Publication Date
7-1-2024
Abstract
Many modern mathematical proofs are very complex, checking them is difficult; as a result, errors sneak into published proofs, even into proofs published in highly reputable journals. Sometimes, the errors are repairable, but sometimes, it turns out that the supposedly proven result is actually wrong. When the error is not noticed for some time, the published result is used to prove many other results -- and when the error is eventually found, all these new results are invalidated. This happened several times. Since it is not realistic to more thoroughly check all the proofs, and we want to minimize the risk of errors, it is desirable to come up with some methods to select the most suspicious proofs -- so that we can be more attentive when checking those. One such heuristic -- developed by mathematicians -- is that if subsequent results are too easy to obtain, the proof most probably has errors. This empirical heuristic works in many cases, which leads to a natural question: Why does it work? In this paper, we provide a possible explanation for this heuristic's success.
Comments
Technical Report: UTEP-CS-24-35