### Shing-Tung Yau

Born 4 April 1949 in Kwuntung (China)

Fields Medal (1982) for his contributions to the theory of differential equations, for the proof of the Calabi conjecture in algebraic geometry, for the proof of the positive energy theorem in general relativity theory (with Richard M. Schoen) and for his work on real and complex Monge-Ampére equations (algebraic geometry, mathematical physics).

Shing-Tung Yau is the fifth of eight children; his father was a professor teaching philosophy, economics and Chinese history. The year he was born, Chinese communists took over the government and his family fled to Hong Kong. Although his father found a job at a college, the salary was so low that the family had to live in a house with no electricity or running water. Inspired by his father, who died when Yau was 14 years old, Yau studied Mathematics at Chung Chi College in Hong Kong. Before graduating, a grant from IBM offered him the chance to go to the University of California in 1969, Berkeley, where, supervised by Shiing-Shen Chern, he wrote his doctoral thesis (Ph.D. 1971). Yau then spent a year at the private Institute for Advanced Study in Princeton. In 1972 he became an assistant professor at the State University of New York at Stony Brook. In 1974 he moved to Stanford University as an associate professor, and 1978 he became a full professor. After that, he returned as a professor to the Institute for Advanced Study (1980-1984). In 1984 Yau took up a professorship at the University of California in San Diego. In 1987 he became a professor at Harvard University where he remains today. In addition to his teaching and research activities, Yau is very interested in the development of mathematical education in China, where he supports several model projects.

In his spare time, he likes to read novels, poems and traveling. He is married and has two sons.

Shing-Tung Yau is the recipient of ten honorary doctorates and is a member of the National Academy of Sciences (1993), the Chinese (1995) and Russian (2003) Academies of Sciences, a member of the Italian Accademia dei Lincei (2005) and the India National Academy of Science (2008). He is a Fellow of the American Association for the Advancement of Science (1993) and member of the American Academy of Arts and Sciences (1982). He has also received numerous awards, including the Crafoord Prize of the Swedish Academy of Sciences (1994), the National Medal of Science from the United States (1998) and the Humboldt Prize (1991).

In the 1970s, physicist Shing-Tung Yau started to examine more closely certain mathematical objects whose existence had been suspected by the mathematician Eugenio Calabi in the 1950s. These were so-called complex manifolds, objects in complex spaces of many dimensions that appear close up like a (high-dimensional) complex plane. Calabi had postulated the existence of a certain class of manifolds.

While Calabi had considered those manifolds from a purely mathematical point of view, Yau had encountered them during his study of Einstein’s general theory of relativity. Einstein had shown that the gravitational attraction of masses corresponds to (and is explained by) a curvature of four-dimensional spacetime. Yau wondered whether empty space can also be curved and may therefore have a gravity – but without the forming of black holes in space, i.e. without singularities. In addition, he claimed that the spaces should be considered to be compact and complete. It was for the discovery that such spaces actually exist, among other things, that Yau received the Fields Medal.

Today the manifolds are called Calabi-Yau manifolds. They play an important role in string theory, some ‘flavors’ of which assume a world with ten dimensions: four dimensions for Einstein’s space-time and six dimensions that are ‘rolled up’ at any point in small Calabi-Yau manifolds.