There are many qualities attributed to mathematicians that we can be proud of: we’re logical, meticulous, intelligent, even creative. Despite maths being revered for needing all of these excellent attributes, one thing we are perhaps not so renowned for is our communication skills: most of the world still finds maths intimidating and opaque. That’s why Chalkdust sat down with science communication expert Dominique Sleet to learn the secrets that will help us to share the beauty of maths as far and wide as possible.

Science explained

Dominique began her science communication life as an explainer at the Science Museum in London. Many London-based Chalkdust readers will be keenly familiar with the Science Museum, but for those who are not, the Science Museum is pretty much exactly what it says on the tin. As well as many more traditional static galleries, it has several interactive galleries aimed at young people, which are like science-themed playgrounds.

Explainers are tasked with (you guessed it) explaining the science behind what they’re doing. “You get to play with some fun things, like putting flowers into liquid nitrogen and smashing them or blowing up a hydrogen balloon. The whole museum ethos is to build an association between fun and science. If there’s some learning in there then that’s great, but there doesn’t have to be; it’s just about nurturing that relationship.” But there’s plenty to learn if you’re looking. “Some of the science behind the exhibits is beautiful. We had this exhibit where you would look through polarising lenses at a thin layer of ice and you could see all these feathery beautiful patterns with amazing colours. I’m a nerd, I like science.”

Those of us who grew up to be Chalkdust editors could spend a cheerful afternoon churning out algebra, but for most children the liquid nitrogen has the more evident appeal. “Maths has its challenges. It’s a lot more abstract. With science, as long as you use the right language, you can make almost anything accessible, whereas with maths, you often need to have prior knowledge.” And don’t forget that intimidation. “People have this barrier, it’s almost like a badge, ‘I don’t do maths.’ And it’s really sad. So before you’ve even begun, you have to overcome this preconception of maths being like an alien language, and only for clever people.” People are often more receptive to the content if they don’t know that it’s maths—”Pattern Pod was my favourite gallery, which was for under-eights and all about maths, but we were looking at patterns and didn’t label it as maths.” Unfortunately, the plausible deniability can’t last forever, and inevitably your audience will notice that they are being subjected to maths: what then? “You need to show why something’s important and make it relevant to everyday life. You can’t get into the depth that you’d need to understand all the maths behind the exhibits, but you can go into some detail about how the maths was used, how it changed the world, and what impact it had on people.” The work does not end there however. How do we get people to turn up for maths in the first place?

A royal invitation

Receiving millions of visitors per year, the Science Museum is well-placed to reach out to people who wouldn’t usually be interested. “But even then there are barriers. I remember doing an outreach programme in south-east London and people hadn’t even heard of the Science Museum. That’s why outreach is really important. Going out into local communities and finding the people where they are in their everyday lives.”

Dominique’s next job was at the Royal Institution (also in London), where she worked on everything from their famous annual Christmas lectures to their extensive year-round masterclass programme. So what’s the trick to running a maths masterclass? “Pick a topic that interests you because if you’re passionate about the topic then you’re halfway there. The kids aren’t going to be excited about something if you’re not excited yourself. In the same breath, you need to realise that, while you might find something amazing, other people really don’t. You’ve got to show them why it’s interesting.”

It was nice to hear a shoutout for one of Chalkdust‘s own, who apparently is quite the master of masterclasses himself. “This will sound like I’m sucking up, but I remember a session with Matthew Scroggs getting the kids to explore different braiding patterns. There’s actually some really interesting maths going on, because some combinations of braid would work and some of them wouldn’t. But at the end he was saying he doesn’t really understand it, he doesn’t know what makes a good braid and what doesn’t.” This open-ended aspect of maths often isn’t apparent until university, and school often leaves people with the idea that all the maths has been done. “Kids have this idea that maths can only be right or wrong, but in fact there can be lots of exploration. And maths can be really quite creative.”

