After reading Gilles Castel’s excellent blog post about his research workflow, I decided that it was as good a time as any to write about mine—deeming it novel enough to hopefully contribute something to the discussion.

Just like Castel, I’m a new PhD student in mathematics, which means no lab work and—in my case—no code. Just you and your inability to understand basic concepts. As such, I often scribble things down on paper or a blackboard first and, when sufficiently convinced that the information is worth keeping around, type it up. Typesetting something is a surprisingly effective way to catch errors in handwritten manuscripts!

As basically my entire digital life happens in either Emacs or XMonad, my setup is very heavily skewed in that direction; I will make use of these tools almost every step of the way. As such, there is a lot of tangential almost relevant bits that I could cover here. However, since these aren’t directly related to my research workflow—and there is a lot of great resources out there already—I decided to not do this here.¹

High Level Structure

Topics

XMonad has a module called TopicSpace, which upgrades the X11 workspace—virtual desktop—concept to so-called topics. These are workspaces with a “theme” associated to them; for example, I have a topic for every project that I’m currently working on. This results in a very clean separation of concerns. Plus, I always know where my windows are!

Every topic has a directory and a “startup hook”, firing when the topic is switched to and empty, associated to it. While most convenient for programming related tasks—e.g., spawn ghcid in the relevant directory or automatically build and open this website—it’s also quite convenient for mathematical projects.

I have set up special keybindings to bring up an Emacs session in the topic directory, or spawn a terminal there. Switching to topics is done fuzzily via the XMonad prompt, which means I only have to type a few characters to get to my destination. This makes it feasible to have 30 topics, instead of the usual 9 or so, in the first place. As a result, it’s rather fast to go from thinking about a certain problem to working on it. When I’m already inside a project, I leverage Emacs’s built-in project.el library to search through files and the like.

Files

Here I keep things relatively simple; I have a big “library” directory in which essentially all books or papers that I’ve ever read reside. This may sound a bit chaotic, but since I never interact with this as-a-directory it is actually the easiest and cleanest solution for me.

To keep a bit of order, all files are named in a consistent and descriptive way: authors_title.pdf, where authors is a list of last names of all authors separated by hyphens and title is the title of the work, also separated by hyphens. For example:

    pastro-street_double-of-a-monoidal-category.pdf

Also in this directory are .xopp files, when I scribble on the relevant PDFs in xournalpp; more on that later.

Instead of navigating to it, all interaction with the library is done via hmenu, a small wrapper around dmenu to facilitate this kind of behaviour. I merely have to press M-y² and can then fuzzy search through the directory. Once I’ve made a choice, PDFs are automatically opened in zathura and .xopp files are opened in xournalpp.

My bibliography is organised in a similar spirit; see Citations.

Note Taking

Handwritten Notes

For handwritten notes I… use real paper! A little elaboration is probably in order, having talked about .xopp files and xournalpp above. I do have a Wacom tablet lying around and I’m quite happy annotating PDFs with it. In lieu of printing everything out, this alleviates a little bit of the usual pain with reading papers, like coming back to one three weeks later and getting stuck on the same calculation as last time. I do love those annotations!

However, there is just something deeply psychologically pleasing about ordinary pen and paper—nothing beats drawing up the first version of many ideas there. It’s a very “pure” experience: there’s no noise or distractions, nothing that could break, no additional layer of abstraction between you and the maths. Chalkboards—but not whiteboards, with their ever empty markers—fall into this category as well, especially when collaborating with others.

Not without my quirks (as I’m sure you’ve noticed), I’m a bit picky about the particular writing setup. It’s either completely white A5³ paper, paired with a good (mechanical) pencil/a very fine pen, or very thick dotted paper, paired with a fountain pen.

Quite enjoying the experience, I tend to write quite a lot of manuscripts by hand first. Of course, anything that’s supposed to be permanent should be typed up properly!

Digital Notes

Not wanting to go insane, I use LaTeX for all of my digital digital note taking. My writing setup for .tex files is pretty similar to Karthik Chikmagalur’s—whose excellent post you should definitely check out—so I will not belabour the point too much here. The tl;dr is AUCTeX, CDLaTeX, and aas.

In case you’re not used to prettify-symbols-mode: the inserted LaTeX code was

\begin{definition} \label{def:day-convolution}
  The \emph{Day convolution} of two functors $F$ and $G$ is
  \[
    F * G \defeq
      \int^{C,D \in \cc} \cc(C \otimes D, \blank) \otimes FC \otimes GD.
  \]
\end{definition}

I do use some smaller packages not mentioned in Chikmagalur’s article, like math-delimiters and change-env. The former is for quickly changing between inline and display math, complete with slurping punctuation symbols into display math and barfing them out of inline math. For example, “$1 + 1$.” becomes “\[1 + 1.\]” (with line breaks) and back.

