In conversation with Anne Skeldon

19 April 2026

It’s Monday morning on Surrey campus, and you’ve woken up nice and early for your 10am lecture. It’s the start of a new term and you’re certain that, with your new morning routine, everything will be different this time: you’ll get perfect sleep every night, and your fellow students will all be in awe of how switched on you seem in lectures.

On your way to the lecture, you catch yourself yawning and realise you’re still tired… but, why? You got eight hours of sleep, had a good breakfast, even practised a new meditation routine! OK, you used your phone a bit before bed but you had that night-time setting on, so that’s fine. You even live next to uni and so your commute through the shaded back garden path is short. No wasted energy on moving, right?

As you wonder why on earth one even needs to sleep, you remember that you study at the University of Surrey and, fortunately for you, Anne Skeldon is your lecturer. She might just have the answers to your queries—let’s just hope you don’t sleep through it.

Cause and effect

Anne Skeldon is professor of mathematics at the University of Surrey, whose research in applied maths has, in recent years, focused on sleep, circadian rhythms and data science. That wasn’t, however, how it all started. “I didn’t start doing maths at university; I started doing physics. I actually found maths was a bit boring at school.”

It was only when Anne began studying physics at Oxford that she (somewhat fortunately) realised that mathematics was hard-coded into the subject, and in fact it was through the maths that she was able to understand the physics.

“I reckon you can explain anything with maths. If you think $A$ causes $B$ which causes $C$, then if I change $A$ in some way, then I should be able to predict something about $C$.” Anne now believes that if someone thinks they understand how something works, a mathematician should be able to swoop in, write down some equations and comment on the argument. “If one’s hypothesis is correct, then this is what we should see.” There is a strong proposition that mathematics deserves to be considered a core part of the scientific method. The power of maths to explain the real world is what really captivates Anne: “I love the ability to write down equations and understand the dynamical structure of things, especially if it applies to something; maths can take you anywhere, right?”

Across Anne’s career, she has researched topics such as pattern formation and bifurcation theory, both from a relatively abstract point of view and in terms of how they interact with the real world. The carbon cycle, tumours, and the social politics of recycling are just a few of the areas where her mathematics has found application. Currently, however, she is focused mainly on a particular application area: what makes a good night’s sleep?

Sleep is a perfect storm

Anne hadn’t come to Surrey with an interest in sleep; she had come for its leading reputation in nonlinear dynamics. One day, Derk-Jan Dijk, director of the Surrey Sleep Research Centre, came to give a talk in the mathematics department. They got talking afterwards and ended up co-supervising a masters student. From there, the idea of more modelling problems around sleep “snowballed” into the research area it is today.

Banks of screens on a wall above a desk containing a number of keyboards

Inside the control room of the sleep research centre. Image: Anne Skeldon

The sleep research centre had previously considered more physiological, psychological, cognitive and behavioural patterns within sleep; the mathematical tools which Anne develops provide a new direction by which to unpick sleep’s mysteries. This has built on a rich tradition of using mathematics in sleep and circadian research which dates back to the 70s and 80s.

Though we may not always give it the thought it deserves, sleep is actually a highly complex phenomenon which is deeply interconnected with many aspects of our lives. “There’s a social science aspect too because it affects your relationships; when you go to bed to sleep is also dependent on social, work and study constraints.” In terms of biology, one can study the impact sleep has on health. There are short-term associations like sleep and mood, sleep and performance, sleep and injury risk, but there are also long-term risks associated with cardiovascular disease and certain cancers. Anne’s interest in sleep arises from the implications of these risks—“The question is: what is the biology that sits underneath that? What happens to your brain when you go to sleep?” Anne points out that, rather fundamentally, researchers still don’t even know why we sleep. “Your car doesn’t get tired… so why do we?”

In Anne’s ideal world, nobody would have to struggle to get out of bed when their alarm clock goes off. We agree; in fact, she goes on to suggest that a perfect scenario would have everyone leaping out of bed or not even need an alarm clock. Sounds utopian! But where do we even start?

“You obviously can’t change your physiology, but you can change your environment. What I’ve done has mostly been around when people sleep.” A significant chunk of Anne’s research is based on taking known data and building quantitative models that are able to explain sleep at an individual level, or can be fit to specific individuals. “We aim to design interventions for individuals to help them sleep at the time they want to sleep.”

