Mathematics writing style

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
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:

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

Remember. The more complicated the ideas and vocabulary, the more we must work to make our writing simple, logical and direct.

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