Over the past several decades, advanced mathematics has discretely become an essential part of many aspects of our everyday life. Mathematics is at the heart of modern technologies, from mobile phones and GPS navigation, to internet security and airport metal detectors. However, no other technology has had a more beneficial effect on our lives than medical imaging, and in no other technology is the role of mathematics more pronounced and yet less appreciated by the general public.

X-rays, computed tomography (CT) scans, ultrasound, positron emission tomography (PET), magnetic resonance imaging (MRI), or more recent hybrid imaging modalities (PET-CT, MRI-PET, ultrasound and MRI, ultrasound and CT, MRI and CT) which combine the advantages of the fused imaging technologies synergistically, have changed the world and fundamentally improved the ability of medical professionals to diagnose and treat patients.

At the core of each modality is a mathematical model to interpret the measurements and a numerical algorithm to reconstruct an image.  In the context of the COVID-19 pandemic, a first step toward understanding new pathogens is to obtain an accurate image of the particle, and analysing how it interacts with proteins and other compounds which can eventually lead to the development of new vaccines and treatments.  Mathematics lies at the root of all of this and, in conjunction with researchers in life sciences, can better our lives.