(FORTUNE Magazine) – In the annals of big business, there may never have been so curious a pair--company and man--as Progressive Corp., a Cleveland auto insurer, and Peter Benjamin Lewis, its 61-year-old chairman, president, and chief executive. Progressive, on the one hand, is a prodigiously growing, solidly successful stock market standout, with a cool, we've-got-it-all-together personality. Lewis, on the other hand, is a total eccentric--though that description hardly goes far enough in capturing either his unique style of managing, or of living. The son of a Progressive founder, Lewis has been CEO now for 30 years. And were there to exist a Fortune 500 prize for outlandishness and riotous comment at the boss level, he would be odds-on to win.

Listen, for example, to this exchange that took place between Lewis and a prospective investor in their first minutes of meeting. Said the investor to the 6-foot-2, fit-looking Lewis: "I've looked at your stock very carefully. It's clear to me that this is a great company. But I also know that you are terribly important to it. So I have one big question: How's your health?"

"Well, I really don't know," answered Lewis in his agreeable, matter-of-fact way, "because I don't believe in doctors. But No. 1, I feel fine. No. 2, I swim a mile every day. And No. 3, I'm single, so I get laid all the time."

In a three-hour interview that took place recently at Lewis's art-filled Cleveland penthouse--his home since he was divorced 14 years ago--this writer did not manage to elicit quite the same wind-up declaration. But Lewis was obsessively candid about almost all other subjects, certainly including the remarkable success of Progressive and his wildly individualistic views about the way the world should be run. By self-classification both a "very liberal Democrat" and a libertarian--is that combo possible?--Lewis doesn't believe much in laws and rules, especially those that attempt to impose on people a code of behavior that is unenforceable. Though he makes his living from collecting auto insurance premiums, for example, he doesn't think drivers should be forced to buy insurance. For some, he says, among them those earning very little, it doesn't make sense--so why make them buy?

On another subject of close personal interest, he believes that romantic relationships in the office are going to occur no matter what the rules, and are perfectly okay just as long as they don't interfere with his most sacred goal, the efficient workings of Progressive. He has, in fact, danced around this thought in Progressive's annual reports, which are both as informative and oddball as Lewis himself. "Intraoffice romances just happen," he says, "and I've had them, both inappropriately and appropriately."

Among the acceptable kind, apparently, is a long-running though definitely nonbinding relationship Lewis has had with Janet Frieden, head of Progressive's travel department. And by the way, his ex-wife, Toby, works at the company four days a week, serving as curator of Progressive's large contemporary-art collection. The once-marrieds, who are parents of three grown children, are good friends.

Similarly, Peter Lewis remains on cordial terms with many of the executives he has fired--a society of large and ever-growing numbers. Says Lewis proudly: "I'm the best person to have been fired by or divorced from that I know." His reasoning: "I can put myself in the other guys' shoes. And I care about how they feel about me when we're not together, because I care about how I feel about them."

Lewis cares also about the good life for himself. He has thoughts of building a huge (25,000 square feet or more), insistently modern house in Cleveland but has so far spent five years noodling inconclusively with Los Angeles architect Frank Gehry over its design. That project is now shelved (not for the first time), and Lewis is making do with his Cleveland pad; additional apartments in New York City and Washington, D.C.; and a house in Aspen, Colorado.

Lewis acquired his Washington digs because (why is this not a surprise?) he was interested in a woman who lived in D.C. But he also visualized the apartment as a base for getting close to a Democratic President. To that end, he contributed heavily to the Dukakis campaign in 1988 and was a major donor to the Democrats during Clinton's run, giving more than $250,000. That kind of money got him a limousine ride in Cleveland with the candidate, during which Lewis helpfully offered his advice about the womanizing issue: "I told him that if there'd been, say, 27 women since he got married, he should just state that was the case, say it was 'juvenile behavior,' and put this problem in the past." After that, Clinton didn't seek out Lewis for further advice. Today Lewis says he's given up his ambitions of gaining political influence.

