Mathematical Writing Fall 2025

Lecturer
Ana Cannas
Temporary coordinator
Chris Busenhart
Teaching assistants
Tom Becker, Levin Ceglie, Esther Petat
Lectures and assistance
Wednesdays, 12:15-14:00 in HG E 1.2
Summary
The goal of this course is to provide guidelines and practice for good mathematical writing, both in general stylistic terms and in concrete technical manner. Soft and hard skills will be trained through writing and reviewing assignments. It is also an introduction to the mathematical community, especially to some culture of the research community.
Assessment
The performance assessment (pass/fail) is based only on eight writing assignments, called papers. There is no further exam at the end of the semester. Details may be found here.
News
[07.11.2025] Below are the guidelines for Paper 6. These are similar to those for Paper 3, with one additional request to add a comment on Moodle indicating the topic.
[10.11.2025] Below are the guidelines for Paper 7. Note, in particular, the possibility for a bonus point and the request for the Overleaf link.
[12.11.2025] Under "References" below there are some papers mentioned today in the lecture.

Writing assignments

Due date Assignment
24.09.2025 Option A: Go through about half of the numbered parts of Exercises 1.2, 2.3 and 2.4 of Vivaldi's book.
Option B: Identify twelve writing problems (spelling, grammar, typography, bad notation, unclear statements, etc) in the paper by Erdös and Szemerédi.
Your solutions to either of these exercise options are not to turn in. But you may discuss them 13:15-14:00 on 24.09.2025.
01.10.2025 Option A: Go through about half of the numbered parts of Exercises 5.5, 5.8 and 6.1 of Vivaldi's book.
Option B: Create your own LaTeX template for Paper 1, eventually by adjusting some Math template on Overleaf.
Your solutions to either of these exercise options are not to turn in. But you may discuss them 13:15-14:00 on 01.10.2025.
08.10.2025 Paper 1: Choose an elementary definition or theorem out of the list provided in the guidelines for Paper 1, and use LaTeX to write a text of at most two pages containing the statement and a proof and/or an example and/or an application (in suitable environnments), plus an explanation of the idea only in words, without using symbols.
Your target audience should be first-year students in the Math BSc program at ETH.
You may use the LaTeX template under "Assistance" below, or your own from the previous week, or any other.
You may use AI for an initial personal revision of Paper 1 following these suggestions.
Your paper submission is to take place over Moodle.
15.10.2025 Paper 2: Write an anonymous referee report for Paper 1 of a fellow student attributed to you by the system. The specific paper for you to review will appear on 09.10.2025.
Please follow these reviewing guidelines.
Your paper submission is to take place over Moodle.
23.10.2025 Paper 3: Revise your original Paper 1 based on the referee report and respond to that report following these guidelines.
In this new submission, you should include: your original Paper 1 (for reference), the anonymous referee report you had received (for reference), your response to that referee report and your revised paper.
Your paper submission is to take place over Moodle.
29.10.2025 Familiarize yourself with MathSciNet, zBmath and other library and online resources to track references and related material, in preparation for Paper 4. Prepare a draft of your Paper 4, including a .bib file with relevant references.
This preparation work is not to turn in. But you may discuss it 13:15-14:00 on 29.10.2025.
06.11.2025 Paper 4: Write an expository paper of about four pages on a chosen topic (Option A: classic, or Option B: recent) out of a list provided in these guidelines; you should research its history, interest, context and applications; detailed guidelines are given in the above handout.
Here are further guidelines regarding the use of AI for Paper 4
Your paper submission is to take place over Moodle.
12.11.2025 Paper 5: Write an anonymous referee report for Paper 4 of a fellow student attributed to you by the system. The specific paper for you to review will appear on 07.11.2025. Please follow this reviewing guidelines.
Your paper submission is to take place over Moodle.
19.11.2025 Paper 6: Revise your original Paper 4 based on the referee report and respond to that report following these guidelines.
In this new submission, you should include: your original Paper 4 (for reference), the anonymous referee report you had received (for reference), your response to that referee report and your revised paper. Moreover, indicate your topic in a comment on Moodle.
Your paper submission is to take place over Moodle.
26.11.2025 Paper 7: Create your own LaTeX template for a specific formatted use and fill it out (a couple of pages), in accordance to these guidelines.
Together with the PDF submission over Moodle, you are asked to submit the LaTeX source file via Overleaf.
03.12.2025 Discuss the first state of your Paper 8 with a teaching assistant. Have you distributed tasks among the group members? How could the collaboration be improved? Do you need to adjust your goals or work plan?
10.12.2025 Paper 8: This is to be organized in the lecture of 26.11.2025. In groups of two or three, collaborate on Overleaf in a common project (total about 10 pages), which can be:
- an expository paper on an intriguing topic for the team, or
- lecture notes for some part of a course the team members are currently taking, or
- a longer slide presentation.
This should be accompanied by a short separate document (about one page) explaining what your target audience is and giving some complementary information, such as in what context that review paper could be used, in what ways you tried to make the lecture notes appealing, what kinds of things you would say in the slide presentation, etc. Explore Overleaf features: review vs. editing mode, AI suggestions, document searches, etc
Explore LaTeX masterfile vs. sections etc! TBA
Your paper submission is to take place over Moodle.
The preferred language is English.

Assistance

Weekly slot
Starting on the second week of the semeter, the second hour (13:15-14:00) will be devoted to topic-oriented small-group discussions and to spontaneous individual assistance, including feedback and clarification of the writing exercises.
Special meetings
If you need to reserve extra assistance time, please email the lecturer or the TAs.
LaTeX template containing code mentioned in the lectures
LaTeX source code and the corresponding PDF output.
Prepared by the TAs
List of common mistakes found in Papers 1, 2 and 3

Summary of the lectures

— Lecture topics are tentative for future dates —
Date Topics Slides
17.09.2025 What this course is about and how it will be organised Organizational and Lecture 1
24.09.2025 Support of mathematical writing through LaTeX Lecture 2
01.10.2025 Online resources of the mathematical community Lecture 3
08.10.2025 References (via BibTex) and cross-references Lecture 4
15.10.2025 Writing proofs Lecture 5
22.10.2025 Scientific integrity and the publishing process — guest lecture by Emmanuel Kowalski Blackboard
29.10.2025 Graphical elements and tools to produce them Lecture 7
05.11.2025 Using AI — guest lecture by Johannes Schmitt Presentation
12.11.2025 Better writing Lecture 9
19.11.2025 Scrutinizing papers — guest lecture by Manfred Einsiedler
26.11.2025 Collaborative writing: tricks, warnings and Overleaf Lecture 11 TBA
03.12.2025 Checking your proofs using Lean — guest lecture by David Loeffler
10.12.2025 TBA
17.12.2025 Upshot and feedback

Reserved books in the ETH Mathematics library
Franco Vivaldi, Mathematical Writing, Springer, also online at ETH
Steven G. Krantz, A Primer of Mathematical Writing, AMS, also online at ETH
Useful websites for the mathematical community
LaTeX technical references and tools
AI resources
Here are some options (as of October 2025):
ETH resources
Further tips and model short papers from students in the Fall 2025
Further references


Last update: 12.11.2025