One afternoon about 12 years ago, Larry Page and Sergey Brin gave John Doerr a call. A few months earlier, the Google cofounders had accepted $12.5 million from Kleiner Perkins Caufield & Byers, Doerr’s venture-capital firm, as well as an equal amount from Sequoia Capital. When they took the cash, they agreed that they would hire an outsider to replace Page as CEO, a common strategy to provide “adult supervision” to inexperienced founders. But now they were reneging. “They said, ‘We’ve changed our mind. We think we can run the company between the two of us,'” Doerr recalls.

Doerr’s first instinct was to immediately sell his shares, but he held off. He made Page and Brin an offer: He would set up meetings for them with the most brilliant CEOs in Silicon Valley, so they could get a better sense of what the job entailed. “After that,” he told them, “if you think we should do a search, we will. And if you don’t want to, then I’ll make a decision about that.” Page and Brin took a Magical Mystery Tour of high tech royalty: Apple’s Steve Jobs, Intel’s Andy Grove, Intuit’s Scott Cook, Amazon .com’s Jeff Bezos, and others. Then they came back to Doerr.

“We agree with you,” they told him; they were ready to hire a CEO. But they would only consider one person: Steve Jobs.

Happily, Doerr was able to persuade them to widen their net and would soon introduce them to Eric Schmidt, who took the CEO spot in 2001. The first couple of years were rocky. As late as 2002, the founders still sounded bitter when discussing Schmidt’s hire. Investors, Brin told a reporter, “feel more comfortable with us” now that they didn’t need to worry what “two hooligans are going to do with their millions.” But as the years went by, and as Google under Schmidt grew into the third-largest technology company in the world, Page and Brin came to genuinely appreciate their CEO. Page would later describe hiring Schmidt as “brilliant.”

Now, after a 10-year run in which Google’s revenues grew from less than $100 million to almost $30 billion, Page is finally CEO again, a role he always felt he could handle. The general public may not appreciate the magnitude of the change—to most, Page is just one of the seemingly interchangeable pair of wacky “Google guys.” But Page is sui generis and could potentially have the kind of impact Bill Gates and Steve Jobs have had. Nobody better encapsulates Google’s ambitions, its ethics, and its worldview. At the same time, Page can be eccentric, arrogant, and secretive. Under his leadership, the company will be even harder to predict.

Google’s 2004 pre-IPO filing with the SEC included a note from Page to prospective shareholders. In it, he famously warned that “Google is not a conventional company. We do not intend to become one.” In the ensuing years, Google made good on that promise. But under its ruling troika, Schmidt helped balance the founders’ idiosyncratic urges with more traditional practices. With Page taking the helm, no one is sure how—or if—that delicate balance will be maintained. Now the company is in the hands of a true corporate radical.

A few ingredients in Larry Page’s stew of traits stand out unmistakably. He is brainy, he is confident, he is parsimonious with social interaction. But the dominant flavor in the dish is his boundless ambition, both to excel individually and to improve the conditions of the planet at large. He sees the historic technology boom as a chance to realize such ambitions and sees those who fail to do so as shamelessly squandering the opportunity. To Page, the only true failure is not attempting the audacious. “Even if you fail at your ambitious thing, it’s very hard to fail completely,” he says. “That’s the thing that people don’t get.”

Page is a reflexive champion of big—sometimes quixotic—ideas. Even Googlers, no Luddites themselves, joke that Page “went to the future and came back to tell us about it.” One engineer recounts the time he went to discuss an ill-fated project with Page and ended up talking about the finer points of nuclear fusion. “What Larry asks himself is not ‘How can I help this person?'” he says. “Instead he’s asking himself, ‘Ten years from now, what is going to have the maximum impact on humanity?'”

Page’s mandate now is to renew Google’s energy and drive, and in some ways he is the perfect person to perform that task. He is also perhaps the quirkiest person to ever run a $30 billion company. Google has had a wild ride over its first 12 years. It’s about to get even wilder.

“You can’t understand Google,” vice president Marissa Mayer says, “unless you know that both Larry and Sergey were Montessori kids.” She’s referring to schools based on the educational philosophy of Maria Montessori, an Italian physician born in 1870 who believed that children should be allowed the freedom to pursue their interests. “In a Montessori school, you go paint because you have something to express or you just want to do it that afternoon, not because the teacher said so,” she says. “This is baked into how Larry and Sergey approach problems. They’re always asking, why should it be like that? It’s the way their brains were programmed early on.”

