I was recently interviewed by Lucia Taboada for La Redada Podcast about my love of maths and how it is used in today’s world to model everything from penalty kicks to the next TV series you watch on Netflix. The interview was translated into Spanish for the actual podcast so I’ve also included the original recording of my answers in English – enjoy!
On your YouTube channel, you present science in an entertaining way. Why is maths so unpopular sometimes, maybe students are afraid of maths?
How would you define the importance of mathematics in our life?
Tom, I’m a huge supporter of a Spanish team called Celta de Vigo. You explain the possibilities using maths to improve the performance of football players. How can Celta de Vigo use this to improve? (unfortunately, we are now in the last positions)
Penalty kicks are a science? Can you predict them?
Have you been hired by any football team?
Do you think football teams should hire math workers?
You are a tutor in St John’s College at the University of Oxford where you teach maths to the first and second year undergraduates. Oxford is a traditional university – how are your methods received there?
You have some maths tattoos on your body, thats right? Explain them to us?
Tom Crawford talks about how mathematics can help win a football league or the real ability of algorithms to manipulate people’s behaviour.
Tom Crawford (Warrington, United Kingdom, 1989) is presented as an atypical math teacher. He teaches mathematics to first and second year students at the University of Oxford (United Kingdom) and carries out an intense dissemination work in which he tries to approach a discipline that is not usually found among the favourites of young students.
In his attempt to popularise science, he does not hesitate to stay in his underpants , using the striptease as a metaphor for his work deepening the meaning of equations such as Navier-Stokes, unveiling them layer by layer, to make something affordable that can result in principle esoteric.
This week, Crawford visited the Student Residence, in Madrid, where, within the Mathematics in Residence cycle organised by the ICMAT, he offered the conference Mathematics of sport . In it, he uses sport as an example of a daily activity that can be better understood and practiced using mathematical equations.
Question. You undress or use sports to make mathematics impose less. Why is it necessary to show that mathematics is fun? I don’t see lawyers or judges, who also deal with very complex issues, trying to present the law as something fun.
Answer. I think it’s because people, for whatever reason, happily admit that they don’t like math, it’s socially acceptable. If you tell someone that you are a lawyer, their default answer is not going to be “I don’t like the law,” and that does happen with math. And it shouldn’t be like that. Everyone should have a basic understanding of math, but many people don’t have it. For me, that is why I want to emphasize that mathematics is fun and accessible. It doesn’t have to be something very hard or something that was taught badly in school.
Q. Do you think mathematics is taught especially badly in school, worse than other subjects?
A. Mathematics has a hard time competing with other subjects in the sense of teaching them through stories. When you learn something, if they can teach you through stories, it is something very powerful, which serves to catch people. And that is easier with literature or history.
A very simple example of how to add stories to mathematics would be trigonometry. The properties of the triangles you learn in high school. If you think about how these functions were discovered or invented, why we invented the sine, the cosine and the tangent, it was the ancient architects who tried to build buildings, churches, pyramids and created those intellectual tools. This is how trigonometry should be taught to me. Imagine they are in ancient Rome and you have to build a concrete building. How would you do it with the technologies available at that time? This prompts you to think about angles and distances and that is where trigonometry is useful and what it was invented for.
Q. A little more than a century ago, in a country like Spain, more than half of the population was illiterate. Do you think it would be possible and desirable to get a large majority of people to be able to handle basic mathematical tools?
A. It is completely possible and I would say that we are already doing it. It depends on what you consider a basic level of mathematics. Most people can, for example, looking at a clock know that the needles return to the same place every 12 hours, it is modular arithmetic, something you don’t study until you get to college. Even being able to calculate changes when they give you a ticket is to do mental arithmetic. Or calculate when you have to leave home if it takes 35 minutes to the station and the train leaves at 12.45. There are many things you do without thinking, but that involve mathematical calculations. So it depends on what you consider a desirable level of mathematics, but a large part of the population already has some capacity to use them.
“You can question whether trying to influence voters is good or bad”
Q. He also talks about the possibilities of mathematics to improve the performance of athletes. There is a movie like Money Ball , which talks about the experience of a baseball coach who uses mathematical analysis to lead a small team to compete against the big ones in the league with much less budget. Do you use math a lot in elite sport?
