When Vikram Pandit became C.E.O. of Citigroup in December, he could have turned his office into a miniature version of the Guggenheim Museum if he had wanted to. Citi’s low-rise executive offices are strewn with objets d’art, the bounty from the companies around the world that Citigroup has conquered.

But there are no lavish decorations in Pandit’s office—no Andrew Wyeth watercolors, no Andy Warhol screen prints. Instead, there is a large sheet of graph paper, reverently framed. On it is a blizzard of numbers, words, and lines, bizarre and seemingly random, but with a kind of maniacal Rube Goldberg logic. It’s a fitting decoration, this being Citigroup—that staggering, lurching, insanely complex Rubik’s Cube of a financial-services company. And for Pandit, a kid from the sticks in provincial India who trained as an engineer and earned a Ph.D. in finance, the diagram is as resonant as a Norman Rockwell painting: It depicts the very first automatic-teller-machine system, inaugurated at Citibank in the early 1970s by his revered predecessor and current adviser John Reed. (View a slideshow of some of the executives who have shaped Citigroup.)

But while Pandit, with his master’s degree in electrical engineering, wins praise for understanding the guts of Citigroup’s myriad businesses, it’s not the scut work that is Citi’s problem at the moment. The bank’s issues now are more M.B.A. than Ph.D.: Has the company grown too big to make any sense? What’s the logic holding it together? What is the future of banking? Should Citigroup even survive intact?

And that, in turn, raises a much bigger question for Vikram Pandit: If dealmaker Sandy Weill was the C.E.O. for Citi’s era of empire building, and lawyer Chuck Prince helped dig the company out of a legal and regulatory mess, is Pandit, a shy academic who built a reputation on managing risk, the right person to reimagine the nation’s biggest financial-services company? Although Pandit’s understanding of the nuts and bolts of finance was key to his getting Citi’s top job—like every other bank in the world, Citi was terrified of its subprime exposure—the demands of the company have morphed and grown. Citi’s challenge is now more structural than operational, a management nightmare ill suited to a C.E.O. running his first-ever public company. “I don’t know who his godfather is,” says one former Citi banker. “He has the background to run a hedge fund, not a bank.”

The stock market has its doubts as well. Citi shares have declined consistently during Pandit’s tenure. While much of that slump can be blamed on dismal business in the financial sector in general, the company seems particularly vexed: Even a smaller-than-expected loss in the first quarter couldn’t boost the stock. Citi shares are down 42 percent on Pandit’s watch.

Citi’s quarterly loss, its third in a row, reflects a widely held view that the company remains uniquely exposed to an economy that is darkening, both in the U.S. and abroad. For instance, worsening consumer credit will hit Citigroup’s enormous credit-card business hard; its most recent quarterly results include a $2.5 billion charge to bulk up against coming credit losses.

Pandit and other senior Citi execs—including a handful who followed Pandit to the company from his previous post at Morgan Stanley—insist that they’re on course. Since almost 50 percent of Citi’s business is outside the U.S. and close to 35 percent is in emerging markets, Pandit says he is focusing on those areas for the company’s future growth. In fact, he talks more about growing in the future than winding his way out of Citi’s past, reciting his strategy in well-rehearsed cadences, reflecting a Pandit-era culture that favors neologisms like globality and clientcentricity.

“When you look at growth patterns, as the world goes from 6 billion to 9 billion people, the overwhelming majority of them are going to be in emerging markets,” Pandit says. “As Wayne Gretzky said, you need to ‘skate to where the puck is going to be, not to where it’s been.’”