New Yorkers, like the two Roosevelts, Thomas Dewey, and Al Smith, led one of the major parties in nine out of the 12 elections between 1901 and 1950. In those years, New York bestrode the Just as New York has come back as a city, it is once again in the center of presidential politics. The Intrade betting market suggests that Hillary Clinton has a 64% chance of winning the Democratic nomination, while Barack Obama has only a one-in-five chance of beating her. Rudy Giuliani leads the Republicans in both the national polls and the Intrade market gives him a 36% chance for the nomination. Intrade even gives Mayor Bloomberg a 25% chance of entering the national election. The three New Yorkers at the top of the presidential sweepstakes remind us of the city’s resurgence and the sources of its enduring strength.

Mr. Giuliani’s parents were working class. His father spent some time at Sing Sing. His rise reflects New York’s ability to provide the opportunities that can turn ordinary people into millionaires or mayors or both.

There are two myths about New York’s ability to turn rags into riches. The first myth is that the city’s capability to make modest people millionaires is particularly American, rather than urban. America is a land of opportunity, but great fortunes also are made by garage mechanics like Soichiro Honda in Tokyo, and grocers like the billionaire Albrecht brothers in Essen, or the children of Lebanese immigrants like Carlos Slim in Mexico City. America has no monopoly on Horatio Alger stories, but those stories do tend to take place in cities.

The second myth is that cities create fortunes by randomly bestowing millions of dollars on normal people. Mr. Giuliani was lucky, but far more importantly, he was skilled. Cities are a great place to learn and they forge the human capital of Messrs. Giuliani, Honda, Slim, and the Albrechts. The urban abundance of intellectual excellence created a rich field of mentors who taught Mr. Giuliani law and politics. The tough battles that Mr. Giuliani faced as New York’s mayor and district attorney gave him the experience that makes him a credible presidential candidate.

New York helped to make Mr. Giuliani, and it attracted Hillary Clinton as well. There were five open Senate seats in the 2000 election, and she chose one in New York. The city’s openness to outside talent is another reason why it is so strong.

New York has thrived on its openness ever since Peter Stuyvesant’s Dutch masters rebuked him for harassing Jewish refugees from Recife. Daniel Moynihan, who wrote about and personified New York’s strength through diversity, invited Mrs. Clinton to run, knowing that his voters would embrace an outsider. In the past six years, all three Clintons have thrown themselves into the life of the city and they seem to be enjoying it.

Mayor Bloomberg’s life virtually embodies New York’s economic resurgence. When Mr. Bloomberg came to Salomon Brothers with a newly minted Harvard MBA in 1966, he became part of the wave of educated financial professionals that renewed Wall Street.

It was when he left Salomon Brothers, however, that Mr. Bloomberg’s life became a textbook illustration of how cities, like New York, foster the innovation that is in their blood. Cities aid innovation because they have a wealth of old ideas which can then be connected to new ones that create breakthrough ideas. By combining financial services and information technology, industries that were already in New York, Mr. Bloomberg made the world more productive while also making himself a billionaire.

New York’s current political prominence exhibits the city’s return to global eminence. It is a reflection of the city’s ability to provide opportunity for working class kids like Rudolph Giuliani, to attract talent like Hillary Clinton, and to generate major economic innovations like those of Michael Bloomberg.

Mr. Glaeser is the Glimp professor of economics at Harvard, director of the Taubman Center for State and Local Government, and a senior fellow at the Manhattan Institute.