A. As far as I know, it is an important part of the scout systems of large teams. Today, these scouts, in addition to the classic analysis of a player’s performance, strengths and weaknesses, include teams of mathematicians and data scientists. As in Moneyball , your job is to analyse large amounts of data and detect marginal gains to take advantage of. That works well in baseball, because you have many controllable factors: The pitching of the pitcher, the batter, the race to the base. It is very formulable and they are repetitive behaviours. In football it is more difficult to find those marginal gains because it is less controllable.
The best example I can think of in football is Leicester City, which won the Premiere League in 2016. A big surprise. They had climbed to the first few years before and suddenly they win. In that victory, N’Golo Kanté was very important. He was the star of the season and won the player of the year award. He had been signed by a French second division team because the scout network had identified him among all the defensive midfielders in Europe at any level. As a defensive camper centre, one of your jobs is to stop the attacks of opponents. You can measure this in tickets, but one of the best ways to do this is through interceptions, which has to do with the player’s ability to read a game. It is something very difficult to assess with a number, quite subjective. But interceptions suggest that you are very often in the right place. And from that point of view, their number of interceptions was much higher statistically than the rest of midfielders. If the average of all midfielders in Europe is two, but most of the players are between 1.9 and 2.1 and Kanté is at 3, we see that it is an atypical case. It was not just a statistical analysis, because the human element is valued, but it was a factor to hire him.
Q. Can mathematics tell us what is the limit of human performance in sport? There have already been examples in the past, such as Roger Bannister’s, which went down four minutes on the mile when almost everyone said it was impossible, in which the predictions were completely wrong. Can these limits be accurately identified using mathematics?
R.If you look at the men’s marathon record during the last century, the marks descend, but not at a constant pace. You can estimate, for example, that every 10 years, 10 minutes are trimmed at the beginning, but then, in the 1940s and 1950s, the curve begins to flatten out and already in the 1990s it seems completely flat. So if we had sat here 30 years ago, when the record was around two hours and five minutes, we could have thought we would never run below two hours, because even if it keeps going down, the pace is getting slower. But in recent years, there has been much progress in long-distance races, such as new shoes that can provide 4% more energy. In addition, there is a professionalisation that allows you to train all day and not have a job besides running.
“I could predict with some confidence that the human limit for the marathon would be about an hour and 55 minutes”
So these are new factors that modify our calculations. In the future, in 30 years, new improvements may appear, but it is certain that we will not run a marathon in less than an hour. Given what has happened in the past, I think I could predict with some confidence that the human limit for the marathon would be about an hour and 55 minutes.
Q. Some people, when talking about the possibilities of mathematics to bring humans to the limit of perfection, may think that sports will become more boring, because there will be less and less space for the unexpected.
A. I think that also has to do with the human psychological trait that is nostalgia. But sport evolves and there is always a human factor. If the study allows you to perfect the place where it is better to throw a penalty, the goalkeepers can also work with that information. And then, there are some players who do not shoot at that supposedly perfect space, such as Eden Hazard, of Real Madrid, who when he threw the penalties for Chelsea waited until the last moment to decide where he threw it, a method that goes against what he says The mathematical model. In the end there are many variables in sports.
Q. Can mathematics help us better understand human groups? Does that technology have the potential to improve living together or to make it worse?
A. With all the data available, there are huge technology companies that can make profiles of people. Knowing that you are white, American, that you earn so much money and live in such a state, they can try to predict what you like or what you do and influence your vote in one direction. But this technology could also be used for good and you can also question whether trying to influence voters is good or bad. I think that ultimately we depend on the big companies that have control over these data so that they assume their moral responsibility and use the data well.
In any case, I think that most of the mathematicians working in this field would say that the idea of using mathematical data, algorithms and models to try to predict people’s behaviour is incredibly new and we don’t know exactly what we are doing. Algorithms may be a part of the decision making process, but not the only criteria for making a decision.
You can read the original article on El Pais here.
This week I had the honour of speaking at the Residencia de Estudiantes in Madrid, which has previously hosted Albert Einstein, Marie Curie, Salvador Dali and Igor Stravinsky amongst many, many others.
