I would say 9/11 opened people's eyes to outside. If the people in need lived next door to me and you, we would all look out on our back yard and say, 'My gosh, that person is starving over there — how do I help?'" Do we consider African lives less worthy than our own? "Bill and I believe one life is worth no more or less than any other. That issue of equity is what the foundation stands for."

As with all successful enterprises, there are personal bonuses for top results — not those, in Melinda Gates's case, of the cradle Catholic looking to secure a better place in heaven. Her charity fulfils her love of cut and thrust, effecting change, meeting deadlines, pinpointing targets; its remit might sound touchy-feely but it is her chance to refocus corporate instincts that she still employs in her position on the boards of The Washington Post and drugstore.com. "I always knew I wouldn't just be raising the children, that I'd take on other passions. For us the foundation is not about generosity, it's about helping to change people's lives." And about the personal satisfaction that would have been delivered by a business career? "Absolutely!" How does it compare with the thrills of early Microsoft? "Early on, you knew you were going to change people's lives and we were all charging up the hill to make this great software, which was a ton of fun. I was working with talented, smart people at Microsoft, and in the foundation we are working with incredible scientists to make a difference in Aids or malaria. It's equally stimulating."

Has she always been so driven? "My parents would say yes," she laughs. "When Bill's mom met my mom, she tried to find out whether I was having that effect on him, and my mom said, 'No, it's him affecting Melinda.' I was goal-oriented from seventh grade." In ways unconnected with her wealth, Melinda Gates is an extraordinary woman: a marathon runner, a fitness fanatic who can be spotted in a kayak on Lake Washington at weekends, a scarily organised achiever who says she and Bill have meetings to audit their home, business and charitable lives, and set six-monthly goals for family and foundation.

Parenthood has helped her connect with the foundation's work; it is her only shared reference with the African prostitutes or enslaved Indian homeworkers she meets. Her children, given the way they're being raised, are unlikely to complain at the zealous disposal of their birthright. "Every time there is a conversation at home about our wealth, there is one about our responsibilities to give back to the world. Our kids have chores and savings accounts. We don't just buy things — they have to wait for a birthday or until they save enough money to buy it."

Of course, the Gateses do not live the down-home, ordinary life they like to portray. Their famed estate is a citadel of brave-new-world technology; they own their air transport, employ bodyguards and are entertained in palaces (Bill received an honorary knighthood from the Queen in March). This low-key woman inhabits a stratosphere of wealth where the privileges are countered by the fears of malicious envy and kidnap, where it is safer to hide from the public gaze. She defies the conventions on that. She could have used her assets to put a woman on Mars, or collect the finest art; instead she has helped reduce childhood deaths from measles by 39%. The figures matter; they're what she's all about. As the argument rages over whether Africa needs charity or trade, Seattle's first couple will keep pouring their fortune and hope into science. A vaccine for malaria or Aids would be a longer time coming without them.

WHERE DOES OUR GOVERNMENT SPEND OUR MONEY?

Since 1997, the budget of the Department for International Development (DfID) has risen from £2 billion to £4.6 billion — the largest percentage increase of any government department. For 2003 to 2004, the total British government aid expenditure was £4,738m; 40% of this was channelled through 'multilateral' organisations, such as the EC, World Bank and IMF; 5% was spent on administration costs. The remaining 55% was spent on 'bilateral' assistance — ie, it is given directly to the governments of poor countries.

During the same period, there has been a significant shift towards spending in sub-Saharan Africa and away from eastern Europe, central Asia and British overseas territories.

This year, the UK announced a new controversial policy on 'conditionality'. Funding in the past five years has included: