# Shing-Tung Yau

> American mathematician from Hong Kong

**Wikidata**: [Q334760](https://www.wikidata.org/wiki/Q334760)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Shing-Tung_Yau)  
**Source**: https://4ort.xyz/entity/shing-tung-yau

## Summary

Shing-Tung Yau is an American mathematician from Hong Kong renowned for his groundbreaking work in differential geometry and mathematical physics. Born on April 4, 1949, he is best known for proving the Calabi conjecture, which led to the development of Calabi-Yau manifolds—geometric structures that play a central role in string theory. Yau has received numerous prestigious awards, including the Fields Medal (1982), the Wolf Prize in Mathematics (2010), and the Shaw Prize (2010), and is a member of multiple national academies of sciences including the National Academy of Sciences (USA), Chinese Academy of Sciences, Academia Sinica, and the Russian Academy of Sciences.

## Biography

- **Born**: April 4, 1949
- **Nationality**: American, Hong Kong
- **Citizenship**: United States, Hong Kong
- **Education**: Chinese University of Hong Kong (CUHK), University of California, Berkeley, and additional institutions including Zhejiang University
- **Known for**: Proving the Calabi conjecture, developing Calabi-Yau manifolds, work in differential geometry and mathematical physics, SYZ conjecture
- **Employer(s)**: Harvard University, Stanford University, University of California Berkeley, University of California San Diego, Stony Brook University, Zhejiang University
- **Field(s)**: Differential geometry, Mathematics, Mathematical physics

## Contributions

Yau's most celebrated achievement is the proof of the Calabi conjecture in 1976, which he accomplished during his time at Stanford University. This proof established the existence of Riemannian metrics with prescribed Ricci curvature on compact Kähler manifolds, a result that was previously conjectured by Eugenio Calabi in 1954. The Yau's solution to this problem led directly to the development of Calabi-Yau manifolds, which have become fundamental objects in string theory and algebraic geometry. These compact complex manifolds with SU(n) holonomy provide the geometric framework for compactifying extra dimensions in superstring theory, connecting pure mathematics to theoretical physics in a profound way.

Beyond the Calabi conjecture, Yau made foundational contributions to the SYZ conjecture (Strominger-Yau-Zaslow conjecture), which proposes a geometric explanation for the mirror symmetry phenomenon in string theory. His work in minimal submanifolds, particularly the proof of the positive mass theorem in general relativity, demonstrated deep connections between geometric analysis and theoretical physics. Throughout his career, Yau has published extensively on topics including Kähler-Einstein metrics, Hermitian-Einstein metrics, Yang-Mills connections, and the geometry of K3 surfaces.

Yau has held professorial positions at some of the world's most prestigious universities, including Harvard University, Stanford University, University of California Berkeley, University of California San Diego, Stony Brook University, and Zhejiang University. He has supervised numerous doctoral students who have themselves become leading mathematicians, creating a substantial academic lineage in geometric analysis.

## FAQs

**What is Shing-Tung Yau best known for?**
Shing-Tung Yau is best known for proving the Calabi conjecture in 1976, which led to the discovery of Calabi-Yau manifolds—geometric structures that have become essential in string theory and algebraic geometry.

**What awards has Shing-Tung Yau received?**
Yau has received numerous prestigious awards including the Fields Medal (1982), Wolf Prize in Mathematics (2010), Shaw Prize (2010), National Medal of Science, Crafoord Prize, MacArthur Fellowship, Guggenheim Fellowship, and the Oswald Veblen Prize in Geometry.

**Where has Shing-Tung Yau worked?**
Yau has held positions at Harvard University, Stanford University, University of California Berkeley, University of California San Diego, Stony Brook University, and Zhejiang University.

**What is the Calabi-Yau manifold?**
A Calabi-Yau manifold is a Riemannian manifold with SU(n) holonomy, discovered through Yau's proof of the Calabi conjecture. These manifolds are used in string theory to model compact extra dimensions.

**Is Shing-Tung Yau a member of any national academies?**
Yes, Yau is a member of the National Academy of Sciences (USA), Chinese Academy of Sciences, Academia Sinica (Taiwan), Russian Academy of Sciences, and the American Academy of Arts and Sciences.

**What is the SYZ conjecture?**
The SYZ conjecture, named after Strominger, Yau, and Zaslow, is a mathematical conjecture that provides a geometric explanation for mirror symmetry in string theory.

## Why They Matter

Shing-Tung Yau's work fundamentally transformed the relationship between mathematics and theoretical physics. His proof of the Calabi conjecture resolved a major open problem in complex differential geometry and simultaneously provided physicists with the exact geometric structures needed for superstring theory. Without Yau's work, the mathematical framework for string theory's extra dimensions would not exist in its current form.

Yau's influence extends far beyond his specific theorems. He essentially created the field of geometric analysis, developing techniques that have been adopted by generations of mathematicians. His work on the positive mass theorem in general relativity provided rigorous mathematical foundations for questions about the stability of spacetime. The Calabi-Yau manifolds have become indispensable tools not only in string theory but also in algebraic geometry, where they connect to topics like mirror symmetry, moduli spaces, and enumerative geometry.

His academic lineage is remarkable—through his doctoral students and their students, Yau has influenced a substantial portion of the current generation of researchers in differential geometry and mathematical physics. Many of his students have become leading mathematicians at major institutions worldwide, continuing his approach of bridging pure mathematics and theoretical physics.