When Dominique learned that the 2019 Christmas lectures would be focused on maths, and feature veritable maths celebs Hannah Fry and Matt Parker, she jumped at the chance to be involved. “My role was Christmas lectures assistant, a kind of catch-all. On the night itself, I’m the one in the front row, on the laptop with little prompts for Hannah—and at the same time, trying to keep an eye on messages from livestreaming venues, to make sure they’re all happy.” And it was a lot of hard work. “Very high pressure and some of the team would work until two o’clock in morning. It was crazy.” One of her contributions turned out to be very prescient, in a segment designed to show how mass vaccination succeeds. “I suggested that we use surgical masks to indicate that the kids were vaccinated and that they can’t catch the virus. Now looking back on it—oh my God! Told the future!”

Of course, communicating maths for TV brings with it some new challenges. “Sometimes there will be conflicting priorities between the production team and the Royal Institution. The production team want everything to look flashy. Whereas obviously the RI still want it to be interesting, but we also want to make sure the integrity of the maths is still there.” Those who watched the Christmas lectures (if you didn’t, you should hang up your maths fanatic hat right now) will recall a specific sequence which involved schoolchildren lining up and then taking a step to either the left or the right based on the result of a coin toss. “What we were trying to show was that probabilities can help you predict outcomes. So we wanted to get this lovely bell-shaped curve from all the students moving about, but we didn’t get what we were hoping for. Partly because it’s hard to instruct a large group of people to do exactly what you’re asking, but also simply because probability doesn’t offer any guarantees.” So where did that leave the narrative of the lecture? “The fact that the kids didn’t do what we thought is actually a really interesting point in itself. But from a TV perspective, that’s the opening demonstration and we can’t go off on a tangent. So we ended up having a montage of two different schools in the lecture.”

Widening participation

As Dominique moves on to her next job working on the outreach programme at Imperial College London, she finds that the university setting has an increased focus on widening participation—so how do we convince young people from underrepresented groups to consider maths? She says an obvious start is making your event free if possible (since financial barriers often have a big impact), and ensuring diverse role models are present. “Representation does matter—look for different people from different backgrounds, from different areas, as well as different topics.” Marketing is also crucial. “You can have the best outreach in the world, but if nobody knows about it and it’s not reaching the right people, then it’s not doing anything.” But don’t think your job is over once you have them in the room. “The audience should be kept at the forefront of your mind. You need to be thinking about who your activity is for, what you want them to learn and how are you going to make sure they actually understand?”

Finally, she encourages everyone to take the necessary time and effort to accommodate accessibility needs. “Putting a bit of effort in to make it as accessible as possible, whether that’s looking at the colour scheme you’re using for colour blindness, not putting too many words on a screen, or having materials available in advance or in large print. All of those accessibility things can feel like extra work but they’re only ever going to improve it. Good for everyone—not just the person you are trying to accommodate.”

Having only been at Imperial for three months, she is is still reasonably new to the job, but has a lot of positive things to say about what she has seen. Her current project focuses on sixth formers. “I think the programme itself is really worthwhile, it’s very intense. There are online courses, with mentoring sessions in small groups throughout the year as well as large welcome and closing events on campus, although as you can imagine these have had to convert to online events in recent times.” Looking to the future, she says: “There is a move to intervene earlier in children’s maths education so Imperial, like many other organisations, have a growing number of outreach programmes aimed at younger students.” We wish her all the best in her latest endeavour.

This interview was conducted on 11 August 2020, and our discussion of the pandemic reflects this.

Given everything we read in the news during this pandemic, it is no longer a surprise to anyone that maths plays a crucial role in solving problems that affect our daily lives. This has been thrown into the spotlight recently, with mathematical modellers advising government policies across the world and statisticians holding the key to decoding the chaos of pandemic data; but it has been going on behind the scenes for quite some time. Operational research (OR) is the branch of applied maths dedicated to using maths to make better decisions, and it can be applied to almost any field. If that sounds vague, fret not, because we sat down with Christina Pagel, professor of operational research and director of the Clinical Operational Research Unit (CORU) at UCL, and a member of the Independent Sage (Scientific Advisory Group for Emergencies) committee, to clear up exactly what it entails.

