My talk is a brief account of the increasing body of evidence that line bundle cohomology can be computed in terms of analytic formulae. Our experimental results include spaces such as complete intersections in products of projective spaces (in particular Calabi-Yau threefolds), toric varieties, hypersurfaces in toric varieties and del Pezzo surfaces. Machine learning plays an important role in finding and generalising the analytic formulae. For certain surfaces, including all toric surfaces, we have obtained and proved the existence of topological formulae for all line bundle cohomologies. Time allowing, I will discuss the relevance of these formulae for string model building and other applications, such as the quantum Hall effect.