Dr. Yau does not buy the emperor bit. Where, he protested recently, is his empire if he holds no political position and two of his most brilliant recent students are currently without jobs? “It’s just a perception as far as I can tell,” he said.

Image The much-honored mathematician Shing-Tung Yau. Credit... Rick Friedman for The New York Times

Certainly, his life is not all roses. In the last year alone Dr. Yau has been engaged in a very public fight with Beijing University, having accused it of corruption, and a New Yorker magazine article portrayed him as trying to horn in on credit for solving the Poincaré conjecture, a famous 100-year-old problem about the structure of space.

Everybody agrees that Dr. Yau is one of the great mathematicians of the age.

“Yau really is a genius,” said Robert Greene, a mathematician at the University of California, Los Angeles. “The quantity and quality of the math he has done is overpowering.”

But even his admirers say he has a political side. “As Shiing-Shen Chern’s successor as emperor of Chinese mathematics,” Deane Yang, a professor of mathematics at Polytechnic University in Brooklyn and an old family friend, wrote in a letter to The New Yorker, “Yau has an outsized ego and great ambition, and has done things that dismay his peers.” But, Dr. Yang said, Dr. Yau has been a major force for good in mathematics and in China, a prodigious teacher who has trained 39 Ph.D.’s.

Richard Hamilton, a friend of Dr. Yau and a mathematician at Columbia, said Dr. Yau had built “an assembly of talent, not an empire of people, people attracted by his energy, his brilliant ideas and his unflagging support for first-rate mathematics, people whom Yau has brought together to work on the hardest problems.”

A Barefoot Boy

That Shing-Tung Yau, born in 1949, had such potential was not always obvious. His family fled the mainland and the Communist takeover when he was a baby. As one of eight children of a college professor and a librarian, growing up poor without electricity or running water in a village outside Hong Kong, he was the leader of a street gang and often skipped school. But talks with his father instilled in him a love of literature and philosophy and, he learned when he started studying math, a taste for abstract thinking.

“In fact, I felt I can understand my father’s conversations better after I learned geometry,” he said at a talk in 2003.