Description
In this episode, George and David explore the concept of impact activation for mathematical scientists. They discuss how PhD holders in math-related fields can transition into diverse areas, adding unique value to social impact projects. The conversation highlights key traits like deep focus, resilience, pattern recognition, and abstraction skills that make mathematical scientists ideal for such roles. Emphasis is placed on the importance of collaboration.
[00:00:06] George: Hello and welcome to the IDEMS podcast. I’m George Simmons, a Postdoctoral Impact Activation Fellow here at IDEMS. And I’m joined again by David Stern, founding director.
[00:00:16] David: Hi, George.
[00:00:17] George: So this is the next in our series of conversations about the concept of impact activation. And what I really want to dive into today is the idea of, when we’re talking about impact activation in the sense of, for example, my role, who is really the people we are targeting for that activation.
So I get the sense from you that you are always talking about people with mathematical minds, people with a mathematical sciences background and maybe even more specifically people with a specific research background. Is that kind of a fair reflection of where you start with this?
[00:01:03] David: The concept, and of course this is something which is very specific to our approach to what I’ve been through, to what Danny’s been through in different ways. Broadly, while I believe that impact activation can apply much more widely, I believe we have some understanding of impact activation of mathematical scientists. And I should be clear, a mathematical scientist is broadly someone academically within pure math, applied math, statistics, data science, computer science, theoretical physics, anything which you only really need your mind and a computer to work on.
This is sort of the essence of it. If I think about impact activation specifically for mathematical scientists, again, I’m not sure we understand what that means for mathematical minds, let’s say coming out of an undergraduate degree, yet, maybe that’s something we’ll figure out.
But right now we know that internationally, there are more mathematics PhDs, mathematical science PhDs coming out than are needed in academia, and that many postdocs or PhD students who are in that position are questioning whether they want to carry on in academia, and quite often they see their only alternative as being going to industry, you know, there’s a big demand for these skills in banks, in tech, in the big corporate work, where they would be very well renumerated.
But there is a long history of mathematical scientists being successful outside of that. But they’re almost always one-offs. And so what I believe we are trying to do is to identify how we can take those very narrowly, highly trained experts in mathematical sciences broadly as defined by having a PhD in the mathematical sciences, and convert them to people who are working in a whole range of different areas, different domains, and adding value because of their training, but not because of their direct expertise.
[00:03:49] George: So it’s not that we’re deliberately not targeting the theoretical chemist who considers themselves have a mathematical mind. It’s just that we think that we have a framework that will apply much more easily, or generally, to people who are coming through a mathematical sciences degree.
[00:04:11] David: A theoretical chemist with a mathematical mind might satisfy my definition.
[00:04:16] George: Even if they don’t classify themselves.
[00:04:18] David: The key point would be, the mathematical mind is part of it, but the key point would be the theoretical. An experimental chemist, that’s different. Within our impact activation fellowship, we’ve also had an anthropologist. And she’s done brilliantly, I’ve loved her, but I’ve worked very hard with her trying to make this a good experience.
But in many ways that’s been a much more collaborative experience because I don’t feel I know how to activate anthropologists, and anthropologists are pretty activated already in ways that we would define. And so, you know, she already has a lot of the skills, or had a lot of the skills, that we would normally be activating within mathematical scientists because her anthropological training did that.
Now, I applied the same sort of principles that I applied to the mathematical scientist to her. So the first task I gave her to was to work with databases, something totally outside of her comfort zone, which is part of the principles. And I’m sure we’ll get to some of these ideas as we go forward, but I would argue, and I hope to continue to, I suppose experiment is not a great word for this, but I feel that’s what we’re doing, to learn about how we could activate people coming from other backgrounds or from other sources because I think that this isn’t something which is unique to the mathematical sciences.
What I feel is that we have quite a deep knowledge and quite a lot of experience now of going through a process with mathematical scientists, which has been successful, and you’ve experienced it yourself and you’ve talked about it yourself, it’s been quite transformative.
