In this talk, we will briefly introduce The Johnson–Lindenstrauss lemma. The lemma asserts that an n-point set in any Euclidean space can be mapped to a Euclidean space of dimension k=O(ε−2log(n)) so that all distances are preserved up to a multiplicative factor between 1−ε and 1+ε. The lemma has many proofs and has been wildly used in several fields. We will discuss one of the proofs.