As written in the author’s preface, “The booklet is intended to provide practical help for authors of mathematical papers” (p.1). Jerzy Trzeciak, the author of the booklet, has been dealing with mathematical texts from the point of view of their grammatical and stylistic structures and lexis for all his professional life. It would be difficult to find any other specialist studying these aspects of mathematical texts deeper than him. At present, Jerzy Trzeciak, formerly of Polish Scientific Publishers, is the senior copy editor at the Institute of Mathematics of the Polish Academy of Sciences and is responsible for such journals as Studia Mathematica, Fundamenta Mathematicae and Acta Arithmetica. What is really important for mathematicians is the fact that he has concluded and structured all his long-term observations and experience with mathematical texts in this book, which will be of great help for not only non-native English speaking writers but also native English speakers who are writing their first mathematical texts.

The book consists of two basic parts: part A, Phrases Used in Mathematical Texts, provides ready-made sentences and expressions typical of mathematical texts. The examples are divided into chapters according to their use: in abstracts and introductions, definitions, notation, assumptions, referees´ reports, etc. The language of various stages of a proof is specified in details (the beginning, arguments, consecutive steps, conclusion and remarks). Part B, Selected Problems of English Grammar, offers its users the most typical problems of English grammar and usage in mathematical texts. It covers and gives manifold examples of what articles, infinitives, ing-forms, the passive voice, quantifiers, numbers and commas are and how they should be used. Authors of mathematical texts are recommended to avoid repetition and organize the word order in their texts. The most typical errors are summarised as well.

The booklet is a revision of the first edition, which was published ten years ago. The structure of the new edition is not significantly different; however, the author of the text has changed and deepened numerous examples, taking them from more recent mathematical texts. It was a good idea to republish this highly important source of information and inspiration, which is warmly recommended to all mathematicians, editors, philologists and language teachers dealing with mathematical texts.

Reviewer:

mbu