Only 28, Bhargava has already impressed many leaders in his field. His Ph.D. advisor, Andrew Wiles (known for solving the centuries-old puzzle known as Fermat's Last Theorem), says Bhargava's thesis was one of the strongest he's seen in 20 years. "We are watching him very closely. He is going to be a superstar," says Peter Sarnak, a Princeton colleague. "He's amazingly mature mathematically. He is changing the subject in a fundamental way." For his Ph.D., which he earned last year, Bhargava extended some work of the legendary 19th-century German mathematician Carl Friedrich Gauss, work that forms the basis of modern algebraic number theory.

As with the tabla, so with numbers: Bhargava does math "intuitively," attacking problems from unexpected quarters when he finds he's making no headway with a straightforward approach: "Often I don't think about a particular problem at all, but just think, and the problem being solved emerges later." A recent accomplishment was an elegant proof of a far-reaching theorem. In 1770, Joseph-Louis Lagrange, perhaps the greatest mathematician of the 18th century, showed that every positive integer can be expressed as the sum of four squares. (Take the integer 10: l0 = 12 + 12 + 22 + 22. Or 30: It's equal to 12 + 22 + 32 + 42.) In 1916, self-taught Indian prodigy Aiyangar Srinivasa Ramanujan discovered 54 other such integer-generating formulas, called "quadratic forms." In 1993, William Schneeberger and John Conway at Princeton proved that if a quadratic form could generate the first 15 integers, it could generate all positive integers. They called this the Fifteen Theorem, but its proof was so intricate they never published it. Bhargava found a proof that was not only simpler but that also expanded the result so that it applied to the generation of any specific set of integers--such as all the odd numbers. Sounds complicated, but "mathematics," Bhargava says, "is about beauty"--about revealing hidden connections between numbers, shapes, and other mathematical objects. His preferred place to contemplate that beauty is in the woods near the Institute pond, where giants like Albert Einstein and John Nash also went to think. There, beneath the forest canopy, he builds on the work of his mathematical forebears.

PHOTO (COLOR): MANJUL BHARGAVA

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By Paul Hoffman