How can mathematics “solve” cancer?

The word “cancer” was inspired by the similarity to the shape of a crab, Photo by Jacob Hinkston on Unsplash

Recently, I took part in a highly motivating workshop one of whose aims was to draw more mathematician’s attention to cancer dormancy, the looming danger that a patient’s cancer will return an unknown time after treatment. Cancer is a notoriously difficult disease and strictly speaking, not just one disease but a disease unique to each patient, hinting at that an abstract, pattern-finding mathematical approach may be called for. The budding field of mathematical oncology is addressing this need: what has been the progress so far?

Motivating the problem

Cancer ranks as a leading cause of disease-related death globally. The World Health Organization lists it as the sixth most common cause of mortality worldwide, resulting in nearly 2 million deaths annually. In the United States and the European Union, cancer is the second most common cause of disease-related death, surpassed only by cardiovascular diseases such as stroke.

Cancer has been recognized as one of the most difficult medical problems since ancient times. Indeed, the word “cancer” originates from the Greek physician Hippocrates (460–370 BC), because when he dissected a women’s breast cancer, the tendrils the cancer was forming in the (healthy) breast tissue reminded him of the legs of a crab (note that is was not a single cancer cell that reminded him of a crab, but the…