Arriving at St John’s in 2008 to begin my study of mathematics, I was certain that within 4 years I would be working in the city as an actuary or an investment banker. Whilst I loved my subject, I saw it as means to obtain a good degree that would set me up for a career in finance. I’m not sure I could have been more wrong…
My current journey began towards the end of my second year, where I found myself enjoying the course so much that I wanted to continue to do so for as long as possible. This led me to research PhD programmes in the UK and the US, and I was fortunate enough to be offered a place to study Applied Maths at the University of Cambridge in 2012. During my time at Oxford, I found myself straying further and further into the territory of applied maths, culminating in a fourth-year course in fluid mechanics – the study of how fluids such as water, air and ice move around. This ultimately led to my PhD topic at Cambridge: where does river water go when it enters the ocean? (If you’re interested to find out more I’ve written a series of articles here explaining my thesis in simple terms.)
As part of my PhD I conducted experiments, worked on equations and even took part in a research cruise to the Southern Ocean. It was on my return from 6 weeks at sea that I had my first taste of the media industry via a 2-month internship with the Naked Scientists. I would spend each day searching out the most interesting breaking science research, before arranging an interview with the author for BBC radio. It was great fun and I learnt so much in so many different fields that I was instantly hooked. Upon completion of my PhD I went to work with the Naked Scientists full time creating a series of maths videos looking at everything from beehives and surfing, to artwork and criminals. You can watch a short trailer for the Naked Maths series below.
My work with the BBC and the media in general ultimately led me to my current position as a Mathematics Tutor at three Oxford colleges: St John’s, St Hugh’s and St Edmund Hall. This may not sound like the media industry, but the flexibility of the position has allowed me to work on several projects, including launching my website and my YouTube channel @tomrocksmaths where I am currently running two ongoing series. In the first, Equations Stripped, I strip back the most important equations in maths layer-by-layer; and for the second series in partnership with the website I Love Mathematics, I answer the questions sent in and voted for by students and maths-enthusiasts across the world.
Alongside my online videos, I am also writing a book discussing the maths of Pokémon – Pokémaths – and have a weekly show with BBC radio called ‘Funbers’ where I tell you the fun facts about numbers that you didn’t realise you’ve secretly always wanted to know. I have also recently presented at conferences in the US and India and hold regular talks at schools and universities, including for the Oxford Invariants and the Maths in Action series at Warwick University where I faced my biggest audience yet of 1200.
Looking back at my time at St John’s, I never would have imagined a career in the media industry lay before me, but the skills, experience and relationships that I formed there have undoubtedly helped to guide me along this path. I think it just goes to show that Maths is possibly the most universal of all subjects and really can lead to a career in any industry.
In October 2017, Dr Tom Crawford joined St Hugh’s as a Lecturer in Mathematics. He has since launched his own award-winning outreach programme via his website tomrocksmaths.com and in the process became a household name across Oxford University as the ‘Naked Mathematician’. Here, Tom looks back on the past year…
I arrived at St Hugh’s not really knowing what I was getting into to be completely honest. I’d left a stable and very enjoyable job as a science journalist working with the BBC, to take a leap into the unknown and go it alone in the world of maths communication and outreach. The plan was for the Lectureship at St Hugh’s to provide a monthly salary, whilst I attempted to do my best to make everyone love maths as much as I do. A fool’s errand perhaps to some, but one that I now realise I was born to do.
The ‘Naked Mathematician’ idea came out of my time with the Naked Scientists – a production company that specialises in broadcasting science news internationally via the radio and podcasts. The idea of the name was that we were stripping back science to the basics to make it easier to understand – much like Jamie Oliver and his ‘Naked Chef’ persona. Being predominantly a radio programme, it was relatively easy to leave the rest up to the listener’s imagination, but as I transitioned into video I realised that I could no longer hide behind suggestion and implication. If I was going to stick with the ‘Naked’ idea, it would have to be for real.
Fortunately, the more I thought about it, the more it made sense. Here I was, trying to take on the stereotype of maths as a boring, dreary, serious subject and I thought to myself ‘what’s the best way to make something less serious? Do it in your underwear of course!’ And so, the Naked Mathematician was born.
At the time of writing, the ‘Equations Stripped’ series has received over 100,000 views – that’s 100,000 people who have listened to some maths that they perhaps otherwise wouldn’t have, if it was presented in the usual lecture style. For me that’s a huge victory.