The change-env package is for changing between different kinds of environments, including display math, while offering to rename labels across the project if necessary. When deleting a label from an environment, it also remembers this for the session!⁴

One very neat feature of AUCTeX that I find myself using more and more often lately⁵ is the in-buffer preview. Usually when writing a draft I’m not that interested in how exactly something looks in the PDF—that part comes later, believe me. In cases like these, just calling preview-buffer is quite convenient and lets me use the screen real estate that a PDF viewer would have taken up for something else.

I always use pure LaTeX for writing papers, drafts, or presentations. However, I also take lots of notes in org-mode, which, as a crude first approximation, is something like a markup language that’s very well integrated into Emacs.

For the actual note-taking, I use the venerable org-roam—a free software alternative to the proprietary Roam Research program—to jot down things that I’d like to remember for more than three days. Org-roam describes itself as a “plain-text personal knowledge management system”, which fits the bill pretty well. In short, it’s a note taking system in the spirit of the Zettelkasten method, which is essentially about having lots of notes with lots of backlinks to related concepts:

In fact, using org-roam-ui, one can even visualise the entire Zettelkasten as an interactive and pretty graph in which notes become nodes and backlinks become edges!

Org-roam suggests keybindings for all of the most important concepts: creating notes, inserting them, showing all of the backlinks of a file, etc. An important extra that I’ve added is having two “types” of notes: references, where things that I learned but are otherwise known reside, and novels, where I put my own ideas.

As I’m predisposed to quite easily forget details, I regularly engage with my Zettelkasten, so as to keep things fresh in my mind. Reading through all of the notes that are relevant to what I’m currently working on, creating new backlinks, filling in gaps, even deleting old information and re-organising some local region of the graph. Indeed, I tag every new entry as a draft until further notice, forcing me to go back there especially. This results in pretty good recollection of the most important facts, even with my brain.

Staying Up To Date

I use elfeed to query the arXiv for new preprints that are of interest to me. Thankfully, the fields I’m subscribed to tend to be moving slow-ish and so I can manage to at least read the abstract of every paper that pops up in my feed. There is also a little bit of elisp involved to print arXiv entries in a more readable way than the default formatting.

When the abstract interests me, I usually directly download the paper into my library and open it with zathura. This is fully automated via arxiv-citation—more on that later. I merely have to press C-c d while looking at a paper and magic happens!

In the above gif, on the right-hand side you can see a score associated to each entry. While reading every abstract has worked quite well for me thus far, it’s nice to get the papers that are “probably interesting” high up, so that I’m more likely to notice them sooner rather than later. I use elfeed-score for this, which integrates seamlessly into the rest of the machinery. It compares certain features of the entry (like the title and abstract) with a list of regular expressions, increasing the total score of the entry every time it matches something.

Speaking of the arXiv, in XMonad I have bound M-s a to look up the given string there. Likewise, zbmath is searched with M-s z. When these commands get a “universal argument”—an Emacs concept that XMonad borrowed—they automatically start a search with the current selection instead. Briefly, pressing M-u before a command can modify it in different ways. All of my search commands act on the primary selection when given such an argument; M-u M-s <letter> will look up the currently selected text on the relevant “search engine”. One instance where this is very useful is for quickly switching between the arXiv and zbmath:

Citations

For citation management, I use a very simple system—no Zotero, JabRef, or similar technology. Concretely, this means that I have a blessed bibliography file somewhere within my home directory and I either symlink (when I’m writing something alone) or copy (when working with at least one coauthor) the file into the relevant project directory. In case of a copy operation, I only have to update a single variable in Emacs (arxiv-citation-bibtex-files), which is good enough for me and doesn’t seem to warrant a slightly more automated, yet probably much more complicated solution.

Adding new citations is done via the now aptly named Emacs package arxiv-citation⁶, with a bit of plumbing on the XMonad side to get Emacs going. The basic idea is that—given an arXiv or zbmath link—we first look up the paper on zbmath to see if it was published and, if not, just use the arXiv data to construct our own bibliography entry instead. By default, my keybinding for this acts on the primary selection, so I merely have to highlight the link, press M-o a, sit back, and enjoy the show. The following gif hopefully helps drive home the point, also showcasing the format of a not yet published paper and a published one.

Final Thoughts

And that’s it! If nothing else, this post helped me to nail down some ideas that I had lying around and got me to finally clean up and publish many of the extensions talked about here—that’s already a win in my book.

I’m sure that some details will change over the course of the next three years as I mature mathematically and my needs change, but overall I feel pretty comfortable with this setup.

Addendum

Thanks to everyone who reached out! I received some inquiries as to my configurations, so here are the most important bits again, for your convenience: my Emacs config, my XMonad config, org-roam, math-delimiters, arxiv-citation, change-env, hmenu.