[00:05:58] George: Yeah, absolutely. Yeah I think that what you’re saying about people with different backgrounds it links nicely to a point you made before, which I quite liked, people from other backgrounds may already have a good idea of what’s available to them, which really suits their skillset already. Whereas part of this is not just allowing mathematicians to add value to things, but also adding value to people with mathematical training to inform their background, their choices as well.
[00:06:30] David: If you’ve done a PhD in anthropology, you feel you can go out and work in international development on causes you care about. You feel equipped to do that in certain ways, in a way that if you’ve done a PhD in pure mathematics, you probably don’t, you don’t see yourself working in international development on social courses. You don’t see how your training has equipped you to do that.
And that’s at the heart of this impact activation process as I see it. As I say, interestingly, I do think that there is a similar process, which would be valuable for anyone. But, the need is not the same, and we don’t understand that as well, recognising the difference between what we know and what we don’t know, this is important. We know mathematical scientists, we’ve got a lot of experience working with them, and we also know the barriers and the difficulties with actually adding value to collaborations working on social impact.
[00:07:33] George: Yeah, I think that’s a really nice framing. So I guess the next step for us is to really then dive into what is it about mathematical scientists that, or what kind of features or assumptions are there about mathematical scientists that can make them thrive in scenarios dealing with social impact, with impactful work.
I know in preparing for the workshop, we came up with a list of five or six assumptions. I dunno if that’s a good place to start.
[00:08:05] David: I’d be really happy to go back through that list with you and discuss them now. What I’d like to maybe do just beforehand is to put this list in context. I think that part of when we were coming up with that list and discussing that, one of the things that we were conscious of is that impact activation as we are framing in this context, or for us, is something which is probably not for everyone.
This is something where we want mathematicians to just be mathematicians to be ivory tower thinkers, moving knowledge forward. And we are not trying to say all mathematicians should be activated. That’s not the point. This isn’t something which I would want to become a blanket recommendation that would remove the power of it. What we are saying is, and I think this is critical, in many of the spaces that I have entered and now our team has entered more broadly, our skills are valued and they’re in demand. They are scarce skills in certain collaborations.
Now, if I think about the collaborations that I’m in, these can be collaborations with 30 to 100 people quite easily working comfortably. How many activated mathematical scientists should there be in that collaboration? You probably only want one to three, no more than, certainly no more than 5% would be, would be a sort of sensible estimation. So this is not about saying mathematical scientists have the answers. No. Actually, it’s the fact that if you get 20 or so people with different skill sets and there’s not a mathematical scientist among them, then probably within that collaboration, an activated mathematical scientist will add value.
That’s sort of the thinking behind this. They shouldn’t be probably the dominant force. But they should be an important voice in the room because they bring a skillset which would probably add value in certain ways. And that’s part of what I think this list makes sense of in some sense, what is that intangible value, which having a PhD mathematician working in a space where you wouldn’t normally have a PhD mathematician can add value?
[00:10:50] George: Yeah I really like that framing. And maybe something even more to say is, I think it’s probably important to separate out these assumptions that we’re about to talk about with the personality or trait that is also something that’s required to actually go out and seek being activated.
[00:11:12] David: And there was a whole list of things that were discussed, humility being one of the most important traits, in certain ways, and arrogance being an interesting, another trait, that combination of both humility and arrogance in the right sort of measures in different times. We’ll almost certainly dig into those in other contexts, but, yeah, let’s start with your list.
[00:11:32] George: So our list started with quite a, I think quite an interesting one, which is simply the ability to focus deeply. And we, as mathematical scientists, we very often find ourselves in the place where essentially nothing happens for a very long time. Except you are just sat there trying to think, trying to find that breakthrough, trying to find that answer.
[00:12:00] David: I used to sort of say this to people that during my PhD I loved the maths I was doing, and I had a comfy chair in my office, and I could sit in my comfy chair, I could close my eyes and I could claim that I was working and sometimes it was true. You know, it’s that ability to be in your mind and actually, need that space, that time to just really go deep.