## Notable For

- Proving the Calabi conjecture (1976), leading to the discovery of Calabi-Yau manifolds
- Recipient of the Fields Medal (1982)
- Recipient of the Wolf Prize in Mathematics (2010)
- Recipient of the Shaw Prize (2010)
- Recipient of the National Medal of Science
- Recipient of the Crafoord Prize
- Member of the National Academy of Sciences (USA)
- Member of the Chinese Academy of Sciences
- Member of Academia Sinica (Taiwan)
- Member of the Russian Academy of Sciences
- Member of the American Academy of Arts and Sciences
- Developer of the SYZ conjecture
- Contributions to the positive mass theorem in general relativity

## Body

### Early Life and Education

Shing-Tung Yau was born on April 4, 1949, in Shantou, Guangdong, China, but grew up in Hong Kong. His family background and early education in Hong Kong shaped his mathematical development. Yau pursued higher education at the Chinese University of Hong Kong (CUHK), where he received his undergraduate degree. He later continued his studies in the United States, attending the University of California, Berkeley for his graduate studies, earning his Ph.D. under the supervision of Chern Shiing-Shen. He also has connections to Zhejiang University, where he received an honorary doctorate.

### Academic Career and Positions

Yau's academic career has spanned multiple prestigious institutions. After completing his Ph.D., he held positions at Stanford University, where he proved the Calabi conjecture, and at the University of California, Berkeley. He later became a professor at Harvard University, where he held a distinguished chair. Yau has also held positions at the University of California San Diego, Stony Brook University, and Zhejiang University. His career has been characterized by movement between leading American and Chinese institutions, reflecting his status as a bridge between Western and Eastern mathematical traditions.

### The Calabi Conjecture and Calabi-Yau Manifolds

The proof of the Calabi conjecture stands as Yau's most celebrated achievement. Eugenio Calabi had proposed in 1954 that for any compact Kähler manifold with a positive first Chern class, there exists a unique Kähler-Einstein metric. This conjecture was a central problem in complex differential geometry for over two decades. In 1976, Yau proved the conjecture by constructing solutions to the complex Monge-Ampère equation, establishing the existence of these special metrics.

The implications of this proof extended far beyond geometry. Physicists working on superstring theory immediately recognized the importance of Yau's result. String theory requires extra dimensions, and the Calabi-Yau manifolds provide exactly the type of compact, complex geometric structures needed. These manifolds have SU(n) holonomy and serve as the geometric background for compactifying the ten-dimensional superstring theory to four-dimensional spacetime. This connection between pure mathematics and theoretical physics represents one of the most profound interdisciplinary achievements in modern science.

### The SYZ Conjecture and Mirror Symmetry

Following his work on the Calabi conjecture, Yau continued to contribute to the interface between geometry and physics. Together with Andrew Strominger and Eric Zaslow, he formulated the SYZ conjecture in 1996. This conjecture proposes a geometric explanation for mirror symmetry—a remarkable phenomenon in string theory where two different Calabi-Yau manifolds can give rise to the same physical theory.

The SYZ conjecture suggests that mirror symmetry can be understood through the behavior of special Lagrangian submanifolds and the dual torus fibrations. This work has influenced much subsequent research in both mathematics and physics, creating new connections between symplectic geometry, mirror symmetry, and string theory.

### Other Contributions to Mathematics and Physics

Yau's contributions span numerous areas of mathematics. His work on minimal submanifolds includes significant results about their existence and properties. In mathematical physics, his proof of the positive mass theorem in general relativity provided important insights into the mathematical foundations of spacetime geometry. He has also worked on the existence of Kähler-Einstein metrics on complex surfaces, Hermitian-Einstein metrics on vector bundles, and the geometry of K3 surfaces.

His research has influenced topics ranging from algebraic geometry to theoretical physics, with applications in quantum field theory, supersymmetry, and M-theory. Yau's approach has consistently been to develop analytic techniques to solve geometric problems, creating tools that have been widely adopted by other mathematicians.

### Academic Leadership and Influence

Throughout his career, Yau has held leadership positions and influenced the direction of mathematical research globally. His students and collaborators have formed a substantial academic lineage, with many becoming leading researchers in their own right. He has organized numerous conferences and workshops bringing together mathematicians and physicists.

Yau's affiliations with institutions reflect his international standing: he is a member of the American Mathematical Society, the National Academy of Sciences (USA), the Chinese Academy of Sciences, Academia Sinica (Taiwan), the Russian Academy of Sciences, and the Accademia Nazionale dei Lincei (Italy). He has received honorary doctorates from Zhejiang University and the Chinese University of Hong Kong.

### Awards and Recognition

The breadth of Yau's recognition demonstrates the exceptional impact of his work. In 1982, he received the Fields Medal, mathematics' highest honor, awarded at the International Congress of Mathematicians. He has since received numerous additional honors including the MacArthur Fellowship (1982), the Oswald Veblen Prize in Geometry (1981), the Guggenheim Fellowship, the National Medal of Science, the Humboldt Prize, the Wolf Prize in Mathematics (2010), the Crafoord Prize, the John J. Carty Award for the Advancement of Science, and the Shaw Prize (2010). In 2006, he received the Great Immigrants Award from the Carnegie Corporation of New York, recognizing immigrant contributions to American life.

### Legacy

Shing-Tung Yau's legacy encompasses both specific mathematical results and a broader approach to mathematical physics. His proof of the Calabi conjecture remains a cornerstone of complex geometry, while Calabi-Yau manifolds have become fundamental objects in theoretical physics. The SYZ conjecture continues to inspire research in mirror symmetry and related areas.

His influence extends through his students, his publications, and the new techniques he developed. Yau's work demonstrated the power of analytic methods in geometry and established differential geometry as essential to modern theoretical physics. The connection between mathematics and physics that his work exemplifies has become a model for interdisciplinary research. Without Yau's contributions, the mathematical structure of string theory would be fundamentally different, and our understanding of geometric analysis would be far less developed.

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