Mathematical models are used everywhere in science and can even be turned inward to study mathematics itself. They are incredibly powerful tools that allow us to trade a problem we don’t fully understand for one we have a better handle on.
But using models is inherently tricky. We can never be certain that our model behaves enough like the thing we are actually trying to understand to draw conclusions about it. Nor can we be sure that our model is similar enough in the ways that really matter. So it can be hard to know that the evidence we collect from the model is truly evidence about the thing we want to know about.