After a brief introduction to N=1 compatifications in String Theory, it will become clear why one needs to know explicit solutions to important PDEs, such as the Kaehler-Einstein metrics. This fact motivates the use of numerical methods to approximate solutions to such PDEs. Instead of using relaxation methods/finite differences I will explain how to use geometric quantization combined with many powerful results in complex analysis (Yau's theorem, DUY, balanced metrics...) to approximate transcendental objects by algebraic-geometric ones. I will finish by showing several examples of these techniques.