Natalia Chechina

How to Write Mathematics

Paul R. Halmos

1. Say something

2. Speak to someone

3. Organize first

4. Think about the alphabet

5. Write in spirals

6. Organize always

7. Write good English

8. Honesty is the best policy

9. Down with the irrelevant and trivial

10. Do and do not repeat

11. The editorial "we" is not all bad

12. Use words correctly

• Never use "any" in mathematical writing. Replace it by "each" or "every", or recast the whole sentence

13. Use technical terms correctly

14. Resist symbols

15. Use symbols correctly

• distinguish "contain" and "include"


• use "then" with "if" in all mathematical contexts


• never start a sentence with a symbol

16. All communication is exposition

17. Defend your style

18. Stop.