The second episode of season 2 of Tom Rocks Maths on Oxide Radio – Oxford University’s student radio station. Featuring the numbers behind the sub 2-hour marathon world record attempt, P versus NP and the battle for control of the world, and the usual dose of Funbers with my super sweet 16. Plus, music from Blink 182, Billy Talent and Hollywood Undead. This is maths, but not as you know it…

# Tom Rocks Maths S02 E01

Tom Rocks Maths is back on Oxide – Oxford University’s student radio station – for a second season. The old favourites return with the weekly puzzle, Funbers and Equations Stripped. Plus, the new Millennium Problems segment where I tell you everything that you need to know about the seven greatest unsolved problems in the world of maths, each worth a cool $1 million. And not to forget the usual selection of awesome music from artists such as Rise Against, Panic at the Disco, Thirty Seconds to Mars – and for one week only – Taylor Swift. This is maths, but not as you know it…

# Sir Michael Atiyah Riemann Hypothesis Proof Interview

I had the honour to sit down with Sir Michael Atiyah to discuss his recently presented proof of the Riemann Hypothesis at the Heidelberg Laureate Forum.

# Sir Michael Atiyah Riemann Hypothesis Proof

Sir Michael Atiyah explains his proof of the infamous Riemann Hypothesis in one slide. Recorded live at the Heidelberg Laureate Forum 2018.

# Science Oxford Interview: From Togas to Tattoos…

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.”

# Navier-Stokes: one equation to rule them all

A leading Millennium Prize Problem is the Navier-Stokes equation, which, if solved, could model the flow of any fluid – that means how aeroplanes navigate the skies, how water meanders in a river and how the flow of blood courses through your blood vessels… Understanding these equations in more detail will lead to scientific advances in all of these fields: better aircraft design, improved flood defences, and better drug delivery in the body. Fluids expert and mathematician Keith Moffatt took me down to the deep dark depths of Cambridge’s maths lab…

- For most fluids, including air and water, the Navier-Stokes equations are based on Newton’s Laws and were first written down in the 19
^{th}century - The millennium problem is to answer the question of whether or not the equations can become infinite
- It cannot be solved with a computer because a computer programme will break down before the singularity at infinity is reached
- A real-world example is when two tornado-like vortices collide and undergo a process called ‘vortex reconnection’

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

And you can read more about the Navier-Stokes equations and all of the Millennium Problems here.

# Perelman and the Poincaré Conjecture

Grigori Perelman is a quiet and unassuming mathematician from Russia, who took the world of maths by storm in 2010 when he not only solved the Poincare problem but then refused the $1 million reward! I went along to the Millennium Bridge in London to meet mathematician Katie Steckles to shed some light on Perelman’s story and to find out why the Millennium Bridge was in fact its own millennium maths problem…

- When the Millennium Bridge opened its resonant frequency matched that of walking pedestrians which caused it to vibrate massively as seen in the video below

- In the field of topology things are considered equal if you can get from one to the other by doing a ‘smooth and gradual change’
- The Poincare Conjecture states that any shape satisfying a set of three conditions can be deformed into a sphere, and this will hold true in any number of dimensions
- It had been proved for all dimensions except 4, which was shown to be true by Grigori Perelman in 2002
- He published his proof on the internet and then refused the $1 million prize money, instantly becoming a sensation

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

# Solve this and you’ll win $1 million

My first ever live radio interview from July 2015 – enjoy! You can listen to the full interview for the Naked Scientists here.

The Millennium Prize Problems are a set of 7 maths problems that have been deemed so important that if you can solve any of them, you’ll be awarded 1 million Dollars. I was interviewed by Naked Scientist presenter Graihagh Jackson to explain exactly what the problems entail…

- The Millennium problems are a second reincarnation of the idea of important maths problems with the first set of 23 being proposed by Hilbert in 1900.
- The prizes are offered by the Clay Institute and so far only one of the seven has been correctly solved
- The 7 problems are the Navier-Stokes Equations, the Mass Gap Hypothesis, the Poincare Conjecture, the Riemann Hypothesis, P vs NP, the Birch and Swinnerton-Dyer Conjecture and the Hodge Conjecture
- Estimates of the time required to solve one of the problems actually results in being paid below minimum wage

If you want to find out more about the Millennium Problems you can find a series of articles I’ve written on the subject here.