The key idea behind this project is that by allowing the audience to become a part of the process, they will hopefully feel more affinity to the subject, and ultimately take a greater interest in the video and the mathematical content that it contains. I’ve seen numerous examples of students sharing the vote with their friends to try to ensure that their question wins; or sharing the final video proud that they were the one who submitted the winning question. By generating passion, excitement and enthusiasm for the subject of maths, I hope to be able to improve its image in society, and I believe that small victories, such as a student sharing a maths-based post on social media, provide the first steps along the path towards achieving this goal.
Speaking of goals, I have to talk about ‘Maths v Sport’. It is by far the most popular of all of my talks, having featured this past year at the Cambridge Science Festival, the Oxford Maths Festival and the upcoming New Scientist Live event in September. It even resulted in me landing a role as the Daily Mirror’s ‘penalty kick expert’ when I was asked to analyse the England football team’s penalty shootout victory over Colombia in the last 16 of the World Cup! Most of the success of a penalty kick comes down to placement of the shot, with an 80% of a goal when aiming for the ‘unsaveable zone’, compared to only a 50% chance of success when aiming elsewhere.
In Maths v Sport I talk about three of my favourite sports – football, running and rowing – and the maths that we can use to analyse them. Can we predict where a free-kick will go before it’s taken? What is the fastest a human being can ever hope to run a marathon? Where is the best place in the world to attempt to break a rowing world record? Maths has all of the answers and some of them might just surprise you…
Another talk that has proved to be very popular is on the topic of ‘Ancient Greek Mathematicians’, which in true Tom Rocks Maths style involves a toga costume. The toga became infamous during the FameLab competition earlier this year, with my victory in the Oxford heats featured in the Oxford Mail. The competition requires scientists to explain a topic in their subject to an audience in a pub, in only 3 minutes. My thinking was that if I tell a pub full of punters that I’m going to talk about maths they won’t want to listen, but if I show up in a toga and start telling stories of deceit and murder from Ancient Greece then maybe I’ll keep their attention! This became the basis of the Ancient Greek Mathematicians talk where I discuss my favourite shapes, tell the story of a mathematician thrown overboard from a ship for being too clever, and explain what caused Archimedes to get so excited that he ran naked through the streets.
This summer has seen the expansion of the Tom Rocks Maths team with the addition of two undergraduate students as part of a summer research project in maths communication and outreach. St John’s undergraduate Kai Laddiman has been discussing machine learning and the problem of P vs NP using his background in computer science, while St Hugh’s maths and philosophy student Joe Double has been talking all things aliens whilst also telling us to play nice! Joe’s article in particular has proven to be real hit and was published by both Oxford Sparks and Science Oxford – well worth a read if you want to know how game theory can be used to help to reduce the problem of deforestation.
Looking forward to next year, I’m very excited to announce that the Funbers series with the BBC will be continuing. Now on its 25th episode, each week I take a look at a different number in more detail than anyone ever really should, to tell you everything you didn’t realise you’ve secretly always wanted to know about it. Highlights so far include Feigenbaum’s Constant and the fastest route into chaos, my favourite number ‘e’ and its link to finance, and the competition for the unluckiest number in the world between 8, 13 and 17.
The past year really has been quite the adventure and I can happily say I’ve enjoyed every minute of it. Everyone at St Hugh’s has been so welcoming and supportive of everything that I’m trying to do to make maths mainstream. I haven’t even mentioned my students who have been really fantastic and always happy to promote my work, and perhaps more importantly to tell me when things aren’t quite working!
The year ended with a really big surprise (at least to me) when I was selected as a joint-winner in the Outreach and Widening Participation category at the OxTALENT awards for my work with Tom Rocks Maths, and I can honestly say that such recognition would not have been possible without the support I have received from the college. I arrived at St Hugh’s not really knowing what to expect, and I can now say that I’ve found myself a family.
Next month (March 2019) I will be hosting the ‘Carnival of Mathematics’ – a monthly blogging round up hosted by a different blog each month and organised by the Aperiodical.
The Carnival of Mathematics accepts any mathematics-related blog posts, YouTube videos or other online content posted during the previous month (February 2019): explanations of serious mathematics, puzzles, writing about mathematics education, mathematical anecdotes, refutations of bad mathematics, applications, reviews, etc. Sufficiently mathematized portions of other disciplines are also acceptable. Links to the previous monthly posts and a FAQ section can be found on the Aperiodical website here.
The deadline to submit your posts will be the 1st March 2019.