“Operational research is a really applied branch of maths, and you can use any kind of maths, as long as you’re answering a real world problem.” But some maths is more typical of operational research than others. For example, queueing theory is the mathematical theory behind modelling queues and making them more efficient, ie deciding who gets served in what order. Another classic of OR is optimisation, which is choosing how to allocate resources given certain constraints and goals, such as minimising costs or maximising profit. “That’s used everywhere from transport, health care, emergencies… The travelling salesman is a really well-known optimisation problem—how do I visit these destinations in the shortest time possible?” Chalkdust would like to apologise to readers for any distress caused by the reminder of their decision maths A-level module.

Data analysis is crucial too. “How do we use the data that people have to help them make decisions? That’s a big branch of operational research.” And of course, as with most branches of maths these days, simulations play a big role. “Say in queueing theory, it’s fine as long as you have Poisson arrivals and exponential service times, but once you get to real life and see that actually you have this funky algorithm for choosing who gets served and how long it takes, then you start having to use simulation because you just can’t solve it analytically.”

But the field is very problem-focused, and for Christina the maths is of only secondary interest to the questions themselves. “I’ve become less interested, as I become older and more senior, in the novelty or difficulty of the mathematics and much more interested in the problem.” And it shows—she has worked on more problems than there are maths puns in an issue of Chalkdust.

Paediatrics, politics, periods…

As director of CORU at UCL, Christina focuses on operational research applied to healthcare. She recently held a position as researcher in residence at Great Ormond Street hospital (GOSH), a children’s hospital in London, helping them solve problems like predicting how many beds they will need, or when the children’s respiratory disease peak will be. The peak is about a month and half earlier than the adult flu peak, and Christina built a model for GOSH to let them know when it begins. This is crucial to know because when it comes, “demand will double very quickly and they don’t have more capacity.”

This is only the tip of the iceberg in regards to all the problems healthcare needs mathematicians to solve. Another classic operational research problem that CORU has worked on recently is investigating the ideal placement of the UK’s 11 specialised ambulance services which transport sick children from local hospitals to paediatric intensive care hospitals, as well as the possibility of changing the number of ambulances at each location. “We also do simple models of vaccination programs for the [UK government’s] Department of Health and Social Care. If I’m introducing a new vaccine, what is the impact of other vaccines? How many times do I have to vaccinate? That involves a mixture of theoretical modelling and then data analysis. Sometimes we mix them together, like in queue models for how many health visitors you need to serve a certain community with certain needs, which is something we’re doing right now for instance.”

For even further evidence of the infinite set of problems mathematicians are in demand to solve (as if we needed it), Christina tells me she began a fellowship in the US in 2016 to study their healthcare system, but unexpectedly found herself more useful in political science. “Within about two months of me getting there, Trump was elected. And it became really clear that he was going to try to repeal Obamacare. He failed, but I didn’t know that at the time.” She felt there was no point working to improve a health system that was about to be upheaved, but she saw politicians arguing about Obamacare and she realised that she had a unique perspective on how to understand their feuds.

“I thought, ‘Do we understand what the goal is in the situation?’ That’s a classic operational research point of view. If you can’t articulate what you’re trying to do, then all of your solutions for getting there are meaningless.” She devised a survey for politicians to understand what their goal was. The survey had thirteen possible goals that were developed with a focus group of serving politicians and academic health policy experts, such as ‘improve health’, ‘reduce costs’ and ‘reduce inequality’, and participants were asked to rank them on importance. Using a voting system, she was able to give the items an ‘overall’ ranking, and used a stats technique for plotting multidimensional priorities to see how people on different parts of the political spectrum felt about healthcare. “It wasn’t anything particularly sophisticated, but they just hadn’t ever done that!” What was common sense to Christina was a completely new way of looking at the problem to political scientists.

