  Consider the graph that has as vertices all bitstrings of length $2n+1$ with
exactly $n$ or $n+1$ entries equal to 1, and an edge between any two bitstrings
that differ in exactly one bit. The well-known middle levels conjecture asserts
that this graph has a Hamilton cycle for any $n\geq 1$. In this paper we
present a new proof of this conjecture, which is much shorter and more
accessible than the original proof.
