So I spent July and August supervising mathematics undergraduates who were doing Lean projects in various areas of mathematics. Conformal maps, Euclid’s SAS theorem, nilpotent groups and the Radon-Nikodym theorem are just some of the topics I’ve been engaging with this summer. Earlier this week we had a summer project conference, where eight students presented 15 minute talks on their work. I recorded the talks, and they’re now up on YouTube. For each talk there were also 15 minutes of questions but I decided not to record these so that attendees could feel free to ask basic questions.

The students behind four of the projects managed to get PR’s accepted into mathlib, and for two of them this was their first mathlib PR (and possibly even their first contribution to open source). These students had to use git and github (some for the first time), but these are skills which I personally now value as important and worth teaching (it is commonplace to teach this sort of thing to computer scientists, but mathematicians seem to miss out here). In 2022 I will be teaching a formalisation course to undergraduates at Imperial and we will be using git and github for this too.

I think the video titles are pretty explanatory, and perhaps now isn’t the time to be going through the technicalities of exactly what the students achieved. However for the most part we stuck to the mantra of: learn the maths first, and once you think you understand it, then try to formalise it. That way, of course, you find out whether you *do* actually understand it 🙂

## What was the set-up?

We ran the entire thing on the Xena Project Discord server, a server for undergraduate mathematicians interested in formalisation of mathematics. This worked very well for me and, I think, for them. Students could share their screen if they had technical questions. Everything was done in voice or text channels, and in particular there are some students which I supervised and who I would not recognise if I met them in the street. Not that this bothered me in the slightest.

Timetabling: I basically promised to be online every Tuesday in July and August from 10am until about 6pm, so the entire thing functioned as a drop-in. Some students talked to me a lot, some students barely talked to me at all, and of course some students talked to other people. Creating a community was, I felt, a bit harder than previous in-person summer projects which I’ve run in the past (where you can just go to lunch with a bunch of UGs and let them talk to each other) but of course these are extraordinary times and we have to make do. One big advantage of running stuff online was that students could be in different countries and still participate, and more generally students could move around (e.g. to and from London) without it disrupting their supervision. I live and work in London and for some students it’s problematic to stay without a serious source of funding, and working online also solved that problem. Going forward — assuming things are far more normal next year I might be tempted to run summer projects in a hybrid way next year.

Thank you to all students who participated. If you are a *mathematics undergraduate* who is interested in formalising some mathematics in Lean (probably Lean 4 next year I guess!) over the summer of 2022, then get in touch with me at some point and we’ll see what we can do.