Bridges in Mathematics

In this lecture I will give my own personal answer to the deeply aesthetical question, "Why are you fascinated by mathematics?". As with all academic disciplines, mathematics finds itself divided and subdivided into hyper-specialized areas of study, and each of these individual theories may have its own internal beauty. However, what I find most fascinating is when one can build a bridge between two of these seemingly isolated theories. I will attempt to share my appreciation for this phenomenon via some examples, in particular, via some bridges connecting the world of polytopes, coming from the world of discrete mathematics, to that of (symplectic) geometry. At a certain point, the numbers 12 and 24 will appear...