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*Australian manual of scientific style *Start communicating effectively

Traditional mathematics writing can be quite formal and dense. But using the same principles of clear and direct language as used in other writing can help readers – whether they are mathematicians, other scientists or a more general audience – to better understand the content.

For example, content written by mathematicians for mathematicians often outlines a chain of reasoning, beginning with definitions and axioms, and defining terminology and symbols, before moving on to the results. In laying out a complex chain of reasoning, active, concise language is a big help to the reader. The work can refer to technical, formally defined components, but at the same time use straightforward grammatical constructions that help the reader follow the logic:

PROOF. We begin by showing that \(B+C\) is self-adjoint. The same argument used to prove Lemma 14(iii) shows that

\(A^2=B^2+C^2=(B±C)^2\).

Because \(B+C\) is clearly symmetric it is now sufficient, by Lemma 3, to …

Source: Bernau SJ (1968). The square root of a positive self-adjoint operator. *Journal of the Australian Mathematical Society* 8(1):17–36.

The pitfalls found in science and technology writing are also found in mathematics writing. These include:

- unnecessarily complex words and jargon
- long sentences, often with unnecessary words
- passive voice and the use of third person instead of first person
- abstract nouns and verbs
- long strings of modifiers (adjectives) before a noun.

See Accurate language for more information on writing about evidence, risk, and data and statistics.