Explore the intersection of quantum field theories and probability theory in this lecture on Yang-Mills theories for mathematicians. Delve into well-posed probabilistic questions that contribute to the rigorous construction of quantum field theories. Examine topics such as lattice gauge theories, quark confinement, mass gap, and gauge-string duality from a probabilistic perspective. Gain insights into the challenges of making sense of quantum field theories and their importance in modern mathematics. Learn about the potential impact of solving these probabilistic open questions on advancing our understanding of quantum field theories.