I've asked this question on MathSE, but apparently people over there don't like philosophy.
Seven Bridges of Koenigsberg is the problem whose solution (by Euler) gave a rise to graph theory and (later) topology. The goal is to determine whether there exists a walk through the seven bridges in Koenigsberg crossing every bridge exactly once. Eveyrone knows it, as it is mentioned possibly in every univeristy mathematics course covering elements of graph theory.
Leonhard Euler came up with the following intuition: The physical map of the city, the exact location of the bridges, distances don't matter. All that matters mathematically is just the list of which regions are connected by bridges.
We could easily imagine a wrong mathematical model of this problem. Yet, it's commonly believed we can accurately describe the problem using graph theory and provide a solution within this theory, that correctly answers the original problem. How to ensure that a mathematical theory can describe a given problem correctly? What criterion to use here? Is it okay if nobody finds any flaw in the mathematical model within one week? One month, year, ten years, one hundred years, a thousand years? There might come a counterexample tomorrow, showing that this is NOT the right model of the problem. Intuition often deceives us.
What do mathematicians and philosophers could say about it?
Some may argue that it's unthinkable it may be wrong. Yes, it's a very easy, natural transition from informal problem to its mathematical description. But we can give examples of more difficult problems to model mathematically that aren't that obvious. I've taken a decision support systems course. We took problems expressed in natural language and tried to model them and find an algorithmic solution. How 'correct' were the models we've come up with? Up to which point in complexity of problems should we trust our thoughts, imagination and intuition?