[00:12:26] George: Yeah. And I think what we’re not saying is that, it’s not just the ability to focus and be able to write pages and pages of documents. It’s that deepness to, as you say, sit in your mind.
[00:12:42] David: Without necessarily writing, you know, or without doing. The ability to, if you want work without writing or doing or producing, just deeply thinking. That skill, and different people have it in different ways, not all mathematicians are the same in this, this really needs to be recognized, some people actually, their deep thinking comes by doing things. There’s different ways that deep thinking or that depth is achieved. But that ability to sit on a problem and not shy away from its complexity, but embrace it deeply, that’s a really important characteristic.
[00:13:23] George: I always really liked the story of one of my professors at Southampton, who, his story’s that his thesis, that breakthrough, came to him while driving away on a family holiday and ended up in the middle of France or something, and suddenly huh, got it. So it was just that process of actually doing something else but your mind is still deeply at work trying to, trying to figure out.
[00:32:52] David: And let’s be clear, this is not necessarily a good trait. There’s nothing more annoying than having someone who’s just lost in another world because they’re not concentrating on what’s happening in the moment, they’re lost in their own thoughts. But this is a skill which as part of a collaboration, as part of a team, you don’t want everyone to have this if you’re working on socially impactful things, you want people to get on and just do things. But having someone in that team who is going to step back, think, and just instinctively want to think more deeply, that’s part of the role, we feel that characteristic is important.
[00:14:28] George: So I think leading on from that ability to focus, and I hinted at this already, but you can spend three and a half outta the four years of your PhD getting nowhere, getting no right answers. But everyone still comes out the other side with that thesis, with that proof, with that magical statement. And we characterize this as the resilience to getting it wrong, really being able to just keep going even though nothing’s working.
[00:14:59] David: And this is really interesting because this is one of the reasons that we are really looking at activating sort of postdoctoral fellows, people who have gone through that PhD program because mathematical minds who haven’t had that PhD, they may never have built that resilience to actually recognising that some problems take years, and you go down so many wrong paths, but that doesn’t mean that you are not making progress.
That ability, that resilience to being able to be wrong, I love in mathematics it’s subjective, if somebody tells me I’ve got something wrong, I say thank you because they’ve pointed out something, it’s not their opinion, they’ve pointed it out to me and I can then understand it. That resilience to getting it wrong and recognising that getting it wrong is part of a process, and you will then learn from that and evolve. That’s important.
[00:15:57] George: Yeah. I agree. Almost every mathematician you speak to will have some experience, their entire experience of their PhD has been definitely down this.
[00:16:05] David: Yeah, the nature of mathematics in many different ways means that you don’t find success without actually learning from your mistakes, which is great.
[00:16:17] George: The third assumption that we came up with was, again, drawing into that right or wrong piece, and we summarised it as having an awareness of what we don’t understand, being able to…
[00:16:32] David: Knowing what you don’t know.
[00:16:34] George: Exactly, knowing what you don’t know, but still being excited by that. I think a lot of mathematicians and groups of PhD students spend a lot of time at least trying to understand what their fellow students, colleagues are doing, even without much success. And that awareness of knowing what we don’t know, what we don’t understand, we picked that out as very important.
[00:17:00] David: I always say to students going through this that, you know, I did well at school and so I thought I knew some maths. By the time I started my PhD, I realized I had more to learn. And by the time I finished my PhD, I realized I knew nothing. There was so much out there that I didn’t know. But I knew I could understand quite a lot of it if I needed to, but I don’t yet know it. I don’t understand it now.
And that awareness of the limits of your current understanding, this is something which, again, as mathematicians, you need that skill, you need to know what you don’t know, because if you pretend to know something, you get caught out really quickly.
[00:17:42] George: Yeah I like that. I think for those listening, I think in our next chat, we’ll be diving into what each of these assumptions actually means for working in the context of social impact or that kind of thing. So this is just the starter of discussing what these assumptions actually mean.
And the next one is actually one of my favourite because I think is just a common story. You walk into any break room of PhD students, which by the way seems to be where the majority of PhD students spend the majority of their time, not actually doing any work.
