Sometimes you just don'\;t have enough time
to read an entire proof\, a brief scan is all you can afford.

\nProb
abilistically checkable proofs (PCPs)\, discovered 25 years ago\, guarante
e that even a brief scan will find an error if there \;is one. \;P
CPs have a variety of implications\, from hardness of computational optimi
zation all the way to secure cloud computing.

A PCP proof is cre
ated by taking a \;normal \; \;proof and splitting it
cleverly into fragments. \;The key is a theorem asserting that \;
locally consistent fragments must be coming from a globally correct proof.

\nRecently\, \;a connection was discovered between PCP &ldquo\;a
greement tests&rdquo\; and a concept from combinatorial topology\, \;s
o-called high-dimensional expanders. We will describe this connection and
some future potential directions that it suggests.