Page grew up in East Lansing, Michigan, where his father taught computer science at Michigan State. He wanted to be an inventor, not simply because of his interests and abilities in math and technology but because, he says, “I really wanted to change the world.”

Page was not a social animal—those who interacted with him often wondered if there were a jigger of Asperger’s in the mix—and he could unnerve people by simply not talking. But when he did speak, he often came out with ideas that bordered on the fantastic. As an undergraduate at the University of Michigan, he became obsessed with transportation and drew up plans to replace the school’s mundane bus network with an elaborate monorail system, providing a “futuristic” commute between the dorms and the classrooms.

Page’s ideas may have been fantastic, but his vision always extended to the commercial. “From when I was 12, I knew I was going to start a company,” he says. In 1995, he went to Stanford to pursue his graduate degree. It was not only the best place to study computer science but, because of the Internet boom, was also the world capital of entrepreneurial ambition. Page had been impressed by the biography of Nikola Tesla, the brilliant Serb scientist who died in obscurity, despite contributions that arguably matched Thomas Edison’s. “It was a sad story,” Page says. “I feel like he could’ve accomplished much more if he had more resources. And he had trouble commercializing the stuff he did. Probably more trouble than he should’ve had. I think that was a good lesson. I didn’t want to just invent things, I also wanted to make the world better.”

Page did invent something. In collaboration with Sergey Brin, a classmate he’d met in the spring of 1995, he created BackRub, a search engine that used the linking structure of the web to deliver results superior to those of the best commercial products of the time. At first Page and Brin, reluctant to leave the PhD program, tried to license the technology to existing web companies. When they failed, they renamed their search engine Google, formed their own company, and sought funding.

“If the company failed, too bad,” Page says. “We were really going to be able to do something that mattered.”

While both founders were technical and imaginative, Page was the driver of the vision. “Larry always wanted it to be a bigger thing—as soon as the opportunity presented, it was full speed ahead,” says Craig Silverstein, Google’s first employee. “I don’t think Sergey has that drive to the same extent Larry does. I don’t feel as confident saying what would’ve happened had Sergey called all the shots.”

Even after Schmidt came aboard, Page continued to set the core precepts of the company. Page wanted everyone at Google to think big. It was a defining habit for him. When someone pitched an idea, Page would invariably counter with a variation that was an order of magnitude more ambitious. In 2003, when executives met to consider opening engineering offices overseas, Schmidt asked Page how quickly he would like to grow.

“How many engineers does Microsoft have?” Page asked.

About 25,000, he was told.

“We should have a million,” Page said, in all seriousness.

At that point, Schmidt put an avuncular hand on Page’s shoulder and brought him back to the real world. Now, with Page as CEO, that hand is less likely to be there.

What will that mean? If history is any guide, Page’s idealistic impulses could result in a vaster, more sprawling company. In 2008, Google participated in an FCC auction for radio spectrum to be used for mobile broadband. By the terms of the auction, if the spectrum was sold above a certain price, the winner would have to allow other companies to run devices on their networks—something Google strongly favored but that telecom companies dearly hoped to avoid. Google executives worried that the telecoms would conspire to keep bidding below that baseline price. So the company got involved in a high-stakes game of chicken. Google would bid on the spectrum, high enough to get it over the threshold, and then bow out. It left Google potentially vulnerable; if nobody else topped its bid, the company would be stuck with a multibillion-dollar piece of spectrum that it was unequipped to exploit. “Google definitely wanted to lose,” the company’s chief economist, Hal Varian, says. To Google’s great relief, Verizon did top its bid, and the company was off the hook.

It turns out, though, that Page had other ideas—according to Richard Whitt, the Google policy person who headed the auction effort, Page urged Google to consider topping the Verizon bid. Later, he justified the impulse by a kind of circular logic. “Obviously, you wouldn’t have made the bid if you thought you were wasting your money,” he said. “If someone else bids, you know you’re probably not wasting your money. So that means you might be willing to pay more. And so you’ve really got to think about that.” (Ultimately, Google let Verizon’s bid stand.)