The methodology was a triumph in and of itself—perhaps fortunately, since the more challenging task of showing that politicians agreed on the goals didn’t transpire quite as planned. “I thought everyone would say improving health is the most important thing. But actually, improving health was only most important for Democrats, and second most important was reducing inequalities and improving access to healthcare. Whereas, for Republicans, the most important thing was reducing costs, and the second most important thing was reducing the involvement of government in healthcare, which to me was really bizarre, but that was important for them. Improving health came fifth out of thirteen, and last was reducing inequality.” But even though they could not agree, the survey still clarified exactly why they couldn’t agree. “It’s really helped them understand how they can talk to each other. For instance, if you’re a Democrat, and you want to push a policy because it reduces inequality, to your Republican colleagues that’s not the angle you use, you have to explain how it reduces costs.”

She is now working on a project looking at women’s period pain. “It’s not really my expertise, but if no one else is going to do it, then I’ll do it.” She is working with the Health Foundation to look at GP records to quantify the problem, which she hopes will convince medical researchers to give the issue serious attention. “80% of women at some point in their lives suffer from really bad period pain, and about 20% have some years of their life where actually it’s debilitating for two or three days a month. People have just found a way to live with it, when you shouldn’t have to live with that—why should you have to live with that? So we’re now trying to take it further and make it into a bigger project.” Picking up a problem wherever she sees one to solve is rather a habit of hers it seems. Of course, healthcare has had one particularly big problem to solve recently.

…and pandemics

Well, we had to talk about it eventually.

Operational research has played a crucial role in managing the pandemic from the beginning, and Christina laments that even better use of it has not been made. “There are loads of places operational research could have helped [the UK government] to do better.” An obvious issue is distribution of PPE (personal protective equipment), but there are many examples. “For instance, 30% of people with Covid-19 in intensive care units (ICUs) had kidney failure, so the whole country ran short of renal medicine, and that had knock on effects on people receiving dialysis.” When medicine is in short supply like that, how should it be distributed and prioritised? “How do you decide how many ICU beds you need when you’re reorganising hospitals? How do you decide how many emergency hospitals you need, like the Nightingales? All of that is OR. Even things like oxygen supply—Covid leaves so many people on supplemental oxygen that hospitals were running short, so how do you manage that? Because if you run out, then everyone in the hospital who needs oxygen is screwed which you obviously don’t want.”

Christina has been playing her part as a member of Independent Sage—or, as she affectionately calls it, “indie Sage”—a group of scientists who produce independent advice on the UK’s handling of the pandemic, to challenge and analyse that given by the government’s official scientific advisory group, Sage. Although initially she was expecting to be doing operational research, it became more a public communication of science role. It turns out this is something she excels at. “Because I’ve been working across disciplines—clinicians, patients, people in the government, local commissioners—I’ve had to always try to explain things to lots of different types of people. That’s been really helpful in indie Sage, in that I’m not in a silo.” She now does weekly YouTube briefings (on the indie_SAGE channel) breaking down where we are at with the pandemic and collating government data from countries around the world, and reasonably regularly appears on TV and radio explaining the latest numbers.

Independent Sage believes the UK government should be aiming to achieve elimination of Covid. “There’s a technical difference between elimination and eradication. Eradication is what we’re trying to do to polio and what we did to smallpox, but elimination is what New Zealand did, which is zero community transmission.” This would mean the virus can only enter the country via travellers, which Christina says could hopefully be handled with effective test and trace, and quarantine. “And once you’ve done that, you can go back to normal life! Masks, social distancing, you don’t have to worry about that stuff.” Critics of the strategy say it is simply unachievable. “But it’s not saying you’re never going to get a case. Small outbreaks are much easier to stamp down. It’s like in my house, I have a zero fire policy, I’m not going to let any fire come out, and if it does I’ll put a tea towel over it. We’re stuck in this limbo where you can open mostly but not completely, and if you relax when you haven’t got it down far enough it goes out of control. We’re saying get it down far enough, and you do that through really, really good contact tracing. You have to break the chain of transmission, that’s what South Korea did, that’s what China did.” Unfortunately, between speaking with Christina and writing this article, it’s starting to seem like this prediction may be coming true.

