Abstract. It is hard to imagine our modern life without machine learning: AI algorithms help us navigate complex patterns of traffic and financial markets, diagnose medical problems, eliminate biases in judgment, and assist with many other complex tasks. Neural nets have been extensively used in data-intensive branches of experimental and observational sciences. Can they also help in 'pure' mathematical research? In this talk, intended for a broad audience, I will tell you two stories. One story is about the cutting-edge algorithms in machine translation, whereas the other involves questions that until recently were reserved for paper-and-pencil type derivations in pure mathematics. The confluence of the two leads to surprising new results and opens new doors for extending rigorous mathematical proofs into completely new domains that until recently remained entirely out of reach.