answering a question of paul erd\h{o}s, antal balog and endre szemerédi proved that a finite set $a \subset \mathbb{z}$ with many three term arithmetic progressions must have a long arithmetic progression. we will discuss the proof of this result which uses the balog-szemer\'{e}di-gowers theorem, freiman's theorem, and szemeredi's theorem on arithmetic progressions. no previous knowledge of additive number theory will be assumed.