The final episode of Tom Rocks Maths on Oxide Radio for 2018 goes out with a bang. We’ve got another million-dollar maths problem, a healthy dose of nakedness, and we try chopping up traffic cones with a saw. Plus, music from Jay-Z/Linkin Park, the Red Hot Chili Peppers and the Foo Fighters. This is maths, but not as you know it…

# How high can bees count?

Bees are not only able to build fantastic hexagonal honeycombs they’re apparently also able to count! But do they deserve their reputation as nature’s mathematicians? Georgia Mills spoke to Srini Srinivasan from the University of Queensland to find out how they discovered counting bees…

- Bees were trained to fly down a tunnel with a reward of sugar water at the end, and a series of identical landmarks labelled 1, 2, 3, 4, etc. along the route.
- One of the landmarks contained the reward and the bees had to test each one to discover its location. This was repeated several times until the bees learned the location of the reward.
- The spacing of the landmarks was then changed, but the reward remained at the same landmark, and the bees had to find it once again.
- They were able to ‘count’ the number of landmarks and would go straight to the correct location bypassing the others that did not contain a reward.
- The highest number of sequential landmarks the bees were able to ‘count’ was 4.
- Four is a universal number as when briefly presented with an image containing a number of objects, the largest amount most animals can recognise accurately is 4-5. This process is called subitising.
- Counting to 4 is useful for bees when for example deciding whether or not to land on a flower to collect pollen. If there are 3-4 bees already there then it is probably not worth their effort.
- Counting has also been looked at in fish birds and chimpanzees, and in each case the number four keeps cropping up, suggesting universality.
- The tunnel experiment was actually designed to investigate how bees navigate and the corresponding ‘waggle dance’ that they use to communicate information.

You can listen to the full interview with the Naked Scientists here.

# BIG STEM Communicators Network

As a new member of the BIG STEM Communicators Network I was very pleased to be featured in the member spotlight for spring 2019. (The original article is ‘members only’ so I’ve copied the text below.)

“As a new member of the BIG community I would like to introduce myself as the ‘Naked Mathematician’ (yes you did read that correctly). I am a Maths Tutor at the University of Oxford with a goal to reduce fear and anxiety towards maths. One of the ways in which I do this is to take my clothes off – what better way to emphasise that the subject is not as serious and intimidating as many people think than by teaching in my underwear! The concept began as a series of videos on my YouTube channel entitled ‘Equations Stripped’ where I strip back some of the most famous equations in maths (and myself) layer-by-layer so that everyone can understand, and has since evolved into a live performance now touring universities across the UK. My efforts to bring maths to a new audience have been recognised by the University of Oxford, where I was awarded first prize in the Outreach and Widening Participation category at the OxTALENT awards, and I have also been shortlisted for the Institute of Physics Early Career Communicator award.

The ‘Naked Mathematician’ is of course not appropriate for every audience and as such is only a small part of the work that I do to share my love of maths. My ‘Funbers’ series was broadcast throughout 2018 on BBC Radio, where in each episode I look at numbers more closely than anyone really should to bring you the fun facts that you didn’t realise you’ve secretly always wanted to know… I also try to involve my audience in the creative process as much as possible by issuing a call for questions on social media and then hosting a vote to decide the topic of my next video in the ‘I Love Mathematics’ video series. Finally, I combine my love of sport with maths in my popular ‘Maths v Sport’ talk which features a live penalty shootout on stage and an attempt to break a running world record (appropriately scaled of course!).

All of the material that I produce is available for free on my website tomrocksmaths.com and associated social media profiles @tomrocksmaths on Facebook, Twitter, Instagram and YouTube. I am very excited to have joined BIG and look forward to working with the community to help to share STEM subjects with the world!”

# Maths at: The Martian

I recently joined the Maths at team to dissect the maths featured in the movie ‘The Martian’. We had a lot of fun and even learned a few things including:

- Everyone’s links to Countdown;
- Ancient Greek Mathematicians;
- How to tell the difference between Jeff Daniels and Jeff Bridges.

So, put your feet up, get comfortable, get naked (if you so wish) and listen to the full episode here.

You can try the Martian’s maths problems for yourself here and find out more about NASA’s mission to Mars with the Opportunity Rover by watching the video below.

# Maths and the Media

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.

