Last month I went to my first ever Electromagnetic Field festival. It made me very happy and filled me with a hopeful joy that I have not felt for a very long time. I don’t have much else to say right now, but here are some links to some photos and stories.

As a fun treat, because it’s something I’ve long wanted to do, I’ve been taking Arabic classes once a week during term times. In lieu of any mathematical updates, I’m using this blog post as an excuse to do some revision before classes start again next month. Today is nominal sentences. I doubt this will be a particularly useful resource to anybody else (and hopefully it’s very clear that I’m a very beginner beginner), since it’s not a tutorial so much as a collection of my random class notes. But 2026 is the year of not worrying about such things when it comes to stuff I do in my spare time.

I managed to forget to write a blog post for the entirety of 2024 — wow! Let’s see if I can zip through some things that have happened in the past 14 months.

Briefly: two very short translations concerning geometry, and the final two seminars of FGA (thus finishing a complete first draft of the entire FGA seminar series).

Hopefully one of my co-authors and I will be uploading a long-awaited preprint on dg-categories, twisting cochains, and homotopy limits to the arXiv “soon”. Until then, here are the small handful of translations that I’ve finished in the year since I last wrote

I haven’t blogged about it in a while, but I’ve been working on just making my translations a bit better, both in terms of content and accessibility. Let’s have a look at what I’ve done, shall we?

This blog now has support for comments! I haven’t had a chance to properly test things yet, and there are still some kinks left to iron out, but please do use this as an excuse to browse back through old posts and say nice things.

Over the past couple of months, between moving countries, teaching, and a bunch of administrative faff, I’ve managed to write two short preprints with David Spivak. I blogged about them over on the Topos blog, but I’ll just write a little crossover post here with some links (so that people don’t think that this blog is entirely dead).

Hello. Yet again I haven’t been blogging in quite a long while, which is, yet again, due to an unexpectedly hectic couple of months. Let’s have a look at what I’ve been doing, shall we?

I haven’t posted anything here in well over a couple of months, so I thought it’d be a nice idea to just say “hello, I am still here, and here’s why I’ve been too tired to post anything”, whence this post.

I’ve had a bit of free time during various quarantines and lockdowns as of late, so I’ve been able to do some more translations. Here’s a quick summary of what I’ve uploaded to thosgood.net/translations recently, as well as what I’m now working on.

I recently submitted a video to the Junior Mathematician Research Archive that gives a brief overview of the work in my PhD thesis. You can watch the video here but, be warned, it’s really probably not the most coherent (ha ha) narrative.

For the sake of it, or in case you’re the sort of person who prefers to read instead of watch, I’ve included the transcript of the whole video below.

I’ve been having quite a bit of fun translating some maths papers into English recently. Of course, I’m still chugging away at the EGA translation project, having just finished another section of EGA II, leaving “only” about 60 pages left before that chapter will be done as well! However, I’ve started putting some of my other translations all together, and they can now be found at https://thosgood.net/translations. There are a lot still in progress, but here’s a summary of what I’ve done so far.

Having finished my defence (entirely virtually, and hence, of course, plagued with many technical difficulties), I have now been able to share my thesis with the world. Most of the technical content can already be found in my two preprints (part I and part II), but I think the thesis is a much more self-contained and leisurely read, with a lot more examples and (hopefully) helpful appendices. It also has geese! You can find a copy of it on here on TEL.

Edit. I’m in the process of moving over from YouTube to Vimeo (no ads, less tracking, and no Google), so you can find my videos there now instead. In particular, the connections and curvature videos can be found here.

This is a very short post just to say that I’ve started uploading some maths-related videos to my YouTube page. At the moment there’s a talk I recently gave at a graduate seminar about connections and curvature from the point of view of somebody trying to avoid differential geometry, and a series I’ve been working on called Nice Analytic Sheaves For All which aims to discuss motivations for coherence conditions of complex-analytic sheaves from various points of view. Hopefully there will be more updates to the latter soon!

On a particularly bad day, when I’d gone into the maths department on a public holiday by accident¹, I saw nobody around. Coming down the staircase to leave, however, I saw a blue tit trapped inside, loitering by the photo of Grothendieck.

Anybody who follows me on Twitter will have heard me go on about Matrix, and Riot, and maybe a whole host of other such things. I understand that most people probably won’t really care much about it all, but I thought that I’d try to explain a bit why I’m quite so passionate about this stuff, and why I’m bothering to try to work on “LaTeX” support (with scare quotes for good reason, as explained later).

I find myself in a mathematical rut more often than I would like. It is very easy, especially as a PhD student, I think, to become disillusioned with maths, the work that one can do, and academia as a whole. I realised only the other day, after talking to my family, some of the things that can contribute towards this. Hopefully this post can serve as a reminder to myself that I am human being who is trying to be a mathematician, and not the other way around.

I haven’t posted anything in a while, and rather than trying to write about maths, I wanted to just share some lovely photos of Skomer island (which I recently visited). I am even less knowledgeable about birds than I am about maths, but I do love them, and this was the first time in my life that I’d actually seen a puffin in the flesh!