How fast should an animal be able to move? And why are the biggest animals, which pack more muscle, not the fastest? That’s what Yale scientist Walter Jetz was wondering, so he and his colleagues looked at hundreds of animal species and have come up with a new theory that successfully puts a speed limit on most species…
There is a theoretical maximum speed that is expected to increase with body size, however, in order to actually get to any speed you need to first accelerate, and larger animals take much longer to do so – much like a truck accelerating to 60mph compared to a motorbike or car.
Large bodied animals simply do not have sufficient energy to reach their theoretical maximum speed.
The general distribution is a ‘hump-shape’ as shown in the plots below. Maximum speed increases with size until we reach a critical mass beyond which the maximum speed reached starts to decrease.
Data for over 450 species were included in the study, across land, air and water.
The study provides insight into evolutionary trade-offs for different species as they evolve to increase their chances of survival.
You can listen to the full interview with the Naked Scientists here.
I was interviewed by Autumn Neagle at Science Oxford about my toga-clad exploits in FameLab and the meaning of my maths-based tattoos… You can read the full article here.
What did you enjoy most about the FameLab experience?
“I’d been aware of FameLab for a few years, but I’d never entered because I thought that you had to talk about your own research – and with mine being lab-based I didn’t think it would translate very well to the live element of the show. But, once I found out that I could talk about anything within the subject of maths then it was a whole different ball game and I just had to give it a go. I think my favourite part was actually coming up with the talks themselves, just sitting down and brainstorming the ideas was such a fun process.”
What did you learn about yourself?
“The main takeaway for me was the importance of keeping to time. I knew beforehand that I was not the best at ‘following the rules’ and I think that both of my FameLab talks really demonstrated that as I never actually managed to get to the end of my talk! This was despite practicing several times beforehand and coming in sometimes up to 30 seconds short of the 3-minute limit – I think once I’m on stage I get carried away and just don’t want to come off!”
What about post-FameLab – how has taking part made a difference?
“Well, I certainly now appreciate the comfort and flexibility of wearing a toga that’s for sure! But on a more serious note, I think the experience of being on stage in front of a live audience really is invaluable when it comes to ‘performing maths’ – and I say ‘performing’ because that’s now how I see it. Before I would be giving a lecture or a talk about maths, but now it’s a full-on choreographed performance, and I think taking part in FameLab really helped me to understand that.
Any tips for future contestants?
“It has to be the time thing doesn’t it! I think everyone knows to practice beforehand to ensure they can get all of the material across in the 3-minutes, but for me that wasn’t enough. I’d suggest doing the actual performance in front of a group of friends or colleagues because – if they’re anything like me – then the adrenaline rush of being on stage changes even the best rehearsed routines and you can only get that from the live audience experience.”
What are you up to now/next?
“I’ve actually just received an award from the University of Oxford for my outreach work which is of course fantastic but also completely unexpected! I really do just love talking to people about maths and getting everyone to love it as much as I do, so the plan is very much to keep Tom Rocks Maths going and to hopefully expand into television… I have a few things in the pipeline so watch this space.”
Are all of your tattoos science inspired and if so what’s next?
“Now that I’ve reached the dizzy heights of 32 tattoos I can’t say that they are all based on science or maths, but it’s definitely still one of the dominant themes. So far I’ve got my favourite equation – Navier-Stokes, my favourite shapes – the Platonic Solids, and my favourite number – e. Next, I’m thinking of something related to the Normal Distribution – it’s such a powerful tool and the symmetry of the equation and the graph is beautiful – but I’ve yet to figure out exactly what that’s going to look like. If anyone has any suggestions though do let me know! @tomrocksmaths on social media – perhaps we can even turn it into a competition: pick Tom’s next tattoo, what do you think?”
In your YouTube video’s #EquationsStripped you reveal the maths behind some of the most important equations in maths, and I noticed that you describe the Navier-Stokes equations as your favourite – why is that and perhaps most importantly can you solve them?
“My favourite equations are the Navier-Stokes equations, which model the flow of every fluid on Earth… Can I solve them? Not a chance! They’re incredibly complicated, which is exactly why they’re a Millennium Problem with a million-dollar prize, and my idea with the video and live talk is to try to peel back the layers of complexity and explain what’s going on in as simple terms as possible.”
Does that mean that anyone can follow your video?