You can follow Tom on Twitter, Facebook and Instagram @tomrocksmaths for the latest updates.

# Maths, but not as you know it… (St Hugh’s College Oxford Magazine)

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.

Of course, not all of my outreach work involves taking my clothes off – I’m not sure I’d be allowed in any schools for one! I also answer questions sent in by the viewers at home. The idea behind this is very simple: people send their questions in to me @tomrocksmaths and I select my favourite three which are then put to a vote on social media. The question with the most votes is the one that I answer in my next video. So far, we’ve had everything from ‘how many ping-pong balls would it take to raise the Titanic from the ocean floor?’ and ‘what is the best way to win at Monopoly?’ to much more mathematical themed questions such as ‘what is the Gamma Function?’ and ‘what are the most basic mathematical axioms?’ (I’ve included a few of the other votes below for you to have a guess at which question you think might have won – answers at the bottom.)

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 25^{th} 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.

You can find all of Tom’s outreach material on his website tomrocksmaths.com and you can follow all of his activities on social media via Twitter, Facebook, YouTube and Instagram.

**Answers to votes (watch by clicking the links):**

- What is the probability I have the same PIN as someone else?
- How does modular arithmetic work?
- What would be the Earth’s gravitational field if it were hollow?
- What are grad, div and curl? COMING SOON

# Carnival of Mathematics

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. **

This incarnation will be the 167th Carnival of Mathematics so here are some fun facts about the number 167…

- 167 is the only prime number that cannot be expressed as the sum of 7 or fewer cube numbers.
- 167 is the number of tennis titles won by Martina Navratilova – an all-time record for men or women.
- 167P/CINEOS is a periodic comet in our solar system.
- M167 Vulcan is a towed short-range air defence gun.
- 167 is the London bus route from Ilford to Loughton.

The previous Carnival can be found at Math with Bad Drawings hosted by Ben.

My favourite Carnival is number 146 which featured Tom Rocks Maths for the first time!

# Climate Change will increase Turbulence on Flights

We’ve seen many recent extreme weather events – from mudslides in Columbia to flooding in Australia – which scientists say are a consequence of climate change; but it’s not just the weather that is affected. The Earth’s atmosphere is made up of several layers of air which all flow around each other in patterns known as jet streams and an increase in temperature will cause these to speed up. This is bad news for air passengers, including the 1 million people currently airborne at this very instant, because an increase in the speed of the jet streams will cause more turbulence making flying less comfortable and potentially more dangerous. I spoke to atmospheric scientist Paul Williams…

- Climate change will cause a 59% increase in light turbulence, 94% increase in moderate turbulence, and 140% increase in severe turbulence.
- Turbulence is measured on a scale from 1 to 7 where 1 means light turbulence, 3 means moderate, 5 means severe, and 7 means extreme.
- Light turbulence is a slight strain against the seat belt, moderate turbulence causes unsecured objects to become dislodged and makes walking around difficult, and severe turbulence results in anything that isn’t strapped down being catapulted around the cabin.
- Turbulence is caused by wind shear – the higher you go up into the atmosphere the windier it gets – and instabilities within these layers of shear generate turbulence.
- As the atmosphere is heated, the temperature increase causes the jet streams to move faster, creating more wind shear and thus more turbulence.
- The researchers hope that results such as this will encourage us to think more carefully about our carbon footprint as there are likely many effects of Climate Change that we do not know about.

You can listen to the full interview for the Naked Scientists here.

# Can ants feel pain?

### Question

Carol asks: Can ants feel pain?

### Answer

I went crawling around for the answer with York University’s Eleanor Drinkwater…

- Ants can sense that they’ve been harmed and react but this is different to actually feeling pain
- Nociception is the sensory nervous system informing the brain that you’ve been hurt, whereas pain is an unpleasant sensation with a negative emotional response
- One can occur without the other eg. when playing sports you often don’t realise that you are injured until afterwards, or people who have lost limbs experience phantom limb pain
- Robots can also be programmed to experience nociception without experiencing pain, for example in the video game The Sims characters will jump around if they’re burnt by fire
- We currently know very little about insect expressions of pain, but we do know that the pain expression systems are different to those in mammals, meaning that insects are likely to experience pain in a different way to humans
- In short, the jury is still out, so best to be nice to any ants that you may come across!

Part of the Naked Scientists Question of the Week series – you can listen to the full version here.