229 – Reflections on the Joint Mathematics Meeting Part 2

[00:00:07] Santiago: Hi, and welcome to the IDEMS podcast. I am Santiago Borio, an Impact Activation Fellow, and I’m here with David Stern, one of the founding directors of IDEMS.

Hi David.

[00:00:17] David: Hi Santiago. 

[00:00:19] Santiago: In our last episode, we were discussing the Joint Maths Meeting and we suggested we’d do a second part of that episode outlining the three other talks that you gave and trying to get a bit of your highlights and what was presented by other people that was particularly exciting.

[00:00:48] David: There were two other talks which I think are definitely worth discussion, and then I’ll mention the final one. So the two other talks, which, if you want, the other big area was related to, I suppose it’s this category theory. It’s the fact that we’ve been building mathematical modelling packages, Python packages, which have ended up using this work from the Topos Institute related to applied category theory.

And so I presented to both a mathematical biological audience, and a category theory audience. And I think it’s worth separating out those two, because they ended up being very different. In both cases, I put something into the special sessions related to mathematical biology and related to the applied category theory, they had special sessions that were there.

And my talk for the applied category theory got put into the special session and my talk to the mathematical biology didn’t. I’m not surprised, I don’t know people from the mathematical biology community in the US. So let me start with that because that was a very interesting session, which also taught me quite a lot about how JMM works and what it is.

But that session was actually a lot of, I believe, postgraduate students, a couple of postdocs, but mostly PhD students presenting their work. And for many of them, this was their first opportunity to present their work. I had planned to go into that session and in fact, my talk was prepared to be speaking to people who were maybe interested in multimillion dollar collaborations, these big ambitious projects.

I very quickly adapted it so that it was actually more accessible and more appropriate for the audience who was there, which was primarily PhD students and postdocs. It was actually very nice session, very nice to hear about what other people are doing in the area and to recognise the role that the conference plays in giving people that first exposure.

This is why it’s one of the biggest maths conferences in the world, because in many other contexts you don’t get these opportunities. But there’s a lot of postgraduate students in the United States in particular, but I guess North America more generally, and this is maybe their first opportunity to present at a conference. They get funded by their institution or by other sources of funding to come and to experience being at a big conference and presenting their work.

So to be in a session where pretty much everyone else in the session, that’s what they were there for, this was their first experience or a recent, one of their early experiences, in early career research. And it was a nice session in the end.

[00:03:52] Santiago: I seem to be getting a common thread here from the last episode and what you just presented. You pretty much had to adapt to the audience in all your sessions.

[00:04:05] David: No, actually, the next one I’m going to mention I didn’t adapt to the audience.

[00:04:10] Santiago: Okay.

[00:04:11] David: Actually, the next session that I’m gonna mention is the applied category theory. It was a full day, I sat in the applied category theory thing all day, and there was a pattern, I’d prepared a certain talk, my talk was titled Real Word Applications of Applied Category Theory, and I sat through all day and it was very clear that this was nothing like any other talk given in the whole day.

All through the day, it was a wonderful series of this, it was actually very nice for me because I hadn’t done category theory for 15 years, really since I was a proper mathematician. And so it was really fun to just sit in and actually realise, I did understand what most of them were talking about, not all of them, but most, and there was some really interesting advances, which I didn’t know about, which were mentioned and there were some very interesting pieces of work.

And there were some people who sort of apologised at presenting from a more applied perspective, but from my perspective, they were still very much central, they made sure they had some nice commutative diagrams and the things you get in category theory. And that’s what everybody did.

And that was one of the only talks I had where I didn’t adapt to the audience. I thought, you know, mine was the last talk of the day, it was literally the last talk of the conference, basically, ’cause this was the last session, the last talk of the last session of the conference. And I thought, you know what, I’m gonna give the talk I planned, which was extremely applied.

It actually went down very well, and one of the organisers came to me afterwards and said, thank you so much, this is what I hoped people would do. So I didn’t adapt to the audience in that case, but the talk was adapted to the audience and, maybe not everybody wanted something quite that applied and quite that far removed from actually presenting the category theory components of it.

But I focused on presenting how we’re coming across problems, which I think are genuinely hard, that they need advances in the mathematics and nobody pays us to do this of course, we are a not-for-profit social enterprise, we don’t get paid to do category theory research. But we do have problems, which are, I believe, related to what are actually some quite hard underlying mathematical problems, where we could benefit from a more theoretical framing.

And we’ve got our colleague George Simmons, who’s been working at that interface a bit. And this is where I was relating this to the work that he’s done and there’s a paper which is due to come out, which is with our colleagues at Topos who have taken some of the work that he’s done and formalised it, and actually over the next few months it should actually appear as a publication.

And so I was confident that there’s substance to what I was saying, but I didn’t focus on that substance. I focused on, well, where are we finding these application areas, why is it that we keep coming back, what is it that’s needed when you are actually trying to solve hard social problems in applied context, parenting, where does category theory come into it? That’s the talk I gave, and it was an interesting one to finish with.

[00:07:41] Santiago: And, of course there’s also the management system that we’re building that is heavily reliant on category theory. 

