Artificial Intelligence (AI) has the potential to significantly advance scientific discovery by finding solutions beyond human capabilities. However, these super-human solutions are often unintuitive and require considerable effort to uncover underlying principles, if possible at all. Here, we show how a code-generating language model trained on synthetic data can not only find solutions to specific problems but can create meta-solutions, which solve an entire class of problems in one shot and simultaneously offer insight into the underlying design principles. Specifically, for the design of new quantum physics experiments, our sequence-to-sequence transformer model generates interpretable Python code that describes experimental blueprints for a whole class of quantum systems. We discover general and previously unknown design rules for infinitely large classes of quantum states. The ability to automatically generate generalized patterns in readable computer code is a crucial step toward machines that help discover new scientific understanding -- one of the central aims of physics.