Ahead of the event I was asked a few questions by the organisers, and here are my answers.
Without revealing all your talk: could you give us an idea about how maths can help to be better at sports?
From calculating the perfect placement of a penalty kick in football to maximise your chance of scoring, to identifying the best location on Earth to try to break a world record, maths can be used to help to improve our performance in almost any sport. The difficultly lies in writing down the correct equations, but once we have them, maths has the answers.
Can you tell us any real example of this maths application?
My favourite example is one that will be featured in my talk: if attempting to break a world record in rowing, the best place to do so is on the equator. This may seem counter-intuitive at first, but as I will explain, by changing the location to the equator you can increase performance by up to 8%, which for an elite athlete is an incredible boost!
In your opinion: what makes maths so useful in different sports context?
Maths can be applied to anything. This is one of the main reasons that I love the subject and travel the world championing its versatility. Given a situation in any sport, you can always use equations to describe what is happening. This might be how a tennis ball moves through the air, or the aerodynamics of a swimmer gliding through the water. Once you have the equations, maths allows you to solve them for the optimal solution, which can then be translated into improved performance by changing your technique appropriately.
You also explain that the mathematical results in sports may vary, how? In which way? What should athletes take into account?
The ideas discussed in my talk are aimed at professional athletes who are already performing at a very high level and therefore need to resort to other approaches to improve performance beyond increased practice. For amateur athletes, whilst the same ideas will still be applicable, they are much more likely to benefit from practice!
What is your personal experience with sports? Have you ever used “math tricks” for optimise your scores?
The idea for the talk came from wanting to combine my two main passions: mathematics and sport. I play football regularly and as the designated penalty taker for my team have ample opportunity to try to hit the mathematically calculated perfect position for a shot. I also run marathons where my knowledge of the history (and mathematically predicted future) of the world record helps me to appreciate my accomplishments in the event.
How did you become a math communicator?
My first taste of maths communication came during my undergraduate degree at Oxford, where I joined the maths outreach group “Marcus’ Marvellous Mathemagicians”. The group was named after Marcus du Sautoy and performed interactive talks and workshops on his behalf in schools across the UK. The next opportunity came during my PhD when I spent two months working with the “Naked Scientists” team in Cambridge to produce a weekly science radio programme for the BBC. I enjoyed the placement so much that I agreed to join the team full-time upon completion of my PhD. After one year of working in radio production, I began to realise that my true calling was in video, and “Tom Rocks Maths” was born.
How are outreach, teaching and research connected in your professional life?
As someone who came from a state school background and worked extremely hard to get to Oxford, I have always had a passion for outreach and the drive to make university accessible to all. My maths communication work is an extension of this, allowing me to not only to visit schools in deprived areas to try to inspire them to consider higher education, but also to encourage the general public to engage more with the subject of maths and to no longer be afraid of numbers.
The teaching role fits perfectly with maths communication as both roles require the ability to be able to explain difficult concepts in ways that can be understood by a given audience. For a public lecture, the mathematical ability of the audience is perhaps less than that of a class of undergraduates, but the need for clear communication remains the same. In this way, I find that each role complements the other perfectly, with many of the topics that my students find difficult providing inspiration for future video ideas.
What do you enjoy most in your outreach talks?
There is nothing I enjoy more than being able to present to a live audience. Whilst I enjoy all aspects of my outreach work – YouTube, television, radio, writing – nothing beats the thrill of speaking to a room full of people who want to hear what you have to say. The small interactions with each individual member of the audience, whether through eye contact or answering a question, remain with me long after the event and act as one of my main motivations to continue with my work.
You are not the speaker one might expect when thinking about a maths communicator, what kind of reactions have you find in this sense? Do you have any anecdote regarding this?
There are two ways of looking at this: first, the notion of a stereotypical mathematician is outdated and from my experience not representative of a large part of the demographic; and second, I hope that by putting myself forward as a public face of mathematics I can help others who may be thinking that they can’t be a mathematician just because of the way that they look.
In terms of anecdotes, I think it best that I point you in the direction of the comments on my YouTube videos…
In particular, what are the reactions with “Equations stripped”? How did you come up with the idea of this series?
