Many people question the usefulness of abstract math problems in real life. Personally, I question the usefulness of somebody’s definition of usefulness if they are even asking that question! Math is about more than building a better mouse trap; it is about deepening our understanding of everything. Yes, everything! Whether or not a certain piece of mathematics helps us understand phenomena in our life is not up to the math but to our imagination and own willingness to seek out structure and meaning.
Here is a delightful and fun example. The Parable of the Polygons. The game and simulation in this article are based on the work of a Nobel prize-winning economist, Thomas Schelling. Using very simple math and profound insight, we can clarify an issue of great importance in society: segregation. If most people only have a slight bias and actually like diversity, why is there so much segregation in the world? Play the game to see one way in which grand global effects arise from small local changes.