The ability to dynamically image, using fluorescent probes, neural activity and other fast physiological events in living brains has begun to revolutionize neuroscience. The fundamental limitation of optical scattering in living tissue, which limits fast imaging to shallow depths, has attracted much attention from hardware inventors, who have developed a diversity of strategies -- ranging from multiphoton laser-scanning microscopy, to adaptive optics approaches that attempt to invert tissue scattering. However, imaging extended volumes of brain tissue, at rates that keep up with fast events like action potentials, remains a challenge. We here propose to invert the problem, and make the living brain, itself, more transparent. By developing chemicals that safely and efficaciously smooth out refractive index inhomogeneities that scatter light, we will enable observation of high speed neural processes throughout extended volumes, e.g. entire cortical microcircuits (and potentially, across arbitrary scales). In this way, neuroscientists will be able to analyze the neural activity patterns across circuits underlying complex phenomena like emotions, decisions, and actions, and that contribute to disease states. Beyond neuroscience, our technology may broadly improve the observation of high-speed physiological events in the living body, of importance to immunity, development, cancer, and other parts of biology and medicine.