A mathematical model is a set of mathematical formulas that mimics the behaviour of the studied system. It allows us to learn about the system in ways that direct measurements cannot achieve. For instance, we can simulate how the system would behave under different boundary conditions or predict its future state. Models can be constructed in various ways: the extreme cases are constructing it from fundamental natural laws describing the behaviour of system components, and treating the system as a black box and seeking a formula that emulates its behaviour, disregarding the system’s true nature.
I prefer modelling systems that are more related to the natural aspects of our planet than to society or technology (although I avoid competing with meteorologists in areas where they excel). Modelling out of curiosity to learn about the system being studied resonates with me more than modelling for system control or simply to predict future states. My recent experiences lean more toward data-driven modelling (machine learning) than first principle modelling. If you notice an alignment with your interests, even if only partial, feel free to check if I would be a suitable mentor for you.