Advanced undergraduateFoundationsLesson available

Mathematical writing

Writing mathematics that others can read and check: structure, definitions before use, notation, examples, LaTeX, and honest statements of what has and has not been proved.

math.found.mathematical-writing

Open lesson Show everything needed to reach this topic

Builds on

Proof: direct, contrapositive, contradiction and induction

Required prerequisites, all the way down: 10

You will learn to

Rewrite a correct but unclear proof so that its structure, assumptions and key steps are explicit.
Typeset definitions, theorems and proofs in LaTeX with consistent notation.
Write a short expository note that states precisely which results are proved, which are cited and which are conjectured.

Definition

A theorem is a principal result, a lemma an auxiliary result, and a corollary a result that follows quickly from another.
Exposition is writing whose purpose is explanation rather than the announcement of new results.

Theorem

Every symbol should be defined before it is used, and every cited result should be identifiable by the reader.
A proof is written for a reader who will check it against the stated hypotheses.

Common misconceptions

Thinking a shorter proof is always a clearer one.
Using 'standard' notation without defining it.
Leaving the status of a claim (proved, cited or conjectured) for the reader to guess.

Leads to

Reading the mathematical literature Computational reproducibility

Optional discoveries

Formalising published mathematics Formalisation blueprints link each informal statement to its formal counterpart, which forces precision in writing.