“Larry always has far-fetched ideas that may be very difficult to do,” Google software engineer Eric Veach says. “And he wants them done now.” In the early 2000s, Veach worked on what would become the company’s advertising system. Page was adamant that the program be simple and scalable—advertisers shouldn’t have to deal with salespeople, pick keywords, or do anything more than give their credit card number. That approach helped create the most successful Internet commerce product in history. But some other suggestions were baffling. During one session, Veach pointed out that not all countries commonly used credit cards. Page proposed taking payments appropriate to the home country—in Uzbekistan, he suggested, Google could take its payment in goats. “Maybe we can get to that,” Veach responded, “but first let’s make sure we can take Visa and MasterCard.”

Still, even as CEO, Page’s nuttier instincts will be tempered by those around him. Indeed, Googlers have learned that the best way to counter some of his more problematic idiosyncrasies is not by having a frank discussion but through misdirection. For instance, Wesley Chan, a top product manager, fundamentally disagrees with Page’s ideas on product design. 1 But he has learned that instead of arguing his case with Page, a better strategy is “giving him shiny objects to play with.” At the beginning of one Google Voice product review, for instance, he offered Page and Brin the opportunity to pick their own phone numbers for the new service. For the next hour, the two brainstormed sequences that embodied mathematical puns while the product sailed through the review.

But while it’s easy to scoff at Page’s quirks—his odd obsessions, his unrealistic expectations, his impatience for a future dangling out of immediate reach—sometimes his seemingly crazy ideas wind up creating breakthrough innovations, and skeptical Googlers wind up admitting Page was right, after all. That was the reaction in 2003 when Denise Griffin, the person in charge of Google’s small customer-support team, asked Page for a larger staff. Instead, he told her that the whole idea of customer support was ridiculous. Rather than assuming the unscalable task of answering users one by one, Page said, Google should enable users to answer one another’s questions. The idea ran so counter to accepted practice that Griffin felt like she was about to lose her mind. But Google implemented Page’s suggestion, creating a system called Google Forums, which let users share knowledge and answer one another’s customer-support questions. It worked, and thereafter Griffin cited it as evidence of Page’s instinctive brilliance.

One complaint of the current, supersized version of Google Inc. is that bureaucracy slows down progress. Expect that to change, because speed is one of Page’s primary obsessions. “He’s always measuring everything,” early Googler Megan Smith says. She was once walking with Page down a street in Morocco when he suddenly dragged her into an Internet cafè9. Immediately, he began timing how long it took web pages to load into a browser there.

“When people do demos and they’re slow, I’m known to count sometimes,” Page says. “One one-thousand, two one-thousand. That tends to get people’s attention.” Paul Buchheit, the creator of Gmail, remembers performing an early demo of that service in Page’s office. Page made a face and told him that it was way too slow. Buchheit objected, but Page reiterated his complaint, charging that it was taking at least 600 milliseconds to reload. Buchheit thought, “You can’t know that.” But when he got back to his office he checked the server logs. Six hundred milliseconds. “He nailed it,” Buchheit says. (Page’s fixation on speed probably drives his notorious bias toward utilitarian—some say boring—design. He maintains a militant opposition to eye-catching animations, transitions, or anything that veers from stark simplicity.)

When Schmidt was at the helm, Page was free to pursue whatever interested him. He devoted himself to passion projects that he felt could make the biggest impact on the company. It was Page who asked for an interview with the head of a small mobile software startup called Android—startling its founder, Andy Rubin, by asking to buy the company. Rubin is now vice president of engineering at Google, and Android is one of the company’s biggest assets.

It was also Page who dreamed of digitizing the world’s books. Many assumed the task was impossible, but Page refused to accept that. It might be expensive, but of course it was possible. To figure out just how much time it would take, Page and Marissa Mayer jury-rigged a book scanner in his office, coordinating Mayer’s page-turning to a metronome. Then he filled up spreadsheets with calculations: how many pages he would need to scan, how much it would cost to scan each page, how much storage he would need. Eventually, he became convinced that the costs and timing were reasonable. What astounded him was that even his spreadsheets didn’t dissolve the skepticism of those with whom he shared his scheme. “I’d run through the numbers with people and they wouldn’t believe them,'” he later said. “So eventually I just did it.”

