If you had married the world’s richest man, how would you live? Perhaps when the private islands, yachts and jets, the parties and Paris couture start to pall, you might schedule in a little light do-gooding. Maybe you’d bestow a gift upon a symphony orchestra or endow a museum. Something elegant with social cachet. The world’s uglier problems – such as the global Aids epidemic – could be locked outside your gated mansion. Unlikely, then, you’d choose to spend your days in stinking slums or Indian hospices, embracing HIV-positive prostitutes or dying babies. Or becoming fluent in the science of infection-preventing vaginal gels.

But Melinda Gates is a rare rich man’s wife. She is not soignée or retinued or grand. Clutching her cardboard coffee cup, she wears a standard American businesswoman-style tan trouser-suit with little make-up, her long hair loose. She is warm, quick to laugh, with a Silicon Valley first-names informality. And she talks like a PowerPoint presentation – so fast that I later struggle to transcribe the tape, rapping out statistics and acronyms, her high-speed systematic mind breaking a subject down to its components, then double-clicking back to the bigger picture. She could still be the fast-track Microsoft executive she was before she married the proprietor and left to have his children. Except, sitting here in the Seattle offices of the Gates Foundation, she is not Bill’s employee or wife but his equal partner.

And it is a job not unlike being co-ruler of a small nation, considering every year she helps gives away more than the foreign- aid budget of, say, Australia. Since it began in 2000, the Bill & Melinda Gates Foundation has donated $17.3 billion (£11.6 billion) and still has $35.1 billion at its disposal. In fact, Bill Gates has donated so much that this year he ceased to be the world’s richest man, after 13 years in the top slot – although the man who stole his title, US investment tycoon (and Bill’s sometime bridge partner) Warren Buffett, has pledged the Gates Foundation most of his $62 billion fortune, which he is already handing over in $1.6 billion annual instalments.

The magnitude of this wealth could change – if not save – the world. The Gateses have pumped staggering quantities into three causes: America’s education system, global development (specifically micro-finance and agriculture) and world health (in particular, mass vaccination programmes to eradicate diseases such as TB and malaria). It is World Aids Day on Monday, and it is HIV/Aids that Melinda Gates says categorically “is the number one problem that needs to get solved – and all the different initiatives it’s going to take to line that up will see us involved for the history of the foundation”.

Their approach to Aids combines the quintessentially American – an unshakeably can-do attitude, boundless energy and faith in scientific progress – together with the maverick risk-taking that created Microsoft. Free from electoral accountability, they can work with whomever they choose, speak out whenever they see fit. They readily took a pop at Pepfar, the Bush administration’s Aids fund and its ABC (Abstinence, Be Faithful, Condoms) strategy, for putting Christian Right morality before saving lives. Melinda cannot wait to work with Barack Obama’s incoming administration, although today, she is quick to praise Pepfar for giving three million people in the developing world access to the life-saving antiretroviral drugs that these days are taken for granted in the West.

The foundation’s priority is targeting women: abstinence is irrelevant if a girl is forced into early marriage, her fidelity does not guarantee that of her husband, and frequently the decision to use a condom is not within her control. “In sub-Saharan African, 55 per cent of people with Aids are female. Most are mothers and will die leaving four to seven children – that’s why there are twelve million orphans in the developing world – and what that does to the family structure is fundamental to what happens across the continent.”

The foundation has championed both the search for the Aids holy grail, a vaccine, and a new potential area of prevention, microbicides. “This is the most exciting development and they’re likely to be available in, hopefully, the next seven years,” says Melinda. “They’re either in the form of an odourless, clear jelly that a woman can use without her partner knowing, or a prophylactic pill that will block the ability of Aids to transmit itself.”

Frank and unembarrassable, Melinda Gates has made it her mission to break down the disproportionate stigma that burdens infected women, insisting on meeting prostitutes in India – to the horror of accompanying government officials. She is fuelled by the suffering of those she meets: a dying mother at Kenya’s Kibera slum lamenting how she was powerless to stop her husband infecting her, and the maid servant of a doctor who returned to her village to die rather than admit she had the disease. “He could have got her drugs in a heartbeat,” she says sadly, “but she was too ashamed.”

But why does she make so hard a life that could be luxuriously easy? Melinda lets out her big, throaty yelp of a laugh. “I’ll say to my mom, ‘I can’t imagine doing the cocktail party thing, the dressing-up, all the time.’ I like it sometimes, but all the time? It would be so meaningless to me. My mom knows that when I’m in India, to get into the slum, you kind of go through a garbage dump. And she says, ‘You know, Melinda, people can’t understand why you enjoy visiting those places so much.’ But I love being in the slums. That’s just a part of who I am, my whole background and experience.”

A Texan who still loathes Seattle’s gloomy British-style weather, Gates, now 44, was raised in a middle-income family – her father was an aerospace engineer – that scraped to fund her college fees but was imbued with a sense of civic responsibility. She quotes the motto of her Catholic school: “Serviam” (I will serve). Following her mother’s lead, she volunteered in local hospitals and schools, helping Mexican immigrant children who struggled with English. The ace student of her year, she graduated in economics and computers, ripe for a career at Microsoft, where she rose rapidly and ended up running a division handling more than $200 million of business.

Bill Gates’s family were wealthy by contrast, and his father, William Gates Snr (at 83, still active in the foundation) was a prominent lawyer. Yet the Gateses, too, had a sense of social duty. Bill’s late mother Mary, while dying of breast cancer, wrote Melinda and Bill a letter, in which she said, “For those to whom much is given, much is expected” – an aphorism that echoes Andrew Carnegie’s famous “He who dies rich, dies disgraced”. It was in honour of his mother, and to find an outlet for his retired and bereaved father, that Bill set up the foundation that will ultimately receive 95 per cent of their wealth, currently valued at $58 billion.

Even the few remaining per cent would ensure a gargantuan legacy for the couple’s three children: Jennifer, 12, Rory, 9, and Phoebe, 6. It is rare to meet a rich parent who does not fret that inherited wealth might sap their children’s drive or even derail their lives. But Melinda Gates says with utter certainty, “I know some families worry about that. I don’t. They know they are going to get an amazing education in the US. And then they are going to work. Believe me, that is already on their minds! We’ve taken them to the slums already, and the two older ones have been to South Africa. All age-appropriate, of course. One of my children is going to be volunteering with me in the local Seattle community, too. So I’d be surprised if it wasn’t baked in. Just as with me it’s baked in. My mom wasn’t dressed up and going to cocktail parties and saying that was important when I was growing up either.”

Times recommends

• How I lost the gift of joy for a while
• How to get Coleen Rooney's post-baby body
• The A-Z of winter style rules