So what does she think the UK should have done to get to such low levels of Covid? “You close down the areas that are really risky. We know outside is safe, but indoor pubs… it’s not a good idea. When countries opened shops, nothing really happened, but when they opened pubs, a few weeks later cases went up. Pubs, restaurants, bars, household parties… all of that causes superspreading events.”

If we had put on more restrictions in the short term while cases were still low, Christina believes we could, in a matter of weeks, have been able to achieve low enough levels to try to eliminate Covid and then we would be in a much better position to reopen schools and have students return to university. The returning of students to university poses a particular concern. “Younger people are much less likely to get symptoms, so they may get Covid and have no idea. And if we don’t have a really good contact tracing system, you can’t stop that. Whereas a really good contact tracing system stops people without symptoms going out, that’s how it works.” To clarify, she doesn’t believe the problem was opening up too early, but rather too quickly. “We opened up schools, and then two weeks later we opened shops, and two weeks later bars, and then gyms and then workplaces. But actually every time you open something, you need to give it about four weeks before you see anything in the data.” More patience with easing restrictions could have avoided the need for local lockdowns. “Local lockdowns are very damaging, whereas if they just waited and got to very low levels of Covid, it would have been fine.”

Master of all trades

Hearing how multi-disciplinary her current job is, perhaps it should not be a surprise that Christina has dipped her toes in quite a few fields before settling on maths, and has four master’s degrees to show for it. “I did maths as an undergrad, because I wanted to be a physicist, which made perfect sense at the time. And I thought quantum mechanics was awesome, so my first master’s was in quantum theory.” But when it came to choosing a PhD, she was told she would have to do a topic that was very heavy on tensors, and she understandably ran for the hills. “I thought, ‘I’m out then, it’s not for me!’ So I got a job and decided to do a part-time MA in classics because I always loved history, I loved ancient history, I loved Latin. I chose maths for my degree because you can’t skip from doing maths A-level to doing a master’s in maths, but you can do that in humanities.” Even though supposedly she needed an arts degree, she was admitted to the MA in classics with a first in maths, simply because people find maths impressive. “People will just give you the benefit of the doubt, it’s actually really handy.” She really enjoyed the opportunity to learn purely for pleasure.

Eventually, physics called her back. “I did a PhD in space physics, because I thought… ‘I want to be an astronaut.’” Again, they were more than happy to accept a student with a background in maths. But she found herself frustrated with the obscurity of her work. “No one would have cared if I got it wrong. Literally, there were ten people in the world interested in that area of physics.” This is what inspired her to go into research that had a very direct application. “I thought this practical use of maths to help concrete problems is really appealing, so then I came to CORU.”

Although she had found her new calling, she couldn’t bring herself to give up her other passions yet. “I did another part-time master’s in medieval history, and again I really loved it.” The final master’s, which she did later in her career, was in statistics. “That was because people in health think if you do maths, then you’re a statistician. So I thought I’ll just do a stats qualification so I can say I am! But it wasn’t nearly as fun.” However, she did enjoy having her talents in maths reaffirmed. “I spend most of my time now doing project management, so it was kind of nice to do maths again and realise I could still do it.”

It is certainly good to hear that mathematicians have this power to jump around to any field they want. “The earlier you switch, the easier it is. For me, I looked at people who were working at CORU at the time, and about half the unit had done undergrads in physics, so I knew it was fine. We advertise that we don’t mind if people come with a different background. Maths teaches you how to think, and it is really flexible. You can’t change field and expect everything to stay the same. You have to be willing to learn a new programming language, a completely different way of looking at things. Operational research suits people who aren’t wedded to methods, or a certain type of way of doing things, but are actually really interested in real problems.” It may be a relief to anyone choosing modules or PhD topics that their choice won’t limit their career options—and in fact, as our conversation comes to a close, she has some advice for people making these decisions now. “If you’re thinking about doing a PhD, it does matter who your supervisor is. It’s quite an intense relationship, they’re the person who is going to be guiding you into becoming an independent scientist, and having someone who doesn’t want to do it or who is not that engaged can just be a really bad experience. And you have to find it interesting—because you’re going to be doing it for three years, and that’s a long time!”