A dozen years ago, I wrote a column not exactly endorsing Michael Bloomberg for mayor of New York, but endorsing the idea of Michael Bloomberg. If a guy who built a wildly successful business wants to offer his services to the city, I argued, we shouldn't let our prejudice against the rich stand in his way. Since then, the idea — the CEO as aspiring public steward — has suffered some setbacks (Mitt Romney, for one). But I feel pretty well vindicated by the mayor himself.

As he would be the first to tell you, he will be a very hard act to follow.

The race to replace Bloomberg sports a field of a dozen candidates so uninspiring that a former congressman caught tweeting photos of himself with an erection to women he'd never met is near the lead in opinion polls.

For better and occasionally for worse, the rarefied experience Bloomberg brought to the job defined his tenure. Most obviously, that began with his billions, which allowed him to self-finance his campaigns and remain largely unbeholden to the city's clamoring interest groups. Freed from the obligations of retail politics, he could staff his government with top talent rather than people holding political chits.

With a few conspicuous exceptions, he hired people of passion and competence.

He invited them to experiment, a rare thing in the risk-averse culture of government, but he held them accountable with obsessive attention to metrics. His City Hall, like his eponymous company, was built on the power of information. The great urban contraption that is New York City government has probably never been run so well.

He was not a model of inclusiveness. Whites are only a third of New York's population, but nonwhites are scarce in Bloomberg's bullpen. He has lived much of his life in a bubble of privilege, and he has an above-it-all demeanor that contributes to a sense, especially in minority and working-class precincts, that he lacks empathy. He can tell you, with a PowerPoint slide to back him up, that the aggressive police practice of stopping and frisking young men of color in tense neighborhoods has saved lives by keeping guns off the streets. He seems not to appreciate that systematic humiliation corrodes the trust between police and entire communities, and that there might be ways to take the edge off.

Bloomberg can be stubborn and tone-deaf. He is easier to admire than to love.

At least as important as his wealth and managerial acumen, Bloomberg brought to City Hall a largeness of ambition that makes the candidates for his job (and, frankly, many of his predecessors) loom small by comparison. It's not just a matter of ego — Ed Koch and Rudy Giuliani had plenty of that. It's a mind-set. Before he became associated with Wall Street, Bloomberg studied to be an engineer. Engineering is not just a set of skills. It is a strategic sensibility different from a politician's. It favors innovative solutions over incremental fixes, calculation over consensus.

Bloomberg's initiatives were not always well-sold, but they were never small ball. No one since Robert Moses has so dramatically changed the face of the city. Recognizing that traditional manufacturing was not coming back, Bloomberg poured money into rejuvenating the decrepit waterfront. He restored and expanded parks and other public spaces — not just landmarks like Central Park and upscale novelties like the High Line. He rezoned not just plots but neighborhoods — a quarter of the city! — promoting growth in transit-rich areas, sustaining local character elsewhere, imposing order on chaos.

Critics complain that Bloomberg gilded Manhattan to the point where nobody but the affluent can afford it, that the service class was pushed to remote neighborhoods with laborious commutes. There is some truth in that. But as Mitchell Moss, a professor of urban policy at New York University and informal adviser to the mayor, points out, "New York City needs wealthy people, because we tax them." In turn, the people priced out of Manhattan (including young creative types) have brought new life and new amenities to parts of Brooklyn and Queens. Of 8 million New Yorkers, Moss said, "1.6 million people live on Manhattan. The rest live elsewhere. And we've made elsewhere more attractive."

Bloomberg recognized early that cities have overtaken national governments as engines of growth and innovation, and that New York competes for talent and investment not just with other American metropolises but with London and Singapore. He has made the city a world leader in sustainability with his devotion to green development and a campaign to get New Yorkers out of their cars. His boldest assault on our asphyxiation by auto — a congestion pricing plan — failed in Albany. Instead, he raised the cost of parking, commandeered roadways for high-speed buses, expanded ferry service and made the city more bike-friendly. After last year's superstorm, he commissioned an impressive blueprint for a more resilient city and has begun by rezoning vulnerable areas. "His response to Sandy at the human level was appalling," said Joan Byron, an urban planner who is director of policy at the Pratt Center for Community Development. "But the infrastructure stuff is brilliant."

To bolster New York's claim on the future, Bloomberg has invested in our intellectual infrastructure, too. The planned Cornell applied sciences and engineering campus on Roosevelt Island should strengthen New York's appeal to the tech industry. Shrewdly, he used that project to goad competing universities — Columbia and NYU — to raise their games.

Bloomberg's father-knows-best approach has paid off with saved lives in the realm of public health. We take for granted now that our restaurants and bars and parks are smoke-free, but at one time Bloomberg was demonized as the Smoke Nazi who was going to put every saloon out of business.

The city made it through a brutal recession thanks in large part to federal aid after 9/11 and Sandy, the bailout of the financial industries and a surging stock market. But any fair judge would say that Bloomberg played a significant part in the rebound. A believer in the wisdom of balancing revenue sources, he raised property taxes early on; when the recession shrank income-tax revenues, property taxes kept us afloat. He has bequeathed his successor a potential fiscal crisis in the surging cost of public-sector benefits, but he has also left a city better positioned to cope than, say, Los Angeles or Chicago.

Bloomberg's most consequential and controversial unfinished business is the public school system. He set the schools on a hopeful course: stabilizing the system under mayoral control, raising and enforcing standards, giving parents more options, among them charter schools that actually work. There is much more to do. Schools are the work of a generation, not an administration. Bloomberg's great achievement was taking on the prevailing defeatist view that urban schools were unfixable.

The mayor's third term, which began with a broken term-limits promise that many New Yorkers have not forgiven, was less successful than his first two, and it felt less successful than it actually was because the city has developed a bit of Bloomberg fatigue. By now, many New Yorkers are ready for a little more consensus, a little less lecturing, a little more attention to those at the bottom.

But Bloomberg leaves behind a great 21st-century city, a dauntingly high bar for his successor, and a pretty good argument for noblesse oblige.