Peer Reviewer Returns Paper With Single Comment: 'Trivial'

A mathematics paper representing eighteen months of research has been returned from peer review with a single comment consisting of one word: "Trivial." The paper, submitted to the Annals of Pure and Applied Mathematics by Dr. Reginald Lemma and two co-authors, presents a 47-page proof of a generalization of a 1978 result in functional analysis. The referee report, received after a seven-month review period, contains no corrections, no suggestions, and no indication of which part is trivial. "The entire thing?" Lemma asked, staring at the report. "All forty-seven pages are trivial? The novel application of spectral theory in Section 4 — trivial? The three lemmas that took me six months to prove — trivial? Or is there one specific trivial step that I could have shortened, and the rest is fine?" The journal's editor, when contacted, confirmed that the report met the minimum requirements for a referee response, which are, evidently, that a response exists. "We ask referees to provide constructive feedback," the editor acknowledged. "'Trivial' is technically feedback. Whether it's constructive depends on your definition of construction." Lemma's co-authors have responded differently to the review. Dr. Anna Corollary has suggested revising and resubmitting to a different journal. Dr. James Hypothesis has suggested finding the reviewer and "asking them to demonstrate the trivial proof at the next conference, publicly, in front of everyone." Lemma has chosen a third path: he has added a footnote to the paper's introduction reading, "The results in this paper may appear trivial to experts in the field, in which case the authors invite said experts to provide the shorter proof, which we would gratefully cite." No shorter proof has been submitted. The paper remains under review at a second journal, where it has been for four months with no response. "Silence is better than 'trivial,'" Lemma reflected. "At least silence doesn't have an opinion."