[00:18:18] David: They are doing the work, even when…
[00:18:19] George: The claim is that they’re doing their work. But everyone is always gathered around the puzzle pages of the newspapers, around the chess board, round the box of interesting mechanical puzzles, and we summarize this as an eagerness to identify patterns or really, more childishly, to solve puzzles. That there’s always just this fascination, even if it’s nothing to do with your mathematical ability, like doing a crossword, there’s always that eagerness just to figure something out.
[00:18:54] David: Yeah. It’s that eagerness, and I don’t like the word solving, for various reasons, because actually that’s, I would argue, one of the things which, and it is not the truth for all mathematical sciences, the solving is not necessarily the motivation. It’s that eagerness to build that understanding, to understand what do I know, what don’t I know? It’s the process, the eagerness is for the process rather than the result. I think that’s really, yeah, that is something which we see time and time again in the sort of mathematical scientists we want, and in our own teams.
One of our colleagues is an engineer. And he said until I was at IDEMS, people used to say, stop thinking so hard about it. And now, you know, with the colleagues, I realize I’m not thinking enough.
[00:19:40] George: Yeah, there’s no off time. There’s just always something, always something. Even when I turn off for the day, it’s always then send a message to Lily should we do a crossword together? And it’s this constant wanting to explore something and do something new.
[00:19:56] David: Yeah.
[00:19:57] George: The final assumption, just to wrap up today, is definitely something that is familiar to a lot of mathematicians. And it’s, I don’t think we’ve come up with a full summarization of this, but it’s the ability to essentially see through all the noise and identify what parts of your problem are specific, what parts are general, and being able to abstract the information that’s important out of the situation that you’re looking at, and figuring out what that pattern is or what that specific answer is, and then being able to then formulate that precisely.
[00:20:38] David: It is the power of abstraction, of generalisation in certain ways, which is again, a differentiator sometimes of mathematical scientists, and I want to be clear, this is not always a useful trait. There’s many contexts where this is not a good trait. It distracts you from actually just getting on and doing what needs to be done because you are abstracting out to something which isn’t important.
But actually, again, you have a room of 20 people, 20 collaborators, having one person in that room who’s trying to do this and who’s thinking about that is often a useful addition. So this trait, which is both good and bad, is a trait, which is often second nature, is maybe the right way, it’s deeply inbuilt to many mathematical scientists. And that’s really part of their strengths, it’s part of their weaknesses.
[00:21:39] George: And I think this process of abstraction can be seen as yet another puzzle. And I think the interesting thing, and this will be our later conversations about working in that room in a collaboration, is working with people who can help you put the reins on a little bit. Because I think every mathematician has come across a situation where there is that one step too far in abstraction and it’s difficult to see why that happens.
That balance that kind of comes from those collaborative settings, I think will be a very interesting thing to dive into in our future conversations.
[00:22:20] David: Absolutely. And I think maybe a good place to finish is to sort of notice that none of the skills we’ve drawn out, or none of these attributes, relate to maybe the key skills we’ve mentioned, the aspect of collaboration, the aspect of working in a team, being part of a group. And I think this is where the activation part really comes in, that we are not expecting and we don’t find that mathematicians come equipped to be good team players in these sorts of collaborations for social impact. But that is something which they can learn. These can be learned skills on top of who they are.
What we are talking about and the things which we’ve described, if you are a PhD mathematician and this resonates with you, that’s not surprising. Many people would associate with some of these. But associating with all of these and these resonating strongly, that’s really, I think, it’s that subset of the population for whom getting things wrong because you automatically want to think about things very deeply, and when you think about things really deeply, you can’t get them.
It’s this combination of skills which defines a narrow part of the population, which are underrepresented in certain social impact spaces.
[00:23:58] George: I think that’s a really nice place to end and I do need to let you go. So remains say thank you for joining me on this podcast, David, and yeah, look forward to all the conversations we have yet to come.
David: Great. Thank you and thank you for driving this effort forward.
George: My pleasure. It’s great to speak to you.

