“My wife and I had a long dialogue about how we were going to take the wealth that we’re lucky enough to have and give it back in a way that’s most impactful to the world,” he says. “Both of us worked at Microsoft and saw that if you take innovation and smart people, the ability to measure what’s working, that you can pull together some pretty dramatic things.

“We’re focused on the help of the poorest in the world, which really drives you into vaccination. You can actually take a disease and get rid of it altogether, like we are doing with polio.”

This has been done only once before in humans, with the eradication of smallpox in the 1970s.

“Polio’s pretty special because once you get an eradication you no longer have to spend money on it; it’s just there as a gift for the rest of time.”

One can see why that appeals to Gates. He has always sought neat, definitive solutions to things, but as he knows from Microsoft, bugs are resilient things. The disease is still endemic in Nigeria, Pakistan and Afghanistan, and killing it off altogether has been likened to squeezing jelly to death. There is another, sinister obstacle: the propagation by Islamist groups of the belief that polio vaccination is a front for covert sterilisation and other western evils. Health workers in Pakistan have paid with their lives for involvement in the programme.

“It’s not going to stop us succeeding,” says Gates. “It does force us to sit down with the Pakistan government to renew their commitments, see what they’re going to do in security and make changes to protect the women who are doing God’s work and getting out to these children and delivering the vaccine.”

Gates does not usually speak in religious terms, and has traditionally danced around the issue of God. His wife, a Roman Catholic, is less defensive on that topic but ploughs her own furrow, encouraging contraception when necessary, in contradiction to teaching from Rome.

“Melinda and I had been talking about this even before we were married,” he says. “When I was in my 40s Microsoft was my primary activity. The big switch for me was when I decided to make the foundation my primary purpose. It was a big change, although there are more in common with the two things than you might think – meeting with scientists, taking on tough challenges, people being sceptical that you can get things done.”

Gates is still chairman of Microsoft but without his day-to-day attention it has taken on the appearance of a weary giant, trailing Apple and Google in innovation. Some have called for Gates’s return to the company full-time to inject some verve but he isn’t coming back.

“My full-time work for the rest of my life will be at the foundation,” he says. “I still work part-time for Microsoft. I’ve had two careers and I’m lucky that both of them have been quite amazing.

“I loved my Microsoft: it prepared me for what I’m doing now. In the same way that I got to see the PC and internet revolutions, now I see child death rates coming down. I work very long hours and try to learn as much as I can about these things, but that’s because I enjoy it.”

He emphasises that the foundation’s effort is part of a global campaign in which governments must play the lead role.

“The scale of the (foundation’s) wealth compared to government budgets is actually not that large, and compared to the scale of some of these problems. But I do feel lucky that substantial resources are going back to make the world a more habitable place.”

In 1990 some 12 million children under the age of five died. The figure today is about seven million, or 19,000 per day. According to the United Nations, the leading causes of death are pneumonia (18 per cent), pre-birth complications (14 per cent), diarrhoea (11 per cent), complications during birth (nine per cent) and malaria (seven per cent). For Gates, though, polio is a totem. The abolition of the disease will be a headline-grabber, spurring countries on to greater efforts. The Bill and Melinda Gates Foundation will spend $1.8 billion in the next six years to accomplish that goal, almost a third of the global effort.

“All you need is over 90 per cent of children to have the vaccine drop three times and the disease stops spreading. The number of cases eventually goes to zero. When we started, we had over 400,000 children a year being paralysed and we are now down to under 1,000 cases a year. The great thing about finishing polio is that we’ll have resources to get going on malaria and measles.”

Gates is no saint. He could be an intimidating boss at Microsoft and his company became notorious for using its clout to reinforce its dominance in the market place, at the expense of smaller rivals. Still, he and his wife are showing generosity on a staggering scale, a counterblast to the endemic greed of the Nineties and early Noughties, and they have convinced others that mega-philanthropy is the way of the future. That wily investor, Warren Buffett, has so far given away $17.5 billion via the Gates Foundation.

The children of Bill and Melinda Gates will never know poverty. They may not become multibillionaires but even the loss to charity of the vast bulk of their parents’ fortune should leave them with a billion or so each.

Gates explains: “The vast majority of the wealth, over 95 per cent, goes to the foundation, which will spend all that money within 20 years after neither of us are around any more.”

So, is it about some new-found faith, all this giving?

“It doesn’t relate to any particular religion; it’s about human dignity and equality,” he says. “The golden rule that all lives have equal value and we should treat people as we would like to be treated.”