BLOOMBERG'S GAME.(mayoral election)

Going back to James (Gentleman Jimmy) Walker, the Jazz Age dandy who spent his evenings at the Central Park Casino and rarely got to work before noon, New Yorkers have tended to elect civic leaders who embody the historic moment. During the Great Depression, Fiorello LaGuardia, the indomitable Little Flower, revived the city's spirit and its economy by building roads, bridges, parks, swimming pools, and affordable housing. Forty years later, when the city was once again skirting bankruptcy, Ed Koch told anybody who would listen that he, for one, wasn't giving up on his home town. And on September 11, 2001, Rudolph Giuliani emerged from a hellish dust cloud to proclaim that New York would recover, and, shortly afterward, to anoint Michael R. Bloomberg as his successor.

Koch turned eighty recently, and Bloomberg threw a cocktail party for him at Gracie Mansion. Bloomberg doesn't live at Gracie Mansion--he chose to remain in his East Side town house after being elected--and he isn't a noted speaker, but he gave a warm and generous toast, lauding Koch as a great New Yorker. At six feet one, Koch towered over Bloomberg, who claims to be five feet nine but appears to be closer to five-six. The sight of them together inevitably raised questions about how the current mayor, who is up for reelection in November, will be remembered.

Not long ago, the answer appeared to be "With difficulty." In contrast to Giuliani, whose last months in office encompassed a bitter public divorce, a terrorist attack, and a halfhearted attempt to postpone the mayoral election, Bloomberg went about his job quietly and without fanfare. (One of his early decisions was to tell his drivers to switch off the emergency lights and sit in traffic with everybody else.) Surveys showed that New Yorkers considered him competent and diligent, but, when asked to cite things that he had done which they liked or disliked, many of them struggled to come up with any. (Smokers were an exception. They hadn't forgotten his ban on smoking in bars and restaurants.)

Recently, however, Bloomberg has been acting more like Koch and Giuliani, infuriating some, delighting others, and forcing everybody to pay attention. Last summer, during the Republican Convention, he stoutly defended the Police Department's aggressive "street-sweeping" policy toward demonstrators, alienating many liberals who had assumed that he was secretly one of them. At about the same time, Bloomberg announced that fifth graders would no longer gain automatic promotion to middle school, a policy shift that many teachers and education experts deplored. More recently, he agreed to spend three hundred million dollars of city money on a new football stadium for the New York Jets, to be placed on the West Side. If New York is awarded the 2012 Olympic Games, which Bloomberg is pursuing, the new arena would serve as an Olympic stadium. Last week, the National Football League announced that the stadium would also host the 2010 Super Bowl, assuming that it is finished by 2009.

The idea of situating a seventy-five-thousand-seat sports arena in the heart of Manhattan has enraged many New Yorkers. In a survey published earlier this month, fifty-six per cent of respondents said that they opposed the stadium, and just thirty-five per cent supported the idea. Bloomberg's rivals in the upcoming mayoral race are accusing him of wasting taxpayers' money and neglecting the concerns of ordinary citizens. "The city's education system is in disarray right now. Ask teachers, they say it; ask students, they say it," Anthony Weiner, a Democratic congressman who is running for City Hall, told me recently. "The Mayor can't change that. He's too busy with the stadium. He's spending money in the wrong place at the wrong time. It's a boondoggle, and New Yorkers know it." Fernando Ferrer, a former Bronx borough president, who is one of Weiner's rivals in the contest for the Democratic mayoral nomination, is calling for a referendum on the stadium. Another Democratic candidate, Gifford Miller, the speaker of the City Council, is trying to introduce legislation to block it.

Bloomberg's emergence as a polarizing figure has surprised many in the political world. "Friend and foe alike would say that Mike Bloomberg knows how to spend his money and his political capital," Mark Green, who was the losing candidate in the 2001 mayoral race, commented to me recently. "Also, he's very competitive, and he doesn't like to lose. Given that, I'm baffled why he's so out on a limb on the Olympics and the stadium, when he's not likely to win on either." Even some of Bloomberg's closest associates are worried that the dispute is detracting from his achievements in other areas, such as reducing crime and balancing the budget. "There is a group inside the administration that doesn't think we should be investing so much time and effort in the stadium," one senior city official said. "The Mayor talks about it every day. It has started to take over from everything else."

Shortly before Christmas, I met with Bloomberg, who is sixty-three, in "the bull pen," a big, open-plan office on the second floor of City Hall, where he works with his senior staff. The bull pen resembles Bloomberg's workspace at Bloomberg L.P., his media company, which specializes in selling financial information to Wall Street firms. (Before starting his own business, Bloomberg worked for many years at Salomon Brothers.) Seven rows of cubicles fill the room, and Bloomberg occupies a cubicle in the center. The atmosphere is informal but businesslike. "You look up from your desk, and you don't know who you are going to see," William Cunningham, Bloomberg's director of communications, told me. "One moment it is a county supervisor, the next it is Mikhail Gorbachev."