Writing Style and Rigor (anmath-writing-style)

When to trigger

• The proof is complete and you are tightening the prose
• You wrote "clearly", "obviously", "it is easy to see", or "trivially" and are not certain
• Quantifiers, hypotheses, or "the constant" are stated loosely
• The English is uneven or the register drifts between sections

The cardinal rule: no hidden gaps

At Annals, an expert referee verifies the proof in detail. A logical gap — especially one hidden behind softening words — is fatal. Treat every "clearly" as a debt to be paid or deleted.