The Gibbons Style Guide for writing assignments

If you've taken proofs classes from different professors, you know that we share some basic beliefs about writing, but we also have our own quirks and preferences. (If you haven't yet taken proofs classes from different professors... get ready! We share some basic beliefs, but we also have our own quirks and preferences). What you'll see below are the guidelines that I consider the standards for submitting to the Gibbons Journal of Mathematics (by which I mean, sending in a writing assignment to be assessed in a proofs class that you're taking with me).

To me, mathematical writing breaks into three (entangled) pieces: Logic, Mathematics, and Style.


The authors

  • state claims (propositions, theorems, lemmas, etc) as logical statements;
  • state claims appropriate to the assigned problem;
  • write proofs with first and last sentences that indicate the proof technique they are using;
    • this criterion relaxes a bit after the first proofs course; if you're proving a theorem directly, you can just get to the proof without repeating the hypotheses at the beginning of the proof. But if you're in your first proofs course, please include the first and last sentences that lay out your hypotheses and conclusions!
  • define notation and symbols before using them;
  • employ a valid proof technique for the statement as written;
  • employ a valid proof technique for the statement appropriate to the problem;
  • include all necessary cases in the proof;
  • write examples with a clear topic sentence;
  • write prose using evidence to support claims;
  • employ sound logic even in mathematical prose.


The authors

  • use definitions, theorems, and other results from the appropriate chapter(s); 
  • cite definitions, theorems, and other results from the appropriate chapter(s); 
  • cite named definitions, theorems, and results;
  • employ correct calculations;
  • do not re-prove prior results. 


The authors

  • use the appropriate LaTeX template for the course;
  • adhere to mathematical style conventions, such as:
    • using math mode for math symbols,
    • writing sentences that do not start in math mode,
    • not writing “two-column” proofs (more here: Paragraph Proofs), 
    • using aligned equations when a string of equations is too long for a page,
    • using inline equations for minor mathematical manipulations;
    • using appropriate LaTeX environments (proof, prop*, example*, etc);
  • discerning when to write an example instead of a proposition and proof;
  • adhere to the conventions of grammar;
  • write clearly and concisely in a way that does not obscure the logic or mathematics. 
Here's a note about the difference between a proposition in math (versus formal logic). In math, we understand propositions (and theorems, lemmas, corollaries, etc) to be statements that are true (and proved/provable) so that we can cite them when we need to use them. You can see the confusion that would ensue if a paper contained "Proposition 1: All even integers are prime" under that assumption, even if followed immediately by a counterexample! So, if you are showing that a statement is not true as part of a writing assignment, here's what that might look like:

Example. It is not the case that every even integer is prime. Notice that the integer 8 is even. Although 8 divides 24 = (2)(
12), it divides neither 2 nor 12. Therefore, by (definition of prime/proposition about prime numbers/whatever it is), 8 is not prime.

To break that down into more of a template:

Example. [Topic sentence: what's the point of this example?] [Supporting mathematical evidence, less formal than a proof, but still following the stylistic conventions of good mathematical writing!] [Concluding sentence.]

Getting Help with Proofs at the QSR Center and the Writing Center

For help with the math:

The tutors at the QSR are great, and they will happily help you think through the math that goes into a proof. In order to make sure that you are getting the best possible math help, here are some expectations about the kind of help you'll get at the QSR when it comes to your proofs assignments. We (the math faculty) ask the tutors to help you with the math, but not the writing, part of the proofs.

Here are some guidelines for working on proofs at the QSR:

  • No working out the math in Overleaf at the QSR!  (It's your job to typeset the math nicely after you have figured it out.)
  • As a corollary: you may only work things out using on paper (or whiteboard, or otherwise "by hand") with a tutor at the QSR. Why? Usually, thinking through a problem and understanding what's happening is necessary before you can write it up, and when you write it up, it may look a lot different than what you worked out on paper first.
  • Figuring out what properties you are using in a proof is a math problem; figuring out what order to write equations or how to break up the math and exposition is a writing challenge.  Make sure you are asking about math, not writing.

As long as you don't abuse the goodwill of the QSR tutors and director, you can also ask simple LaTeX questions if you can't find an answer on the internet or elsewhere. (Many of the tutors are also LaTeX gurus, and they can help troubleshoot your code, but don't forget that Google is a great debugger, too!)

Conversely... for help with the writing:

If you've figured out the math but you're having trouble writing it up, make an appointment to talk to a Writing Center peer counselor! There are usually a couple tutors at the Writing Center that have been recommended by math faculty, and we ask that they help you with the writing, but not the math, part of the proofs.

The Upshot: You can use both centers for an assignment to get help with the math and the writing! But, you can't use one center for both.

A day of work in honor of MLKjr's legacy

You know I’m an academic because my first instinct was block out space for an abstract for this blog post.

Abstract: On MLK day, I, a white mathematics professor, consciously and intentionally dedicated myself to working only in honor of Martin Luther King Jr.'s legacy. That is, all of my professional activities were focused on social equity, especially along the axes of race, ethnicity, and socioeconomic status. I’m writing this post for accountability, transparency, invitations for collaboration on any of these ideas, and for constructive feedback for those feeling generous. The content? A break down of my day, starting at 9am.

Book Club!

I have lots of thoughts to jot down about the end of the semester, but first: would anyone like to join a virtual book club?

Wrapping up the remote semester - a scratchpad of thoughts

Last day of classes! Finals, and then we're finished up.

A couple links to helpful things that I didn't get a chance to share earlier
Questions for an exam:

Tools that have been invaluable for teaching remotely
Gradescope (for grading)
Slack (for project-based learning)
Piazza (for asynchronous class discussions that support LaTeX)
Overleaf (for collaborative document editing, especially with the track changes panel!)
Explain Everything (for explainer videos)
Zoom (yeah yeah, privacy stuff aside: can't imagine teaching without some face-to-face)
Google Apps Suite (for all sorts of things but especially forms)
Google Calendar with Zoom integration
Boomerang for Gmail for the "Pause Inbox" function (helpful for focus)

To be continued, I'm sure!

Mentoring Undergraduate Research

I wrote a short piece for the Early Career section of the Notices of the American Mathematical Society, and you can read it online:

Working at odd hours

Due to a combination of too much screen-time and an out-of-date glasses prescription, I get really bad headaches if I work for too long in front of the computer. (I know, right?) 

To compensate for the breaks I take during the day, I've been finding myself up at 1 or 2 am trying to catch up. I used to do this before This Happened, but not as often: I intentionally left work physically at work so I would break the habit.

Anyway, a few weeks into this habit confirms for me that it's not actually worth the tiredness the next day even if I do get caught up. But I can't seem to shake the feeling that I am falling behind. Maybe a better way to say it is that I can't seem to make peace with falling behind.


Remote Semester Orientation

Advice from Abbi Jutkowitz, Film Editor, who has worked from home on and off for 5+ years, and worked from home exclusively for the past 8 m...