Mathematical Conversations

In primary school, I never got beyond adding integers and the questions have only been piling up since! What do sets of integers $A$ look like if they generate only a few sums with the elements of another set $B$? Meester Jaap (my primary teacher) can't be blamed for not having an answer as only in recent years this isoperimetric question (which dates back to antiquity and queen Dido of Carthage) is starting to be understood. Join me in exploring how the continuous world of the geometry of $\mathbb{R}^n$ is instrumental, but ultimately insufficient, in answering these questions.