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There were once a young man and an older man. Their mathematics paths crossed and their names became merged into the long-lasting notion of CalabiYau manifolds. How did this happen? Why did Calabi make his famous conjecture? How did Yau prove it? Why are Calabi-Yau manifolds so important? And how are they used? All these and other questions take time to answer and real experts to explain. They can probably be best understood through the interactions between math and physics, and that’s where their true value lies. Although these questions have a long history, the future will undoubtedly bringmore questions and surprises regarding Calabi-Yau manifolds. Indeed, one must go back to more than 150 years ago, when Riemann introduced the concepts of Riemann surfaces and Riemannian metrics. His mapping theorem motivated people to endow each Riemann surface with a canonical Riemannian metric, and from there one of the greatest theorems in the history of mathematics, the uniformization theorem for Riemann surfaces and surfaces with Riemannian metrics, took shape. What happened to higher dimensional Riemannian manifolds? What kind of geometric structures

Calabi-Yau Manifolds at the Interface of Math and Physics