Virology is at a crossroads. We can sequence genomes with high throughput, image the building blocks of life with unprecedented precision, and leverage AI technology to recreate missing structural information in our quest to understand biology at the nanoscale. Despite this, our ability to fully exploit this vast structural complexity in biotechnology is often hampered by a lack of mechanistic understanding of how these building blocks interact and function. Over the past two decades, I have developed the Mathematical Microscope, a unique combination of mathematical and computational approaches, to decipher the mechanisms by which viruses form, evolve and infect their hosts. In this talk, I will illustrate how the Mathematical Microscope enables us to better understand viral infections, and how this knowledge can be used to address challenges in bionanotechnology.