On different reliability standards in current mathematical research

Abstract

In this note I expose the reliability standards I share, and give examples of different reliability standards. Contents1. On different reliability standards 1 2. Reviewing peer review system 7 References 91. On different reliability standards By 'reliability' I understand validity and novelty of results. This is closely related, but not the same, as clarity. This is independent of value and importance of results.Reliability standards in mathematics change. E.g. a long time ago, oral proof was considered as reliable. As proofs gradually became more complicated, there appeared the understanding (and then the rule) that only written proof can be considered to be reliable or not (and so could constitute a fair claim for a result).

A short exposition of the Patak-Tancer theorem on non-embeddability of $k$-complexes in $2k$-manifolds

“…(The first question was raised by M. Tancer, see letter of May 8 below, and the other two turned out to be relevant.) Discussion of our actions in such practical situations reveals our understanding 'for whom research is done' [Sk21d]. Such an understanding is sometimes concealed, so we are grateful to M. Tancer for stating his opinion, in spite of it being partly different from ours.…”