[00:07:50] David: It’s interesting, so I’ve been doing some other work on that. We believe that there is a category theory foundation to this. But it’s really, that foundation, is in the version control and it’s in the underlying structures. The system itself, we can build it with current technologies, there isn’t really an unanswered problem for us to do.

The problem, which is actually interesting there, and I’ve been discussing this with somebody else who’s been a very interesting person I’ve been introduced to, working on PPODs, which is, let me see, People Project Organisations… and I’ve forgotten what the D stands for in PPOD.

But to come back to the category theory session, I was, as a mathematician who doesn’t often get to be a mathematician, I enjoyed myself, that was a really enjoyable day for me. But the fact that I didn’t adapt to that audience and I gave the talk I wanted to give, which broadly challenged them to say, look, we’re actually, we know a bit about applied category theory in different cases. We can’t afford the time to really invest in the theory, but we’re opening the door if you want to actually collaborate, if you want to find ways to see if you can help us solve these real problems and dig into the theory behind what we’re doing, we’re gonna do it anyway, whether there’s a theoretical foundation or not.

But could a theoretical foundation help us? Could you actually bring the theory which helps us to make it easier? And the hard problems are within technology, it is about enabling communities to own, manage technology in different ways. That’s at the heart of what we’re trying to do, where we believe there is this category theory foundation that we keep bumping up against about how do we translate between different contexts and between different communities.

And that’s sort of where, yeah, I mean, it’s a hard problem, there’s some underlying mathematics, which we think would be useful, but whether you do that maths or not, we are needing to build the systems that work differently. And that’s one of the things that we’re working on.

[00:10:18] Santiago: Okay, so those were the two category theory talks. And the last one?

[00:10:28] David: Oh, the last one, this is a passion project, I couldn’t go to a conference like JMM and not talk about the maths camps and enjoying mathematics in low resource environments. So I gave a maths camp talk, which went down very nicely and was just great fun to give, fun mathematics in low resource environments. I enjoyed that one. It wasn’t as serious maybe as some of the others, but it was a nice one to tell people about. People don’t know about the math camps in Kenya, in Ghana, in Ethiopia, and Rwanda, Togo, Benin, et cetera.

[00:11:00] Santiago: And how was it perceived? Because the maths camps that I am aware of in North America and the US particularly are very different to our math camps.

[00:11:13] David: Well, that was what was very interesting. And so now actually it’s really good to switch and talk about where some of the other things I found out and the people I met. So there are maths camps in the US, which are very similar in certain ways to this maths camp. So one of them, it wasn’t called a maths camp, it was called something else, and I’m very sorry I don’t remember the name of it, but it was amazing. And it was a six week long event. And the thing which was amazing was that they had over time figured out that this wasn’t about the maths.

The maths was part of it, but this was all about building up the relationships between children, it was about peer support, it was about building up confidence, it was about the human side of the kids. And yes, they learned maths as part of that, and it started off with the maths as a focus, but it was all about, just like the math camps that we’ve got, it’s about creating that enjoyment, that connection, that fun, really changing people’s perceptions, not just of mathematics, but about how to interact, how to collaborate. Wonderful.

[00:12:25] Santiago: And how to value education as well.

[00:12:28] David: Absolutely. And they also had, just like our maths camps, they have multiple layers to it. The volunteers, actually, it was for them as well as for the participants. Everybody gains, everybody learns, just as we have as one of our principles. This was run by the kids where the kids were supporting other kids of different ages, but everybody was gaining, it was beautifully conceived.

It’s been replicated in a couple of places. I did actually follow up afterwards. Apparently they had one attempt at trying to do this in Africa and that didn’t work. But that’s the sort of thing where I think I can understand why for them to get some of these ideas to work in the African context, they’d have to understand more about the African context first.

This doesn’t surprise me that them trying to take what worked in the US and just say, oh, this will work in Ghana, wasn’t the right approach. But what they’re doing is exactly relevant and there’s some really interesting cross-learning that could happen. So that’s a connection which I made, and I hope to interact with and maybe something will come from that.

[00:13:36] Santiago: I’m very glad you had that talk. I think the maths camps is one of our most exciting projects, that we support. That’s my personal opinion.

[00:13:50] David: It’s how we met and it predates IDEMS by almost a decade.

[00:13:54] Santiago: It’s not quite how we met.

[00:13:56] David: That’s true.

[00:13:57] Santiago: We met, discussing the textbooks of the future, something that we are finally getting to, our regular listeners will know.

[00:14:08] David: No, you are absolutely right. We met at King’s College School when you were a teacher there, and discussed textbooks of the future. But it was the, I suppose we got to know each other at a maths camp.

[00:14:19] Santiago: That is correct. That is correct.

[00:14:23] David: And I guess, the fact that that’s become something, which, although I was at a maths camp for just a day last year, it was the first time in a long time, I’d even been present at one. I was at the Ethiopian Maths Camp for the closing ceremony because it overlapped with the STACK conference. And that was amazing.

