Italian-born and a Catholic, Sonia Gandhi is the unexpected matriarch of India's ruling dynasty. In the 18 years since the assassination of her husband, the former prime minister Rajiv Gandhi, she has become a formidable force in the world's biggest democracy. Leading the Congress Party to victory in 2004, she declined the prime ministership, instead nominating the economist Manmohan Singh for it, yet she is widely accepted to be the real power behind the throne - particularly given that in 2007 she also selected the president, Pratibha Patil. Gandhi's influence looks sure to continue into the next generation, as both of her children, Rahul and Priyanka, have been manoeuvred into public life.
32: David MacKay
The Cambridge physicist David J C MacKay used £10,000 of his own money to publish Sustainable Energy: Without the Hot Air, which, thanks largely to a word-of-mouth campaign that had it circulating like ecological samizdat, very quickly entered Amazon's top 60 bestsellers. (It is also available as a free download from MacKay's website.)
Much of MacKay's research has been in the field of information theory, neural networks and software development. Among the many achievements that earned him a professorship in 2003 and election to the Royal Society this year is Dasher, a data-entry interface that enables disabled people to use computers. But Sustainable Energy is the reason MacKay really matters, and the reason he has just been appointed chief scientific adviser to the Department of Energy and Climate Change.
For too long, he argues, the climate change debate has been disastrously polarised: between those who think the point of "peak oil" is imminent and those who insist we are not heading for an energy crisis any time soon, and between proponents of renewable energy and supporters of nuclear power. He cuts through all the noisy polemicising by settling on a simple unit of measurement that allows us to calculate a country's power consumption. If we know how much power is consumed by land area, then, because most kinds of renewable energy are harvested on land, we will be able to "quantify the potential power production from renewables".
MacKay does the maths and makes an empirically watertight case for the use of energy crops, windfarms and solar power. He calculates that if Britain adopted a mixture of wind, solar and nuclear power, 10 per cent of the country would have to be covered by wind turbines; the area occupied by solar power stations would be five times the size of London; and the 50 nuclear power stations needed would occupy some 50km². "The effort required for a plan like that is very large," he says. "But [it is] imaginable." The argument over energy will never be the same again.
33. Ellen Johnson-Sirleaf
If one good thing emerged from the civil war in Liberia, it was the leadership of Ellen Johnson-Sirleaf. When she took office in January 2006, she became the world's first black female head of state. In her three years as president, she has led the charge against corruption in her country and worked tirelessly to attract investment to Africa, particularly by building relations with the US. In 2007 George W Bush awarded her the Medal of Freedom, the highest US civilian honour. In return, two years later, Johnson-Sirleaf made the US television host Jon Stewart a chief.
The X man
He could be on the list for The X Factor alone. The queues across Britain, the thousands lusting for stardom, are an annual fixture. Millions tune in every week to watch the judges weed out the mad or the painful of voice. All the while, Cowell pockets a fortune by signing the winners to his label, Syco. His influence extends beyond the music industry, however: the X Factor and Britain's Got Talent TV formats are now copied around the world. He might not be loved (he came in at number 33 on Channel 4's list of the all-time 100 Worst Britons), but he shapes much of the world's entertainment.
35. Oprah Winfrey
Chatelaine of chat
Some - Vanity Fair, Time, CNN - have said that Oprah is one of the most influential women in the world. Oprah isn't just a name, a TV show, or a brand - it's a culture with millions of followers. Her approval can turn a book into a bestseller, or even elect a president (one academic study suggested that she delivered roughly a million votes for Barack Obama in the 2008 Democratic primaries, essentially winning him the nomination). And now, there is talk of her entering the Senate. But Oprah also represents the ultimate American story: the self-made woman from the humblest of beginnings who became, at one point, the world's only black billionaire. Now she's giving back - her extensive philanthropy includes setting up a girls' school in South Africa.
36. Muhammad Yunus
As a young economist in Bangladesh, Muhammad Yunus became interested in microcredit, the idea that small loans could make a disproportionate difference to the lives of those too poor for banks to lend to. In 1976, he raised the funds to set up the Grameen Bank on these principles, advancing nearly all its credit to women, whom he thought were more likely to use the funds responsibly. He was proved right. The concept was so successful in helping lift customers out of poverty that it has been copied around the world, and Yunus was awarded the Nobel Peace Prize in 2006.
Carolyn Porco, a Nasa adviser with an asteroid named in her honour, holds the future of space travel in her hands. Renowned for her work in exploration and imaging of the outer solar system, she was part of a mission to Saturn's moons that, in her own words, "possibly stumbled upon the holy grail of modern-day planetary exploration" by finding an environment in which there could be living organisms. Porco bridges the gap between scientific discovery and popular culture, acting as consultant for the 2009 Star Trek film. There is even an online petition to get her a cameo appearance in the sequel. How many scientists can say that?
Japan's new prime minister is spearheading the most progressive political shift in his country's postwar history, which includes plans for a 25 per cent cut in greenhouse-gas emissions by 2020, not to mention high-profile talk of a modern international "fraternity" (cemented, perhaps, by an Asian single currency), both of which would have been unthinkable in Japan just two months ago. Unlike Barack Obama, Hatoyama has a huge parliamentary majority to support his ideas.
39. Rex Tillerson
As chief executive of ExxonMobil, the largest non-state energy company on the planet, Rex Tillerson is the quintessential villain of the
environmental camp. Since taking over the company in 2006, he has abandoned his predecessors' hardline approach, openly acknowledging the possibility of global warming - this year, he sanctioned a $600m investment in algae fuel research - but even this is a drop in the ocean of Exxon's oil reserves. He stands firm on saying that energy demand will increase in the next 20 years, and that Exxon will supply the oil and gas to satisfy that need.
40. Usain Bolt
Usain Bolt is the fastest man on earth. His tauntingly casual stride across the finishing line has become one of the resonant images of the 21st century: his yellow Jamaica vest alone at the front of the pack. He is now recognised as the most extraordinary athlete in the world, ever. His success, combined with his humour and popularity, has reignited the world of athletics and the Olympic Games, tainted in recent years by drug scandals. Bolt's performance signals the end of US dominance in track and field sports. But most of all, he has shown the peak of physical ability - a human being at the limit of his bodily powers.