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Marissa Mayer is sitting in URLs, the Yahoo! cafeteria, making the case for the future of a company that almost everyone in Silicon Valley views as doomed. Employees swarm around her, assembling rows of chairs for the afternoon’s FYI, a new weekly ritual where employees get to lob questions at Mayer and her executive team. It’s been a long July, in which Mayer’s one-year anniversary as chief executive officer was marked with an uninspiring second-quarter earnings report. Mayer prefers to focus on the company’s increase in Web traffic. She won’t give numbers but says it’s enough to erase the entire decline from the previous year. “Name another Internet giant that went through three years of decline and then started to grow again,” she says. “It’s a very good sign.”

When Mayer left her executive role at Google, she knew she was taking on what might be the hardest job in the Valley. Yahoo has had a lost decade, laboring under a series of failed product strategies and CEOs. It was a Web directory under founders Jerry Yang and David Filo, then a Web portal under Tim Koogle. Terry Semel made it a tech company with Hollywood pretensions, and, most recently, it languished under Carol Bartz and Scott Thompson as a dot-com relic known mostly for losing its top talent to competitors.

Now Mayer wants to transform it into a media company for the mobile age. She’s refocusing her 11,500-employee company on the kind of personalized, habit-forming content that people view on tablets and phones. That means new kinds of e-mail, messaging, and news applications, tailored to the location-aware and always-on nature of the mobile experience. “I hope that at some point we are looking at a world where mobile is a majority of our revenue,” she says.

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Brad Stone is a senior writer for Bloomberg Businessweek in Bloomberg’s San Francisco bureau. Follow him on Twitter @BradStone.