By age 5, Greene was already a typical prodigy, multiplying 30-digit numbers by 30-digit numbers on huge pieces of construction paper he'd taped together to accommodate his scrawling. His sixth-grade teacher (at I.S. 44, on the Upper West Side) sent him to Columbia with a note to the math department imploring someone, anyone, to please take him on and make use of his talents. At Stuyvesant High School, Greene was a Westinghouse finalist and won citywide math competitions four years in a row. He graduated in the top ten of his class at Harvard and won a Rhodes scholarship.

While he was at Oxford, Greene called up the man who would later become his postdoctoral adviser and politely pointed out an error in a paper he'd just published. ("I was surprised, then very impressed," says Shing-Tung Yau, the humbled professor.) At 30, Greene received a Young Investigator's Award from the National Science Foundation, and one year later, he won an Alfred P. Sloan Foundation fellowship. By then he was teaching in the Cornell physics department; and at 34, he was recruited by Columbia.

Columbia wanted Greene because both the math and the physics departments decided they needed a leading figure in string theory. (Because it is so intensely theoretical, string theory requires as much sophistication in math as it does in physics.) Greene, a switch-hitter, filled the bill perfectly. The university sweetened the deal with the prospect of letting him build his own small string-theory fiefdom, fortified by bright young graduate students and additional faculty.

Greene's legacy may amount to even more than a fiefdom; it could be a modest empire. He and several colleagues just received a $2.5 million grant from the National Science Foundation to restructure high-level courses in the Columbia math department, with the hope of broadening their application to physics.

Greene is making his way over to Room 831, where he teaches a quantum-field-theory class to students at both Columbia and Duke, with an assist from a video-teleconferencing hookup. He's late. On the way there, he runs into Samuel Devons, a stooped gray eminence with squinty eyes, a cane, and a long beard. Devons looks at Greene once, twice, then three times before recognizing him. "Oh," he finally says. "It's you! Hello." The two men chat briefly, then Greene hurries on to his class. "He's a real deep thinker," Greene explains.

In the classroom, there's a huge television monitor attached to a video camera sitting at the front of the room. Onscreen, he can see the grainy image of a professor and a couple of students waiting at Duke. Greene slings a microphone around his neck, steps in front of the TV, and waves hello to the people in Durham. "You're late," one of the grainy faces scolds. "I know," Greene replies. "But everyone's so late to this class. I guess I got lax." He hoists his foot up onto the table and starts tying his shoe. Meanwhile, his Columbia students are still trickling in. Almost all of them are men. Almost all of them wear T-shirts and flannel. Almost all of them have astonishing amounts of hair. Before long, the room is practically full.

"Greene is a messianic teacher," says Norman Christ, the chairman of the Columbia physics department. "When he teaches, as many people who can fit in the room will be there."

Students adore him. He makes physics funny, they gush, and he explains complicated ideas with diamond clarity. He also knows how to make people relax. "Sometimes," recalls Shani Offen, one of Greene's former students, "he would throw out questions in the middle of his lectures, like 'So then we add two and two and we get . . . Anyone?' "

Greene chats casually with a student at Duke for a few more minutes ("So, Chris, how's the Higgs mechanism?") before gazing up and asking if anyone has any questions. Silence. "Uh, is anybody here?" he asks. Smiles. Then he's off to the chalkboard, scribbling furiously, until he has completely surrounded himself with a confetti halo of numbers and Greek superscripts.