“The early parts yes absolutely, I purposefully start with the easier bits – the history, the applications, and then gradually get more involved with the physical setup of the problem and finally of course the maths of it all… And that’s pretty much where the idea to ‘strip back’ the equations came from – I thought to myself let’s begin simple and then slowly increase the difficulty until the equation is completely exposed. Being the ‘Naked Mathematician’ the next move was pretty obvious… as each layer of the equation is stripped back, I’m also stripping myself back until I’m just in my underwear – so almost completely exposed but not quite!”
Where did the whole idea of ‘stripping’ equations come from?
“I suppose I don’t really see it as ‘stripping’ per se, it’s there for comedic effect and really to show that maths is not the serious, boring, straight-laced subject that unfortunately most people think it is. Stripping for the videos is fine – it’s just me alone with my camera, but then earlier this year I was asked to give a live talk for the Oxford Invariants Society and they were very keen to emphasise that they wanted to see the Naked Mathematician in the flesh – quite literally!”
And how did it go?
“Well, barring some slightly awkward ‘costume changes’ between the layers of the equation – I went outside for the final reveal down to my underwear for example – it was good fun and definitely something I’d be keen to try out again… Perhaps maybe even an Equations Stripped Roadshow. I’m keen to try out anything that helps to improve the image that people have of maths.”
Interview with the University of Oxford’s Blueprint magazine about my mission to popularise maths and my outreach work with the St John’s Inspire Programme. The full interview with Blueprint’s Shaunna Latchman can be found in the online magazine here.
While some avoid arithmetic at all costs, Tom fully immerses himself daily teaching maths to the first and second year undergraduate students at St Hugh’s College. He also arranges activities for St John’s College as the Access and Outreach Associate for Science, Technology, Engineering and Maths (STEM) for the Inspire programme. Another activity is planning and filming content for his own outreach programme – Tom Rocks Maths.
‘It was the subject that felt most natural to me’, explains Tom, who first realised his love for numbers aged seven when his class had been set ten long multiplication questions. He raced through the whole book. However it wasn’t until he received ten A*s in his GCSEs that he began considering an Oxbridge education. ‘Academically there isn’t much of a difference [between Oxford and Cambridge]’ Tom comments, ‘but Oxford felt more like home.’
Later, after completing his PhD in Applied Maths at Cambridge, he was offered an internship with public engagement team, the Naked Scientists. The group strip back science to help make a complicated theory easy to digest. Weekly podcasts are broadcasted through BBC Radio 5 Live and ABC Australia, where audiences reach up to one million listeners a week.
Tom saw an opportunity to bring his appreciation for maths to the masses, but he wanted to do it with a twist. Eager to move away from the stereotypes of maths being a serious subject taught by older men in tweed jackets, he thought ‘what is the best way to make maths less serious? Doing it in my underwear!’ And so, the Naked Mathematician was born.
Since joining St Hugh’s, Tom continues to break down day-to-day activities on his YouTube channel to prove that maths is an integral part of everything we do.
His passion for engagement doesn’t end there. The Inspire programme, part of the Link Colleges initiative, is a series of events, visits, workshops and online contact for pupils in years 9 to 13. Tom works with the non-selective state schools in the London boroughs of Harrow and Ealing.
The Link Colleges programme simplifies communication between UK schools and the University. Every school in the country is linked with an Oxford college, with the hope that this connection will encourage students to explore the possibility of attending university.
‘The aim is to have sustained contact with the same group of students over five years,’ says Tom. ‘There are still students who haven’t thought about university, or maybe it’s not the norm in their family or area to attend university. So, we explain what it is, how it works and the positives and negatives. We want to inform and inspire them.’
Tom is responsible for arranging all STEM events across the year for 60 students in each year group. He calls on the expertise of his colleagues at Oxford as well as encouraging a partnership with the University of Cambridge and several universities in London. ‘The syllabus includes various topics such as the science of food and using maths to improve diet.’
During Tom’s famed Maths vs Sport talk, students are encouraged to participate in an on-stage penalty shootout – but only after learning about the mathematical makeup behind such a pivotal moment in a football game, of course.
Tom believes maths is made more accessible by relating it the world around us. He encourages his students to question things, like why bees make hexagonal shapes in their hives and how many Pikachus it takes to light up a lightbulb.
Whether visiting schools up and down the country to deliver talks, recording the weekly dose of Funbers for BBC radio – fun facts about numbers that we didn’t realise we secretly wanted to know – or in front of his class of students, Tom is certainly making waves in the world of maths.