The “Equations Stripped” is possibly my favourite of all of the things that I do because it helps to tackle the idea that maths should be serious. The concept of the videos came from thinking about this opinion and trying to come up with what I thought was the best way to present the subject as anything but serious. The result is me talking about maths in my underwear!
My role with the “Naked Scientists” also played a part, as the name would often lead to listeners (or even guests) suggesting that we should all be naked when recording the show, and of course being a radio programme no-one could prove or disprove the theory! I always thought that we should have had more fun with this concept, and when “Tom Rocks Maths” was launched Naked Maths seemed like the way to go!
A special edition of Tom Rocks Maths on Oxide Radio with music inspired by Tom’s recent visit to Slam Dunk Festival. We’ve also got Pokemon and drinking games, a mind-bending Einstein Puzzle, and news of Tom’s antics running around the streets of Oxford in his underwear… This is maths, but not as you know it.
Tom “rocks” maths on the internet – lecturer from Oxford arouses enthusiasm with crazy ideas…
The graduate mathematician Tom Crawford not only has rock music as a hobby, but he also looks like a rock star with his tattoos and piercings. However, some of his tattoos are related to mathematics. For example, the first 100 decimal places of Euler’s number wind around his arm and the number pi has been encrypted as an infinite series. On his Youtube channel “Tom Rocks Maths” he presents science in a fun way – the clothes sometimes fly during a striptease: “I want to show that maths is not always only downright serious, but fun.”
The math lecturer from Oxford came as part of the Heidelberg Laureate Forum (HLF) in the Electoral Palatinate. Since there is no Nobel Prize in mathematics, the winners (Latin: laureates) of comparable awards are invited to the HLF. The best math and computer scientists in the world meet here for a week with junior scientists and journalists. Crawford was on the ground as a publicist and presenter, and took the opportunity to speak to some of the awardees. For example, Martin Hairer, who received the Fields Medal for his seminal studies, had an appointment for an interview. In the end, they played Tetris for an hour and talked about “cool math”: “Such a relaxed and profound conversation is only possible at the Heidelberg Laureate Forum,” the Brit enthuses about the inspiring atmosphere at the HLF.
Tom Crawford was already “packed” in the elementary school of mathematics: “When we were learning multiplication, I did not want to stop working on difficult tasks until late in the evening – it did not feel like work at all.” Even later in high school, he always did math tasks first and gladly. “I was a good student in my eleven subjects, but math was the most fun.” The satisfying thing is, “in maths a result is right or wrong, there is no need to discuss it.”
After studying in Oxford, he went to Cambridge to write his PhD in fascinating fluid dynamics. “We wanted to model how fluids move and interact with the world. I was excited about the prospect of being able to analyse experiments as a mathematician.” From this, models of reality were developed: what path does a river take when it flows into the sea? The findings help to understand the pollution of the oceans and possibly stop it. During his PhD he worked for the BBC in the science programme “The Naked Scientists”: this meant that the scientists liberated their theories from the complicated “clothes” and reduced them to a comprehensible basis. In this way, a layman will discover “naked” facts – in the sense of comprehensible ones. The radio broadcasts were a great success.”But you also have to visualize maths,” so he started to make his own videos and took the concept of the “naked mathematician” literally. In some lectures, he reveals the equations “layer by layer” and in each stage falls a garment – until Tom remains only in his boxer shorts. And then his tattoos are also visible, on whose mathematical background he will give a lecture in Oxford soon – with many guests guaranteed!
With unusual ideas, the only 29-year-old mathematician arouses the desire and curiosity for his subject. His original internet activities have now been honoured with an innovation prize. Even when attending school in Schwetzingen Tom Crawford had unusual questions: “In the stomach of a blue whale 30 kilos of plastic have been found: How much would that be if a person swallows just as much in relation to their own body weight?” The students calculated that in the human stomach, six (empty) plastic shopping bags would be located. Or, “How many table tennis balls are needed to lift the sunken Titanic off the ground?” And which example impressed him most in mathematics? “It is terrific how Maxwell’s equations, which deal first with electricity and magnetism, follow the wave property of light with the help of mathematics alone. Math is just fantastic! ”
The original article published in the Die Rheinpfalz newspaper (in German) is available here.
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.