But anyway, let’s talk about a few other things. I mean, of course, one of the big things in the education discussions, and I went to a number of sessions related to this, was AI in maths education and AI in education more generally is a huge topic right now. And there were some very exciting things happening.

There are things that we’re involved in. I mentioned a bit what we presented on. But one of the things that I didn’t know about and I really liked was, there’s been some work using, regular listeners will know, I like small language models. There’s been some work related to specific AI agents for specific interactions about linear algebra proof.

And so it’s training a chatbot to be able to have the assessment being your interaction with that chatbot around proof in linear algebra. I believe that’s, I hope I’ve represented that right, but it was a fantastic idea and a really imaginative way to rethink what assessment looks like, what it means to integrate AI in interesting ways.

Totally different from the sort of things that I’ve seen before. And really what I would argue is responsible about a use of AI in assessment where you are actually able to then use the transcript of the interaction between the student and the chatbot as that’s the assignment.

They’re in a class for an hour interacting with this AI agent and how you interact with it, that’s your assignment. What a wonderful way to turn this on its head and to actually use those interactions.

[00:16:40] Santiago: So it sounds like a sort of oral exam. 

[00:16:45] David: Exactly. It’s not an oral exam, of course, because it’s an interaction with an AI agent, you’re typing things in. But it is like an oral exam, which you’re doing with a chatbot, but not really seen as an exam, it’s seen more as formative assessment because the whole point is this was for learning more than summative assessment, you know, for examination.

[00:17:07] Santiago: How does it relate or compare with WeBWork, which we mentioned in the previous episode, and with STACK?

[00:17:16] David: Well, it is totally different from anything you could do at the moment in STACK or WeBWork. You know, I’d see this as potentially a whole nother question type. And the question is, you’ve gotta train the AI agent to be specific and to just interact on a particular topic. And then it’s about how much depth you can get and understanding on that particular topic.

It’s a really, really interesting, I’m not saying all assessments should be like this, and in fact, as I understand it, the particular experiment that was done was only one topic in one lecture, taking the equivalent of one lecture and turning it into an interaction with this special chatbot. It’s a very small piece of research. And I don’t think this is something which would take over everything, but it’s imaginative and it’s different, and it’s interesting, and it’s responsible.

[00:18:08] Santiago: And you suggested it’s a small language model rather than a large language model.

[00:18:14] David: I’m trying to remember how they implemented it. I believe at the moment they implemented it as a trained agent within a large language model, but there is no reason why this couldn’t be done in the future. The whole point is you are bounding it. The more you bound something, the more realistic it is to get similar performance with a small language model.

I don’t know if it was this group or another group that were already doing that, and they were saying that, you know, a few years ago the large language models weren’t very good but it was a similar sort of interaction between students and the chatbot, and the language models now improved so that they were much better at this.

But the whole point is that you can now get towards similar performance with less, well, with a smaller model. You know, this is the whole thing of a small language model.

[00:19:07] Santiago: Okay. We’re almost out of time, so any final highlights that you would like to mention?

[00:19:13] David: I think I mentioned enough in the other episode, the highlight of the WeBWork 30 year anniversary. It was an incredible session, incredible set of people. It wasn’t just, what was amazing about them was it wasn’t just WeBWork. This was their 30 year anniversary and yet they invited in so many other groups around what they’re doing to inspire each other. And I was invited in as representing STACK.

And I apologise that it’s DOENET rather than doughnut, but I can only think doughnut when I, when I say it, it’s another sort of system. There were a whole set of other people who were talking about different ways of electronic assessment of mathematics in ways that were so interesting, which relate to, or don’t relate to WeBWork or are complimentary to it.

And it was an incredible audience, incredible atmosphere. That was one of the few sessions I was at, that was in a really tiny room, and it was overflowing. It was put in the wrong room, there were so many big rooms, there were other sessions which were, you know, almost empty, but that one was overflowing.

Oh, and I did also mention related to this the Project Ember Session and the Project Ember in general. And that was, again, inspiring. The work they’re doing resonates so deeply with things that I believe are needed more generally. And the fact that this is a really hard problem to get good maths education at undergraduate level, and that’s the heart of what Project Ember is trying to achieve.

This is a problem which is understudied, there’s not enough work in that area. And so I was delighted to see what’s happening there, the advances they’re making. It’s great, inspiring. I don’t often get to go to these sorts of events anymore, so maybe it’s just that I’m starved of that sort of thing, but I really appreciated it. I thought it was a really well organised event. Huge. I have to confess, I didn’t go to a single plenary. I never made it to the exhibition hall, both of which were really interesting, but I was just, there was so much going on. Yeah, it was great.

[00:21:19] Santiago: Well, I’m very glad you enjoyed it. And it sounds like you gained a lot from it, and you gave a lot to it as well.

[00:21:27] David: I hope so. And, again, I want to thank JMM, the American Math Society, the Math Association of America, and all the other organising groups behind it, because organising such an event at such a scale, and doing so broadly, the special sessions, this is what I loved. I really appreciated the care that was given to the special sessions. And they were well thought out, well organised, interesting people leading them. It was great.

[00:22:00] Santiago: Great. Well thank you very much, David.

[00:22:03] David: Thank you.