String theory remains to date our best framework to construct a quantum
theory that unifies gravity and the other three fundamental forces of Nature.
Although it has emerged as a fantastic arena in which mathematics and physics
ideas constantly cross-fertilize, its credibility relies on the power of its testable
In this talk, I will review progress made since the defining work of Candelas, Horowitz,
Strominger and Witten in 1985 on Calabi-Yau string compactification, in the quest to
predict the mass of quarks and leptons, which mathematically requires the explicit
form of the Ricci flat metric on non-trivial Calabi-Yau manifolds.