Pasadena Last December

 

 

 In December 2023 I went to the the Workshop on 

Open-source cyberinfrastructure supporting mathematics research 

organized by Robert Beezer, Steven Clontz, and David Lowry-Duda at the American Instittue of Mathematics (AIM), CalTech, Pasadena.  There was a report on the workshop activities and some Workshop videos were recorded.

For me it was very good to meet a whole community that I wasn't aware of. This community is committed to thinking about the accesssibility of learning mathematics, and everyone is trying to think about how to use digital tools for that. But of course the experiences, the tools and the approaches are all very different. 

 

There are people interested in computer algebra systems and in theorem provers, just like in the Dagstuhl Seminar  23401 "Automated mathematics: integrating proofs, algorithms and data" that I went to in October 2023. But there were also people interested in visualizations, in publishing textbooks and on all sorts of teaching systems. The emphasis was definitely on the teaching aspects, more than on the research side that I tend to concentrate on.

However, there was a momentous little story that I should write down now, or I will forget it. Kim Morrison was giving a tutorial on Lean for Mathematics on Tuesday morning at 9 am. When they went to  explain Lean's blueprint and show an example of its action, Kim stopped and said: oh well, when I was writing my slides last night after dinner, this (the "blueprint" for the proof of the theorem Gowers, Tao, Green and Manners had proved recently) was still blue. But now there's nothing to show, it's green! 

 

The theorem had been proved by someone in Lean while we were sleeping! It felt somewhat magical, the dawn of a different kind of mathematics. It was a bit like when, on a tip of a number theorist friend in Cambridge, I went to hear Wyles talk about the proof of Fermat's last theorem. His formal announcement in the Isaac Newton Institute, that many years ago. I didn't understand anything of Wyles proof and I still hardly understand what a Lean blueprint is, but the magical side of maths just happens!

If you want to understand the history behind the theorem the Quanta magazine article ‘A-Team’ of Math Proves a Critical Link Between Addition and Sets by Leila Sloman explains it very well!

I confess that instead of enjoying the magic, I went directly to the Lean Zulip to check that there were no reports of vandalism or hacking on mathlib, no triggering of the green, by mistake. Only when everything seemed normal over there, I managed to enjoy the moment! Proofs more than 20 years in the making are like fine wine.

Dagstuhl in the Fall (2023)

 

In the spring of 2022 I got sick, not as sick as I thought then, but sick enough to end up in the emergency room of the hospital in Stanford twice in the same week in May. So the whole year of 2022 got pear-shaped and many of my plans had be cancelled. I had a small procedure at the end of the year--on the day before Thanksgiving exactly-- and this made the year of 2023 a year of recovery.

The year of recovery meant I was going to try to do  three trips (since I had to cancel many in 2022): one simply to Chapman, South California, one to Bloomington, Indiana and one to  Pisa and Padova, in Italy.  All of them went well, mostly: I got covid when returning from Indiana. So I  decided to do another three trips: to St. Louis, Missouri, to Dagstuhl, Germany and to Pasadena, CA.

The one I was most worried about was the one to Dagstuhl, as I do not speak German and Dagstuhl can be fairly inaccessible. But I partnered with Jacques Carrette and Stefania Dumbrova and all went well getting there and getting back home. And being at Dagstuhl is always a pleasure! I have met several people who, like me, are concerned about using digital tools to make mathematics more accessible.

The schedule of the talks and discussions is in https://www.dagstuhl.de/23401/schedule.pdf. I really need to read a bit more about some of the work that I did not manage to grasp while there.

Preparing for Network Mathematics 2023

 

 

(source: Twitter/X account Stonehenge UK)

This post is a continuation of Preparing for Networked Mathematics.

During 2023 we had a few more talks on theorem provers and automated deduction. And on how the work in math provers can impact the world.

On the 27th April we heard Georges Gonthier on

Foothills and cathedrals: organising the libraries behind big proofs

 

Not exactly like the picture below, but close:

On the 4th May we had Michael Barany on

How Categories Come to Matter: On the history and sociology of categories in modern mathematics

 

 

 

 

which wasn't so much about math provers, but about why category theory matters so much right now. And, as usual with Michael, how to study the `relationship between abstract knowledge and the modern world'.

On 18th May we had Clark Barrett on

Proof Certificates in Satisfiability Modulo Theories

 

and on the 31st August we had Nat Shankar on

Abstraction Engineering with the Prototype Verification System (PVS)

 

Then we had Leonardo de Moura on the 7th September talking about

Lean 4: Empowering the Formal Mathematics Revolution and Beyond

Yes, we already had Jeremy Avigad, Kevin Buzzard and Johan Commelin talking about LEAN in 2022, but it was good to hear from the main creator of the Lean  prover too!

 

(He even talked on the 7th September, a Brazilian National Holiday, and neither of us noticed it!) 

In 12th October we had Dominic Orchard talking on           Programming for the Planet

 Tom Leinster from Edinburgh University on

Entropy and diversity: the axiomatic approach

and then in November we had Minhyong Kim with a beautiful talk on

Who Owns Mathematics: A Question of Identity

 

 

 

 

 

 

Of course these last three talks say more about how I feel about the role of mathematics in the world than about how we can use provers to do more  mathematics. But I think this is essential too!

Formal Math: are we there yet?

 I have not touched my blog much this last year. A shame. I need to write more and I need to try to correct pictures and links that stopped working. Now the programme in Bonn, on Prospects of Formal Mathematics is coming closer, so writing should help me decide to organize my time in Germany. But first things first. I need to email a few more people about our arrangements.