Friends--and others--attempting to describe the phenomenon that is Lewis ransack their vocabularies for the right words. Says a friend who knows him well and seems genuinely to like him: "He's a frame or two off the ordinary radar screen. He's a big, overgrown child. His threshold of embarrassment is very high. There's no way to jerk his chain because he doesn't have one. He's a rock star without any musical ability." And then a summation: "He's weird. That's it, weird."

And yet there is this essential fact: Peter Lewis is an extraordinary businessman, who in his three decades as CEO has taken Progressive from an industry gnat to a large, powerful competitor. In 1980, just 15 years ago, Progressive was the 48th-largest auto insurer in the country. Last year, when revenues hit $2.4 billion, it was No. 6. Numbers three through five in the industry, Farmers, USAA, and Nationwide, had better keep checking their rear-view mirrors. At the moment, State Farm, with $23 billion in auto insurance revenues, and Allstate, at $12 billion, seem too far in front to catch. But can Lewis imagine overtaking State Farm? "Yes," he says, looking thoughtful. "I can imagine that."

These aren't dreams fueled by fantasy. Financially, Progressive has the stuff to keep forcing the race. Soundly capitalized, as an insurer should be, it is also a star earner, making $274 million in 1994 and managing in that year, as in most, to return better than 20% on equity. The stock market has cheered: For the ten years ended in 1994, Progressive had an annualized total return--that is, stock appreciation plus reinvested dividends--of 27.3%, which ranked it 19th among the Fortune 500. Had you put $10,000 into Progressive stock when it went public in 1971 and held on, you would today have roughly $1.7 million in stock. As for Lewis, he owns 14% of the stock, worth just over $400 million.

Perhaps even more bizarre than this seeming paradox of a man and his company is the fact that he has documented in a book --often outrageous in its detail--both the story of how Progressive got so good and how Lewis himself became the Ted Turner of the insurance business. Called Progressive History, the book is technically unpublished, because Lewis says it does not yet meet his standards of quality. Nevertheless, he has sent it in its quasi-finished form to many, many people, including some former Progressive executives whose firing by Lewis is baldly described in its pages. Learning of the book, Fortune began asking around for it, and one day a photocopy arrived in the mail, sent by an anonymous donor. Thank you. The pages sent cover the period from 1937, when Progressive was founded, through 1993.

Forget the dull title. What Lady Chatterley's Lover was to 1920s literature, this book just may be to corporate histories. It is self-revealing beyond belief. In the late 1960s, for example, Lewis shared lunch with a female Progressive employee and "felt overwhelmed by the need to have an extramarital experience." Was she willing, he asked, to go to a motel and do it with him? "She was and we did," he writes. Somewhat later, though possibly not as a result, Lewis turned to psychiatric therapy, "beginning a lifetime of intense introspection" that focused unremittingly on one issue: "my not being interested in or able to achieve [a] loving, monogamous, committed relationship with a woman." Maybe that was because he was giving his all at Progressive. In one passage, Lewis describes his then-office--"a palatial penthouse designed to reflect and indulge my hedonism and appreciation of contemporary art"--and says his decision to hold a particularly important business meeting there was a way for him to "show off my success, symbolize my position, and emphasize my ample supply of testosterone."

Though those passages do not suggest a man seeking to hold anything back, the book may have an omission of note. Nowhere is there mention of a habit some people claim Lewis has: the heavy use of marijuana. Says one person who has been around him a lot: "He is a functioning pothead."

Since possession of marijuana is illegal in the U.S. --though many people argue that it should not be--and since alcohol and drugs are issues for auto insurers, the question of whether Lewis has a marijuana habit can't easily be dismissed as irrelevant. Given both his frankness and his related reputation for absolute honesty, direct inquiry about this matter seemed logical. So in a phone interview, Fortune asked the threshold question: "We hear that you are a user of marijuana. Is that right?" He didn't choose "no" as an answer but went instead to "I'm not going to comment." Later he called to remind us that a "no comment" does not amount to an affirmation.

Whatever the reality, Progressive cannot easily be discerned to have suffered. One person who avows Lewis to be a heavy user of pot hurries on to laud his business accomplishments as well, while wryly recalling President Lincoln's rebuff to certain advisers who complained to him of General Grant's drinking habits: "You just tell me the brand of whiskey Grant drinks--I would like to send a barrel of it to my other generals."

