Topology refers to the properties of a space that remain unchanged under continuous deformations such as bending or twisting. Often, topology on its own is sufficient to characterise the essential physics of a system and to organize large data sets. As machine learning supplies a modern tool for investigating Big Data, we apply this technology to explore aspects of quantum field theory connected to topology. Two case studies involve analysing correlations among knot invariants, which can be defined in terms of some of the simplest quantum field theories, and studying Calabi-Yau manifolds, which enable string theory constructions of the Standard Model of particle physics.