Dynamical control of cellular microenvironments is highly desirable to study complex processes such as stem cell differentiation and immune signaling. We present an ultra-multiplexed microfluidic system for high-throughput single-cell analysis in precisely defined dynamic signaling environments. Our system delivers combinatorial and time-varying signals to 1500 independently programmable culture chambers in week-long live-cell experiments by performing nearly 106 pipetting steps, where single cells, two-dimensional (2D) populations, or 3D neurospheres are chemically stimulated andtracked. Using our system and statistical analysis, we investigatedthe signaling landscape of neural stem cell differentiation and discovered "cellular logic rules" that revealed the critical role of signal timing and sequence in cell fate decisions. We find synergistic and antagonistic signal interactions and show that differentiation pathways are highly redundant. Our system allows dissection of hidden aspects of cellular dynamics and enables accelerated biological discovery.