# The Poincare Conjecture

I’ve saved the best until last because this one’s been solved! Hallelujah! Praise the Lord! God save the Queen! Slap my thighs and serve me a milkshake! And the story of the man that did it is fascinating. But we’ll get to that… first up I’d better tell you what the problem is/was.

For the Poincare Conjecture we venture into the shape-shifting world of topology. This is a real favourite amongst mathematicians because it’s great for blowing people’s minds. The classic example: in topology a donut and a teacup are the same item. Yes, you did read that correctly. The reason? They both only have one hole: in the centre of the donut and in the centre of the handle of the teacup. It’s the number of holes that’s key. If you have a muffin and a donut how would you tell them apart? And no you can’t eat them. In topology what you would do is take an elastic band and put it around each object. Then you squeeze it in tightly until the object becomes one ball of mass. Well the muffin does, but the donut doesn’t. Not without breaking it at least – that’s the key. The hole in the donut means that you can’t shrink it and squeeze it down into one little ball without breaking it somehow. There’s no way to remove the hole.

If you’re still struggling to get to grips with topology, think of it like this: you have a donut made out of Playdoh and you need to mould it into a teacup with the only rule being that you cannot create or destroy any holes. You can do it. It’s a little fiddly yes, but it can be done. Now imagine you need to make a muffin with the same rule. No hole destroying. You can’t do it. You’ll always be left with a loop of Playdoh hanging off your perfectly crafted muffin.

The Poincare conjecture is based on this same idea: imagine you have a smooth shape made out of Playdoh and it has no holes, then the question is: can we mould it to make a sphere? Sounds easy enough in our three dimensional world, you can literally get a ball of Playdoh and make any shape you want – you can always get back to a sphere. But what happens in higher dimensions? Time is often referred to as the fourth dimension in Physics, but what comes after that? We as humans are not programmed to visualise it, but in maths higher dimensions exist. The interesting thing with this problem is that we know you can make a sphere in any number of dimensions except four and this is what the Poincare Conjecture asks. Can you take any four-dimensional smooth object that doesn’t contain any holes and turn it into a sphere? Turns out you can, just ask Gregori Perelman (photo credit: George M. Bergman – Mathematisches Institut Oberwolfach (MFO), GFDL, https://commons.wikimedia.org/w/index.php?curid=11511619).

Perelman is a Russian mathematician and he is quite the character. He showed that the Poincare Conjecture was true and then without really telling anyone just posted his solution online in 2002. No big event, no announcement, just a casual ‘oh here’s what I’ve been working on the past few years – I solved a Millennium Problem’. You have to love him for it. And it gets better. It took the Clay Institute eight years to verify that his solution was indeed correct and Perelman did not like this, not one bit. He couldn’t understand why they had to check his work – he is a mathematician; he doesn’t make mistakes! When the time came around for him to be presented with his money he declined, flat out turned it down. He was also awarded the maths version of the Nobel Prize, the Field’s Medal, and didn’t want that either. He was so annoyed at the way in which he was treated following his work that he gave up the subject and it is rumoured that he now works in Computer Science. Get your bets in now that he solves the biggest problem in that subject within the next few years…

This is a nice story for me to end on as it brings me back full circle to my starting point for these articles. The Millennium Maths problems were the first set of problems to get me really excited about maths. Whether it was because of the money or just the idea that these things even existed, I don’t know (it was probably the money), but what I do know is that Gregori Perelman is the perfect example of everything that is great about mathematicians. He started working on the Poincare Conjecture in 1995 before it was even a Millennium Problem, and then he turned down all of the fortune and fame that came with his solution. He simply wanted to be left alone to ‘do the maths’.

If after reading my articles you were thinking of attempting to solve one of these problems yourself by all means get stuck in, but as I started with a word of warning about the difficulty of these problems, let me end with another. Estimates of the number of hours spent by Perelman in solving the Poincare Conjecture actually put the $1 million prize money at less than the minimum wage. You have to love the subject to tackle these problems and I hope that I have and will continue to help you do exactly that.

You can listen to me talking to mathematician Katie Steckles about the Poincare Conjecture here.

I’ve written a series of articles on each of the 7 Millennium Problems which can be found here.