"Wherever they may lead": Effective field theories in nuclear physics (Feshbach 2020 Prize Talk)*

Effective field theory (EFT) provides a paradigm to describe nature through the controlled expansion of observables in a small ratio of distance scales. I will relate our progress in deploying EFTs to make sense of striking features in the emergence of nuclear structure from the Standard Model of particle physics: pseudo-Goldstone bosons (pions) provide the long-range components of the interaction among nucleons, which are singular but renormalizable; few-nucleon systems are close to the unitarity limit where discrete scale invariance holds; nuclei heavier than the alpha particle often have cluster substructures; nuclear matter saturates at finite binding energy per nucleon and density; and nuclei offer a unique arena to test fundamental symmetries such as lepton number and time reversal.