Without question, Lewis is completely dedicated to making Progressive a great company, and he also brings some enormous abilities to the job. When channeled into business, Lewis's unorthodoxy spins out as creativity. He is an instinctive challenger of assumptions and a constant generator of ideas--and yes, a good number of those must be immediately and forcefully flattened, volunteers Progressive's chief financial officer, Charles Chokel, with a smile. Beyond the vision are serious analytical and quantitative abilities, as well as a perfectionist's passion for testing and for measuring performance. "We measure everything," says Lewis, dramatically stretching out the word.

Lewis also seems to possess a skill for extracting superb work from the people below him--obviously not including those departed. He is an absolutist about untiring effort, a point he hits colorfully and memorably in speeches he gives to new claims adjusters brought in to Cleveland for training. "I'm going to tell you how to succeed," Lewis says to them, his voice dropping conspiratorially as he describes the moment. "It's so simple. There are 50 of you out there--and you're beautiful, every one of you is beautiful--and you're between 23 and 27, and you've got a college degree, and you've had one other job, and you're absolutely the handsomest people I've ever seen. And as the years go on, there is just one thing that will matter. The thing that will differentiate you is who will work the hardest."

When Wall Street analysts look at this improbable package--the personal eccentricities of Lewis arrayed against his perfectionism and the incontestable success of his business--some don blinders and others come on like Lincoln talking about Grant. Thomas Sargent of Conning & Co. says that in the insurance business, conventional thinking tends to produce conventional returns, while the real rewards go to companies that "think about the world differently." In his opinion, that's the Peter Lewis payoff.

As an insurance executive, it needs to be noted, Lewis has one big, and self-acknowledged, limitation: absolutely no expertise in investments nor any skill in landing and keeping an investment chief who might serve as his right arm. Lewis's worst disappointment on this front involved Alfred Lerner, now 62, a successful Cleveland businessman who, upon Lewis's ardent bid for his services, became chairman of Progressive and ran its investments from 1988 into 1993. Lewis had a kind of idolizing crush on Lerner, but nonetheless eventually sent him packing from Progressive because they fell to arguing about almost everything (and because the tension of it all caused Lewis to suffer sneezing jags).

Summing up the Lerner years in his book, Lewis described them as evolving "like a classic romance: introduction, friendship, seduction, marriage, joy, accomplishments, problems that festered, irritation, and then an emotionally agonizing separation." Even today Lewis's comments about Lerner remain remarkable: "Al Lerner is a standoffish, supercilious, dominating kind of guy, who in my view is absolutely lovable and adorable."

Well, sure--and, if nothing else, such comments erase all doubts that Lewis is in any way a linear thinker. Yet in that part of the company identifiable as operations, Lewis has in the 1990s employed his peculiar brand of thinking to great effect. He has drawn exceptional help from his executives, starting with Progressive's chief operating officer, Bruce W. Marlow, 46, and, under unusual business pressures, has changed just about everything in the company's kit--its attitudes toward costs, its distribution methods, and its product line.

Historically, Progressive has filled a niche: the sale of "nonstandard" auto insurance, bought typically by drivers with a history of accidents, perhaps caused by substance abuse. Many insurers won't cover that kind of driver at all. Progressive loves to do it--at a price. It is an acknowledged master at pricing high-risk policies, bought, say, by an unmarried 22-year-old Texas dude who drives a green Corvette and cracked it up recently while totally bombed.

Nonstandard policies account for only about 15% of the total auto insurance market, and for many years the industry's leaders largely ignored this corner of the business, allowing Progressive to work it aggressively. The company specialized in a top-quality claims service and worried not at all that it was a high-cost operator, a luxury it could afford knowing that its customers, short of alternatives, would pay up for policies. And in most years the company hit the tough targets that Peter Lewis demands of it: an underwriting profit (in contrast to the underwriting losses that most auto insurers run up); a return on equity that is at least 15 percentage points above the rate of inflation; and growth in written premiums that is at least that high also.

