Tim Cooks takes over Apple as CEO, following in the steps of iconic leader Steve Jobs. (Claudio Villa/GETTY IMAGES)

This piece is part of this week’s On Leadership roundtable exploring Tim Cook’s succession of Steve Jobs as CEO of Apple, and how to follow in the footsteps of an icon.

It’s tough as a new CEO to fix a troubled company suffering under a legacy of misleadership, as Meg Whitman is about to learn at Hewlett-Packard. But it’s even tougher to follow in the footsteps of an icon—a leader who didn’t just win big with the company, but changed the industry’s game.

Just ask James Parker, who took over Southwest Airlines after larger-than-life Herb Kelleher and stepped down after three underwhelming years. Or ask Jeffrey Immelt, who has spent a decade as CEO of General Electric but still can’t escape the shadow of Jack Welch, Fortune’s “Manager of the Century” for the 20th century.

So it’s fair to say that Tim Cook, Steve Jobs’s successor at Apple, is stepping into the toughest job imaginable—taking over for everyone’s choice as “Manager of the Century” for the 21st century. How should Cook lead in the footsteps of such a legend?

First, stay fiercely loyal to the strategic ideas around which Steve Jobs has built Apple and its unprecedented track record of success. When most of us think of Apple, we think of its alluring gadgets and graceful retail spaces. But as Silicon Valley futurist Paul Saffo puts it, “Apple has beautiful products, but what Jobs has been building is a company whose legacy is ideas.” Those ideas involve the power of elegant design, the interplay between hardware and software, and the vital role of technology “ecosystems” in reshaping the logic of how entire industries work. Simply put, there is no room for compromise or second-guessing on the point of view that has separated Apple’s business plan and product roadmap from every other company.

Second, stay true to yourself. Don’t try to channel Steve Jobs’s individual performance at public events and product unveilings (his so-called “reality distortion field”) or his borderline tyrannical persona inside the company. Sure, Apple’s 50,000 employees are fanatical in their devotion to the greatest American innovator since Thomas Edison. But with Jobs’s perfectionist style came a certain mental exhaustion, physical fatigue and even fear within the ranks that “Tim being Tim” (as opposed to “Tim trying to be Steve”) could go a long way to relieve.

Finally, use this moment of leadership succession to recalibrate how Apple (and all of us who play such close attention to Apple) think about the idea of leadership itself. There’s no doubt that Steve Jobs will go down as one of the most creative, visionary, high-impact leaders of his generation—or any generation. But his genius has been of a uniquely personal kind: the “smartest-guy-in-the-room” syndrome that is deserved in his case, but is decidedly underserved among so many CEOs who overrate the power of their intellect or the acuity of their vision. The reason so few leaders at other companies come close to Steve Jobs’s record is that they share many of the most demanding and controlling features of his personal style, but little of his insights and creativity.

Tim Cook has a chance to show the world that you don’t need to be as smart and visionary as Steve Jobs—who is?—to lead the company that Jobs built. Indeed, the best leaders I know don’t want the job of thinking for everyone else. They understand that if they can tap the hidden genius inside the organization, and the collective genius outside the organization, they will create ideas much more powerful than what even the smartest individual leader could come up with on his or her own. In other words, nobody alone is as smart as everybody together.

The folks at IBM, who just celebrated the company’s 100th anniversary, call this new leadership mindset “humbition”—the subtle blend of ambition and humility that drives the most successful leaders at their company.

Humility was never a big part of the Steve Jobs leadership repertoire—and that worked out fine for him, his company and his customers. Yet what Tim Cook has the opportunity to demonstrate, to audiences inside and outside of Apple, is that he can be as committed as his predecessor to beautiful products, elegant designs and transformational strategies, without pretending that he can wield the lone genius of his predecessor.

In that sense, the great leadership opportunity facing Tim Cook is to extend the legacy of Steve Jobs, by showing that you don’t have to be Steve Jobs to maintain his record of innovation and imagination. Here’s wishing him luck.

William C. Taylor is a cofounder of Fast Company and the author of Practically Radical. Follow him on Twitter @practicallyrad.

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William C. Taylor: Tim Cook, here’s how to lead Apple

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