Mathematics Editing and Proofreading Services

The proof is four pages of correct steps. Somewhere in the middle is the idea — the substitution, the auxiliary construction, the inequality that turns out to be sharp enough — and it is presented in the same tone as the routine verifications on either side. A reader who follows every line still leaves without knowing what made the theorem work.

We edit what mathematicians write — research papers and preprints, proofs and their structure, expository and survey articles, lecture notes and textbooks, applied and computational mathematics papers, statements of results for non-specialist readers, grant applications and research statements, and theses and monographs. Our editors work on the proof's structure and where the difficulty actually lies.

A proof is a piece of writing as well as a verification, and its failure is a correct argument that never tells the reader where the work is. Every proof has a small number of steps that matter and a larger number that are routine, and the writing should say which is which. We work through these so the shape of the argument is stated before it begins — what will be shown, in what order, and where the main difficulty sits — since a reader who knows the plan reads three times faster; so the key idea is announced as such rather than left to be discovered, because a sentence naming the essential construction is worth several pages of the reader's time; so routine verifications are marked as routine and either compressed or deferred, given that giving equal weight to every step hides the argument inside its own bookkeeping; so hypotheses are used visibly, as a reader wants to see where each assumption enters and a hypothesis never used should prompt a question; so notation is introduced where it is needed and kept stable, since notation churn is the commonest reason a correct paper is hard to read; so the statement of the theorem is precise and self-contained; and so what fails without each hypothesis is indicated, often by an example. Papers written this way are read, understood and used.

Everything you send is treated in confidence, including unpublished results and preprints before posting. We are editors rather than mathematicians, and we offer no view on correctness, novelty or the validity of any argument. What we can do is make the structure of the proof visible.