In this talk I will describe some of our efforts in the area of translational medical imaging, and illustrate how mathematics and formalism play a fundamental role. I will start with our work on brain imaging, where we have developed entire analysis pipelines, going from fixing basic mathematical errors in the classical formulas of high resolution diffusion imaging (HARDI), all the way to studying gender and kinship in brain connectivity networks and to helping neuro-surgeons in deep brain stimulation procedures. I will then present some of our work on the analysis of the structure of HIV and other viruses with data obtained from cryo-tomography, a critical step in vaccine development. Additional applications for helping surgeons in the operating room will be mentioned as well.