In the 80’s Siu and Yau gave a proof of the Frankel conjecture in complex geometry stating that every compact Kähler manifold of positive holomorphic bisectional curvature is biholomorphic to the complex projective space. The same result was independently obtained in the same years by Mori using methods of algebraic geometry in positive characteristic. In this talk I will present the proof given by Siu and Yau that uses only differential geometry tools.