A woman sleeping in a dark room. She has probes attached to her head.

A participant sleeps soundly while being monitored. Image: Anne Skeldon

Thinking like an oscillator

It’s intuitive that different forms of light will affect how you sleep: how sunny it is outside, for example, or whether you have lamps on in your room, or even the brightness of your phone screen that might be filtered by blue-blocking glasses. “Your eye doesn’t know what the source is. It’s a photon, in the end!” Anne tells us. “But it does know something about the amount of energy and the flux.

“If you were an engineer, and you were designing a solar cell, you’d probably be interested in watts per square metre. But that’s not the unit that biologists use, because your eye has receptors that are responsive to different wavelengths;

The key to understanding sleep patterns is undoubtedly one’s body clock (or biological clock). Our body clocks have a natural period, but, for a given individual, that natural period may not be exactly 24 hours. “Imagine yourself as an oscillator; if you’re trying to live on a 24-hour cycle, which is away from your natural period, your natural rhythm needs to be entrained.” This idea frames each individual as having their own self-sustained internal (circadian) oscillation which is then altered by an input signal from the light-dark cycle.

Cartoon of Anne in front of a whiteboard, with a drawing of the sun next to both a cross and a tick.

Cartoon Anne telling us that light is both the problem and the solution

Whatever helps you sleep at night…

Biologically speaking, an important cue that sends you to sleep is melatonin, a hormone whose concentration in the bloodstream naturally increases during the evening and into the night. Anne tells us light suppresses melatonin—that’s one reason why having bright light in the evening has an acute effect on when you decide to sleep!

“If you want to entrain a rhythm, the input signal needs to be strongly rhythmic with a strong 24-hour component—there has to be significant contrasts between day and night.” Anne says that this entrained oscillator model would work really well if we were still hunter-gatherers. The sun would come up and we’d naturally be outside; the sun would go down and we’d know to go to sleep.

Every individual has their own body clock which, for most of us, runs slightly slow. But for others it can be too fast. The key idea is that depending on the time of day, light can either speed up or slow down your clock. This process can be modelled via velocity response models; for example, in the Winfree model, the rate of change of phase $\theta$ is given by
$$ \frac{\mathrm{d}\theta}{\mathrm{d}t} = \omega + \ell(t)\sin\theta. $$

In the absence of light, phase advances uniformly with angular velocity $\omega$. When light is present, $\ell(t)$ is non-zero, and thus whether light speeds us or slows down the rate of change of phase (in the case of humans, our body clock) depends on the phase (the time of biological day). “If you have a slow internal clock, and you need to speed it up to 24 hours, you need to have lots of light in the morning and not too much light in the evening.” It’s encoded in our biology.

We were also interested to know if these models had actually been tested and matched with data. Returning to her analogy with hunter-gatherers, Anne explained to us that there have actually been experiments to try to recreate those conditions. “There are these neat cave experiments where people hid themselves away from external cues to try and figure out why we actually get up in the morning.” It was a burning question; is it just the sun comes up and we get up, or does there exist some internal rhythm? The experimenters relieved themselves of technology new and old, set down their watches and alarm clocks, removed any thermal cues in order to remove any contrast between night and day, and took themselves away from all natural light and into cave systems.

“And they found that they did still have a rhythm,” Anne concluded, “but it actually wasn’t 24 hours.” There were individual differences amongst the subjects in that most people went to bed slightly later each night and got up slightly later each day, though some people would do the reverse and get up earlier.

Anne’s model as featured on YouTube. Image: Peter Caires

“As a society I think there are a lot of people who struggle on that temptation to go to bed later and wake up later—you often see that on holidays.” It poses an interesting question from a psychological point of view: “What is it that takes us to bed in the end? Do you look at your watch and think, I really ought to go to bed now, it’s three in the morning?”

As the sun set on our conversation with Anne, we were left to reflect on what she had said meant for our own sleep cycles. Of course, sleep is incredibly complex, and many other aspects of our routine can affect our sleeping patterns (caffeine intake, diet and stress to name a few). But perhaps as a society we have come to overestimate our own roles in these matters and forgotten the importance of the natural rhythm influencing all of life on Earth: the solar cycle.

Sweet dreams!

Sam Kay

Sam is a PhD student at Durham Univeristy working on structures in the solar wind. His pastimes include pestering Clare about Linux and making Adam feel old. Seriously, who remembers the 90s?