Shortly before the iPad tablet went on sale last year, Steven P. Jobs showed off Apple’s latest creation to a small group of journalists. One asked what consumer and market research Apple had done to guide the development of the new product.

“None,” Mr. Jobs replied. “It isn’t the consumers’ job to know what they want.”

For years, and across a career, knowing what consumers want has been the self-appointed task of Mr. Jobs, Apple’s charismatic co-founder. Though he has not always been right, his string of successes at Apple is uncanny. His biggest user-pleasing hits include the Macintosh, the iMac, iBook, iPod, iPhone and iPad.

But as he takes a medical leave of absence, announced on Monday, the question is: Without him at the helm, can Apple continue its streak of innovation, particularly in an industry where rapid-fire product cycles can make today’s leader tomorrow’s laggard?

There is no near-term danger. Apple’s surging sales and profits have made it the world’s most valuable technology company, surpassing Microsoft last year. Apple reported on Tuesday that its profits and sales jumped more than 70 percent in the fourth quarter, exceeding high expectations.