But in the mid-1980s, giant Allstate, looking around for growth in its essentially mature market, finally focused on how much money Progressive was making in its nifty niche and within a couple of years whipped by Progressive in nonstandard business. That was a foghorn wake-up call for Lewis. A second blast came from Proposition 103, an initiative passed by California's voters in 1988. Prop. 103 eventually cost Progressive $50 million in refunds, established a tough new regulatory climate in this hugely important state, and generally sent Lewis into a panic. He worried that similar uprisings might sweep the country. His libertarian soul also recoiled at the idea of Progressive having to refund premiums that he considered its legitimately earned property.

But then, egged on by his Princeton classmate Ralph Nader, Lewis focused on a brain-rocking thought: Suppose that California voters were right in believing auto insurance a hateful, overpriced product? On a more pragmatic front, he asked himself and his troops just how high-cost Progressive could compete with Allstate, when that rival's cost structure--incorporating a captive-agent system that permitted relatively low distribution expenses--was so much more favorable.

Lewis then introduced Progressive to a rebuild-this-wreck period, achieving a transformation, says one competitor, "that makes you realize just how good Pete is." Insurers measure their efficiency by an "expense ratio" that expresses operating costs (not including claims and related expenses) as a percent of earned premiums. Allstate's expense ratio in 1988 was 24.1% and Progressive's was a sky-high 33.2%, a differential that guaranteed Progressive could not match Allstate's prices. By last year Allstate had whittled its ratio to 23.6%. But Progressive had pulled off a near miracle, getting down to 22.4%, an improvement of nearly 11 percentage points.

"We'll cut still more," says COO Marlow, a fanatic about details who brings reality to Lewis's claim of being a "good delegator." Marlow, a Harvard MBA, is also a rare bird at Progressive in that he is a survivor of a period in the late 1970s when Lewis was on a kick of bringing in dozens of graduates from top business schools and immediately flooding them with big responsibilities. Most of those MBAs have since left, many sacked by Lewis--their belated reward being that they have been able to read in Lewis's book precisely how they fell short. Lewis says, however, that the best of the MBAs are still around and that Marlow, for one, is a highly creative "genius."

So we have Lewis, who's creative, and Marlow, who's that plus detailish, and the combination has proven to be nothing short of spectacular, especially in the 1990s, when the two have teamed up to launch revolutionary programs aimed, oxymoronically, at bringing "delight" to the two most painful experiences of being an insurance customer: buying a policy and seeking resolution of a claim. It seems to be working (see box).

So where, with this wild card named Lewis, will it all lead? What will Progressive look like in the future--say, five years down the road? Lewis says the company will have remained primarily a personal-lines insurer, will probably have added homeowners' insurance to its line, and above all will have met its financial objectives. If Progressive does that, he says, "it will be because we have revolutionized auto insurance."

Lewis himself has no retirement date in mind and shows signs of intending to stay CEO indefinitely. But the Progressive board, he says, would like to see some succession plans firmed up. He has thought about bringing in an outsider--including one executive, Richard Haverland, whom he fired 12 years ago. And within the company, he says, are maybe ten to 12 executives with the stuff to be CEO, including Marlow and at least one woman, Moira Lardakis, 43, president of the company's Ohio division. Lewis loves the idea of having a female prospect--"I'm an admirer of women in every sense of the word"--and exults generally over how good his CEO candidates are: "They are really --there are women in the group, so I can't say it-but one could say they are really studs."

The whole subject, of course, raises a large question: Is Lewis essential to Progressive? Answering, his executives --those studs--are generous and convincing in their praise of Lewis, but argue unsurprisingly that he has built a Progressive culture that would endure if he were gone. One outsider who agrees is Francis Gouillart, senior vice president of Gemini Consulting, who has studied Progressive closely and believes that it has developed a team of executives who could keep the company moving briskly along the path Lewis has set.

Truthfully, it is unknowable whether Progressive could thrive without Lewis. He is linked inextricably and almost mystically to the company, just as the institutional investor suggested when he asked, "How's your health?" So Progressive's shareholders should just hope Lewis keeps swimming his mile a day. As for those other lifestyle things, the shareholders had better accept them or sell.