Lean­ing In! 2025 from the or­ga­niz­er’s point of view

Lean­ing In! 2025 has come and gone. How did it go?

The in­spi­ra­tion for do­ing Lean­ing In! came from the tu­to­r­i­al at BOBKonf 2024 by Joachim Bre­it­ner and David Chris­tiansen. The tu­to­r­i­al room was full; in fact, it was over­full and not every­one who want­ed to at­tend could at­tend. I’d kept my eye on Lean from its ear­li­est days but lost the thread for a long time. The im­age I had of Lean came from its ver­sion 1 and 2 days, when the project was still close­ly aligned the aims of ho­mo­topy type the­o­ry. I didn’t know about Lean ver­sion 3. So when I opened my eyes and woke up, I was in the cur­rent era of Lean (ver­sion 4), with a great lan­guage, hu­mon­gous stan­dard li­brary, and pret­ty sen­si­bile tool­ing. I was on board right away. As an or­ga­niz­er of Rack­et­fest, I had some ex­pe­ri­ence putting to­geth­er (small) con­fer­ences, so I thought I’d give it a go with Lean.

I an­nounced the con­fer­ence a few months ago, so there wasn’t all that much time to find speak­ers and plan. Still, we had 33 peo­ple in the room. When I first start­ed plan­ning the work­shop, I thought there’d only be 10-12 peo­ple. This was my first time or­ga­niz­ing a Lean work­shop of any sort, so my ini­tial ex­pec­ta­tions were very mod­est. I booked a fair­ly small room at Spielfeld for that. Af­ter some en­cour­age­ment from Joachim, who po­lite­ly sug­gest­ed that 10-12 might be a bit too small, I re­quest­ed a some­what larg­er room, for up to 20 peo­ple. But as reg­is­tra­tions kept com­ing in, I need­ed to rene­go­ti­ate with Spielfeld. Ul­ti­mate­ly, they put us in their largest room (a more ap­pro­pri­ate­ly sized room ex­ists but had al­ready been booked). The room we were in was some­what too big, but I’m glad we had the space.

Lean is a de­light­ful mix of pro­gram ver­i­fi­ca­tion and math­e­mat­ics for­mal­iza­tion. That was re­flect­ed in the pro­gram. We had three talks,

that, I’d say, were def­i­nite­ly more in the com­put­er sci­ence camp. With Lean, it’s not so clear at times. Lukas’s talk was mo­ti­vat­ed by some ap­pli­ca­tions com­ing from com­put­er sci­ence but the top­ic makes sense on its own and could have been tak­en up by a math­e­mati­cian. The open­ing talk, Re­cur­sive de­f­i­n­i­tions, by Joachim Bre­it­ner, was about the in­ter­nals of Lean it­self, so I think it doesn’t count as a talk on for­mal­iz­ing math­e­mat­ics. But it sort of was, in the sense that it was about the log­ic in the Lean ker­nel. It was com­put­er sci­ence-y, but it wasn’t real­ly about us­ing Lean, but more about bet­ter un­der­stand­ing how Lean works un­der the hood.

It is clear that math­e­mat­ics for­mal­iza­tion in Lean is very much ready for re­search lev­el math­e­mat­ics. The math­e­mat­ics li­brary is very well de­vel­oped, and Lean is fast enough, with good enough tool­ing, to en­able math­e­mati­cians to do se­ri­ous stuff. We are light years past noodling about the Peano ax­ioms or How do I for­mal­ize a group?. I have a guy feel­ing that we may be ap­proach­ing a point in the near fu­ture wher Lean might be­come a com­mon way of do­ing math­e­mat­ics.

What didn’t go so well

The part of the event that prob­a­bly didn’t go quite as I had planned was the Proof Clin­ic in the af­ter­noon. The in­ten­tion of the proof clin­ic was to take ad­van­tage of the fact that many of us had come to Berlin to meet face-to-face, and there were sev­er­al ex­perts in the room. Let’s work to­geth­er! If there’s any­thing you’re stuck on, let’s talk about it and make some progress, to­day. Think of it as a sort of mi­cro-un­con­fer­ence (just one hour long) with­in a work­shop.

That sounds good, but I didn’t pre­pare the at­ten­dees well enough. I only start­ed adding top­ics to the list of po­ten­tial dis­cus­sion items in the morn­ing, and I was the only one adding them. Pri­vate­ly, I had a few dis­cus­sion items in my back pock­et, but they were in­tend­ed just to get the con­ver­sa­tion go­ing. My idea was that once we prime the pump, we’ll have all sorts of things to talk about.

That’s not quite what hap­pened. We did, ul­ti­mate­ly, dis­cuss a few in­ter­est­ing things but it took a while for us to warm up. Also, do­ing the proof clin­ic as a sin­gle large group might not have been the best idea. Per­haps we should have split up into groups and tried to work to­geth­er that way.

I also learned that sev­er­al at­ten­dees don’t use Zulip, so my as­sump­tion that Zulip is the one and only way for peo­ple to com­mu­ni­cate about Lean wasn’t quite right. I could have done bet­ter com­mu­ni­ca­tion with at­ten­dees in ad­vance to make sure that we co­or­di­nate dis­cus­sion in Zulip, in­stead of sim­ply as­sum­ing that, of course, every­one is there.

The fu­ture

Will there be an­oth­er edi­tion of Lean­ing In!

Yes, I think so. It's a lot of work to or­ga­nize a con­fer­ence (and there's al­ways more to do, even when you know that there's a lot!). But the com­mu­ni­ty ben­e­fits are clear. Stay tuned!