Page was disappointed when critics glossed over the benefits of the book search project and launched a series of legal challenges that might eventually sink it. “Do you really want the whole world not to have access to human knowledge as contained in books?” Page asks. “You’ve just got to think about that from a societal point of view.” He chalked up a lot of the opposition’s passion as phony—a negotiating tactic. Page also says that, while privacy is important to him, he thinks the criticism of Google’s privacy policies is often overblown. “There’s a 10 percent chance of any product becoming an issue, and it’s not possible to predict which one,” he says. “Oftentimes the thing that people are upset about isn’t the actual thing they should be upset about.”

Page’s blithe dismissal of Google’s critics is impolitic at the least. And his black-and-white view of corporate morality—with Google always wearing white—has probably contributed to some of the damage the company’s reputation has sustained in recent years. Yet his refusal to dwell on shades of gray has also given him the fortitude to order up risky moon shots, like Book Search and Google’s recently announced autonomous vehicle project. Critics said that the latter effort was an indulgent distraction. But if you take into account Page’s core vision—making Google into a learning machine that processes massive data—it’s easy to see how the self-driving cars, loaded with lasers and sensors that continuously gather information, fit into it. “This is all information,” says Sebastian Thrun, the AI scientist who heads the project. “And it will make our physical world more accessible.” Even more satisfying for Google, some people considered it impossible. With Page in charge, Google will undoubtedly take on more moon shots.

Page has one task that may indeed prove to be impossible: making a company of more than 24,000 employees act like a startup. Page and Brin have long been obsessed with keeping Google nimble—an impulse that sometimes leads them toward simple denial. As early as 2001, as the company reached 400 employees, Page worried that a growing layer of middle managers would bog it down. So he and Brin came up with a radical solution: They decided to do away with managers entirely. The HR team begged them not to, but the founders went ahead with the plan. When it soon became clear that the idea was a disaster—more than 100 people were reporting directly to an overwhelmed head of engineering—Google quietly reinstated the managers. But it was only the beginning of a long struggle to maintain the speed and hunger of a small company even as it grew.

One way Page tries to keep his finger on Google’s pulse is his insistence on signing off on every new hire—so far he’s vetted well over 30,000. For every candidate, he is given a compressed version of the lengthy packet created by the company’s hiring council, generated by custom software that allows Page to quickly scan the salient data. He gets a set every week and usually returns them with his approvals—or in some cases bounces—in three or four days. “It helps me to know what’s really going on,” he says.

Page has little patience for the bureaucracy that most large companies require. In 2007, he noticed that having an assistant made it easier for his coworkers to schedule meetings with him. “Most people aren’t willing to ask me if they want to meet with me,” he says. “They’re happy to ask an assistant.” That was an undesirable situation, Page says, “because my favorite meeting is the absence of meetings.” So one day, Brin and Page abruptly got rid of their assistants. Anyone who wanted to talk to them had to stalk them. Like the plane spotters who log the peregrinations of aircraft, Googlers often swap data concerning Page’s and Brin’s ambulatory patterns. Even so, it can sometimes be tricky to catch Page; he is a master of the drive-by greeting, flashing a wide, happy-to-see-you smile while slightly picking up his pace, leaving a potential interlocutor talking to his receding back.

But Page’s least favorite interactions are with the press. “Larry can be a very, very sensitive and good person,” says a former PR employee. “But he has major trust issues and few social graces.”

The question now is whether Page has developed the tolerance, will, and grace to dispatch the mundane duties of a CEO while still retaining the qualities that make him unique. Schmidt seems to think that Page has grown into the role. “Sergey and Larry are not kids anymore,” he told me in early 2010. “They are in their midthirties, accomplished senior executives in our industry. They are learning machines, and 10 years after founding the company, they’re much more experienced than you’d ever imagine.” When he announced in January that Page would assume the CEO role, Schmidt was more specific. “Larry is ready,” he said. Later that day, he tweeted his further approval: “Day to day adult supervision no longer needed!”

The accuracy of that statement remains to be seen. But within days of the announcement, Googlers took note of a development that seemed to indicate the new CEO was growing into the position: Larry Page has taken on an administrative assistant.

Adapted from In the Plex: How Google Thinks, Works, and Shapes Our Lives , copyright © 2011 Steven Levy, to be published by Simon & Schuster in April.

[March 18/6:30 p.m. EST appended]: Wesley Chan is a Google product manager,

not a production designer.

fLarry Page