In this work we introduce XLuminA, an original computational framework designed for the discovery of novel optical hardware in super-resolution microscopy. Our framework offers auto-differentiation capabilities, allowing for the fast and efficient simulation and automated design of entirely new optical setups from scratch. We showcase its potential by rediscovering three foundational experiments, each one covering different areas in optics: an optical telescope, STED microscopy and the focusing beyond the diffraction limit of a radially polarized light beam. Intriguingly, for this last experiment, the machine found an alternative solution following the same physical principle exploited for breaking the diffraction limit. With XLuminA, can we go beyond simple optimization and calibration of known experimental setups, opening the door to potentially uncovering new microscopy concepts within the vast landscape of experimental possibilities.