1. It is time to look back, to see what has been achieved over the past 25 years. Powerful mathematical models are used in the optimization of radiation treatments, they are used to implement adaptive therapies to prevent resistances, they are used in medical imaging and cancer  diagnosis, and they are used as mathematical models in any of the hallmarks and enabling characteristics of Hannahan and Weinberg (2000, 2010, 2022). During the FieMO we will collect and showcase mathematical success stories. We invite participants to present cases where a mathematical model made a significant impact on cancer diagnosis and treatment. During the FieMO we will collect these success stories into a textbook, which will form a great resource for future research. 

 

2. It is time to look broadly on the impact on mathematical oncology on other disciplines. Not only has mathematical oncology impacted medical research, it has also a huge impact on mathematical and statistical sciences. As Fields is a mathematical institute, we will use the FieMO to highlight the mathematical aspects of our research. For example, the mathematical models of angiogenesis has stimulated the new area of biased reinforced random walks and the analysis of coupled hyperbolic and parabolic partial differential equations (PDEs). Optimization of treatments has initiated a full analysis of singular arcs in optimization schedules. Mathematical modelling was the first tool that allowed us to fully understand the development of treatment resistances based on genetic and epi-genetic effects. And detailed microscopic observations of moving cancer cells stimulated the analysis of kinetic transport equations, their qualitative behavior, and their scaling limits that lead to anisotropic diffusion. These are only a few examples where mathematical oncology has stimulated mathematics.

 

The well structured and uncompromisingly rigorous methods of mathematical modeling has a lot to offer for future developments in cancer research and treatments. Not only does it guide researchers in the right direction, it also, unceremoniously, tells us when something does not work, and why. At the FieMO we will highlight those connections and investigate new and open mathematical problems in this area.