Starting from my love of multiplication questions at primary school, I talk about my new role as a maths tutor at the University of Oxford, what a typical day looks like for the Naked Mathematician and give a sneak preview of my upcoming talk at New Scientist Live later this year… Live interview with BBC Radio Cambridgeshire.
Saturn is one of the most well-known planets in the solar system, perhaps owing to its distinctive set of rings. The largest of these rings, the H-ring, was only discovered as recently as 2009 and cannot be seen from Earth. Now, using images taken by NASA’s WISE spacecraft, scientists at the University of Maryland have given us the first insights into the structure and formation of Saturn’s outermost ring. I spoke to lead researcher, Doug Hamilton, to try to remove the shroud around Saturn’s most mysterious ring…
Doug – We’ve been able to look at the structure of the ring in these images and what we’ve discovered is that the particles are dominated by fairly small dust grains. So, 10 microns in size, a hundredth of a millimetre, very very small.
Tom – The rather catchily named H-ring was discovered in 2009 by the Spitzer space telescope, but what led to its formation?
Doug – This one seems to have come form the satellite Phoebe. So, Phoebe is a distant object of Saturn, its got a tilted orbit around Saturn, which means that it goes up and down and the height that it goes up and down matches the height of our ring. It tells us that Phoebe is the source of the dust particles.
Tom – So how does the material come off Phoebe to actually form this ring?
Doug – Its an impact onto Phoebe. There are collisions form other objects out at Phoebe’s distance, so think of a comet tail and all of the debris that come off of it, all of those bits are hitting the satellites and kicking off debris that form part of the ring. And then where Phoebe is located there are another 50 small satellites and occasionally they collide producing more debris.
Tom – The main rings of Saturn are visible from Earth – you can even see them with your own telescope on a clear night, so why can’t we see this new ring?
Doug – Since the dust particles are black they are really hard to see with visible light. You’ve got black dust particles set against the blackness, the darkness of space. So what we do is we realise that those black dust grains will absorb sunlight quite efficiently and they heat up and they re-emit heat, they re-emit red light. We use telescopes that are sensitive to that light.
Tom – You visualise this using infrared light, what does it look like on these images?
Doug – This is pretty neat aswell. It’s fairly planar, so it’s flat. You want to think of a coin, sort of a coin edge on. It’s a flat, yet extended structure. And we see it just because of how the dynamics of the particles work, we always see this thing edge on from the Earth. So you have your coin and you flip it on its side and you’re looking at it like that. So what we see in the sky is a rectangle.
Tom – What makes this ring particularly interesting?
Doug – It’s turned our whole idea of what rings are on its head, because we always think that rings are formed close to their parent planets and then you get moons and satellites further away. And this has just flipped it around – so we’re as far away from Saturn as you can get and still be in orbit around the planet and there’s satellites out there, but there’s also a ring. And so this teaches us – it makes us think differently about rings and hopefully we’ll open our minds a bitand learn a bit more abut how they form.
Tom – The analysis of these new images from the WISE spacecraft has given us greater insight into the structure of Saturn’s latest ring, but how does this new ring compare to the others?
Doug – We have the massive rings that you see on the telescope images, those have been known for a long time. Those are composed of big house-sized chunks of ice. And then we have Saturn’s E-ring. So that’s a ring that’s bigger than the main rings of Saturn and it’s extremely tenuous and it’s made up only of small dust grains. This large ring that we have at great distances is in-between. So we have big particles like you find close to Saturn, we have the small particles like you would find in Saturn’s E-ring and everything in-between.
Tom – Are there any other applications, any other knowledge you’ve gained from studying this ring?
Doug – We like things that are the biggest, the brightest, the furthest and so on… And this is the largest ring in the Solar System. So that’s kind of nice just on a gee-whizz level. On a deeper level what it teaches us is not to be too bound by our expectations. So nobody expected a ring to be this large and so as we go forth and look at exoplanets, and we’re looking in the data for signals, we’ve been surprised over and over with exoplanets. And back here in the Solar System we’ve been surprised by this ring and what it teaches us is to be open-minded. The universe has a lot of things it can do – it hasn’t shown us all of its secrets.
You can listen to the interview for the Naked Scientists here.
Stripping back the most important equations in maths so that everyone can understand…
Logarithms turn multiplications (hard) into additions (much easier) which enabled scientists in the 1600’s to calculate the trajectories of comets and the orbits of the planets around the sun. Nowadays, they are mainly used in Information Theory and Thermodynamics, but still have an important role to play mathematically in helping us to understand trends in experimental data.