Resumen
Probabilistically checkable proofs (PCPs) are arguably fascinating objects. They offer a certain robustness to the logical process of verification that may not have been suspected before. While the process of proving and verifying theorems may seem of limited interest (say, only to mathematicians), the authors stress that the notion of a "convincing" argument/evidence applies much more broadly in all walks of life. PCPs introduce the fascinating possibility that in all such cases, the time taken to assess the validity of the evidence in supporting some claims maybe much smaller than the volume of the evidence. The goal of this article is to mainly highlight the notion of a PCP, and its utility in computational complexity. One of the somewhat strange aspects of PCP research has been that even though the existence of PCPs seems to be a "positive" statement (verification can be vely efficient), its use is mostly negative (to rule out approximation algorithms).