BBC News – Maryam Mirzakhani’s Legacy

Live interview on BBC News about the legacy of Iranian Mathematician Maryam Mirzakhani who tragically passed away today (July 15th 2017). She was the first female winner of the Field’s Medal – the mathematical equivalent of the Nobel Prize.

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Naked Maths Trailer

Naked Maths is finally here!

Here’s the trailer for the new video series I’m making with the Naked Scientists taking a look at the maths that’s all around us.

 

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Wimbledon Tennis

The important facts and figures of the Wimbledon tennis tournament courtesy of the Naked Scientists… Listen to the audio here.

Grab your rackets, your strawberries and cream and – as long as you’re old enough – a glass of Pimms; because Wimbledon’s underway… and to celebrate we’re having a rally of our very own!

Female – And it’s a match of the titans today. Georgia Mills and Tom Crawford have come armed with their top tennis facts. If anyone’s guess, who will be crowned champion? It’s you’re Quick Fire Science on Wimbledon. And they’re up!

Georgia – Once upon a time, tennis rackets were made out of wood which was weak and warped over time. But now, we use carbon fibre set in glue which is high strength and low weight.

Tom – And not all rackets are vegetarian. Some strings are made from cow intestines but most are the polymer nylon.

Georgia – If you hit the ball in a certain way, you create top spin which makes the ball fall sooner than a ball without it. This relies on something called the magnet effect: Whilst the ball is spinning through the air, a thin layer of air around it is also rotating, and the differences in pressure between the air on top and the bottom of the ball creates a force.

Tom – This is what pushes the ball faster towards the ground and is why you have to use top spin with your balls if you want to be too fast for your opponent. Rafael Nadal is one of the best. He could spin a ball at 3,600 rpms.

Georgia – Over the course of Wimbledon, they sell around 320,000 glasses of Pimm’s. If one person managed to drink that and miraculously didn’t die, it would take around 36 years to sober up. Cheers!

Tom – Wimbledon is one of the very few tournaments that still use grass instead of clay or acrylic. The grass used is perennial ryegrass, scientific name Lolium perenne because of its resistance to wear and impressive regeneration capabilities.

Georgia – Grass courts make it slightly less predictable where the ball is going to bounce but also makes for a faster game. This is because grass as a surface isn’t very even and also has less friction.

Tom – The winner of a coin toss decides if they want the first serve. But the odds aren’t exactly 50/50. Coins have a 51 per cent chance of landing on the side that was faced down at the start.

Georgia – Plus, some statistics have shown a very small advantage to being the first serve on the first set although this effect does seem to disappear if the players are very evenly matched.

Tom – It’s not just balls that are served. Over 28,000 kilograms of strawberries are consumed by hungry punters. That’s the equivalent weight of 4 African elephants. Luckily, there’s 10,000 litres of cream on hand to go with them.

Georgia – The ball’s yellow colour may be iconic, but Wimbledon used traditional white balls until 1986. The yellow ball first started being used when research showed that they showed up better on television.

Tom – Each tennis ball is hollow and is filled with a gas which is usually nitrogen that’s held at a pressure higher than the air outside. This means that over time, the gas leaks out which is why the balls need to be replaced.

Georgia – This is why when you open a new can of balls, you get that lovely popping sound as the cans are pressurised to keep the balls in tiptop condition. It’s also why you’ll often see the players squeezing their balls on the pitch to see if the pressure is good enough.

Female – Game, set, match. What a game ladies and gentlemen, what a game!

Pokémaths: how many Pikachus does it take to power a light bulb?

The mascot of the Pokémon world and probably the most famous of all the Pokémon: Pikachu. It’s pretty much just a short, chubby rodent with two red circles on its cheeks that it apparently uses to store electricity. So the obvious question to ask here then is how many Pikachus would it take to power a lightbulb?

The official Pokédex tells us that Pikachu is able to ‘release electric discharges of varying intensity’ and is also known to ‘build up energy in its glands that needs to be discharged to avoid complications’. Quite what these ‘complications’ might be I’m not sure – suggestions on a postcard. The Pokédex also says that the tail of a Pikachu plays an important role as it acts as a grounding rod to prevent the creature from electrifying itself and also allows one Pikachu to recharge another one that’s running low on juice. Another fun fact about Pikachu’s tail is that a female will have a v-shaped notch at the end which is not present on males. Next time you’re out Pikachu hunting, now you know.

When a Pikachu uses its signature move, thunderbolt, it releases 100,000 volts of electricity. You might think that this would be enough to kill you, never mind just power a lightbulb and you wouldn’t be wrong, but there’s a little more to it than that. When someone dies from electrocution, it isn’t the voltage that kills them, it’s the current. If a current of just 7 milliamps reaches your heart for around 3 seconds its lights out. The current is tiny, but it disrupts the hearts natural rhythm causing it to stop. You can of course be electrocuted and live to tell the tale, but this means that you were very lucky in that the path that the electricity chose to take through your body must have avoided your heart. In general, electricity will flow along the path of least resistance, as with most things in nature it’s lazy and so takes the path that is the easiest.

I’ve now mentioned three terms, which means a good old fashioned physics formula triangle. The particular one we want here is Ohm’s Law:

triangle2

The resistance of your body is around 100,000 ohms, which means thunderbolt generates a current of 1 amp that will flow through your body. In other words, if it hits your heart you’re toast.

Now onto lightbulbs. They come in all sorts of different shapes and sizes, and different amounts of wattage or power. The standard one is 60 watts and that’s the one we’re considering here. None of these fancy energy saving bulbs that start off really dim so that you can’t see a thing and gradually build up in brightness… (don’t get me started on them). The key bit of physics that we need relates power (in watts) to Ohm’s Law above and states:

trinagle1

For a 60 watt light bulb attached to the UK mains supply of 230 volts, this generates a current of 0.26 amps. If we were to connect the bulb up to a Pikachu using thunderbolt the current decreases hugely to only 0.0006 amps. The light bulb will still work but the current will just be very small. This means only a small wire is required and also has the added benefit of reducing the chance of electrocution… However, 0.0006 amps is still enough to kill you if it hits your heart, so be careful next time when you’re hooking up your lightbulb to a Pikachu!

Solve this and you’ll win $1 million

My first ever live radio interview from almost 2 years ago – enjoy! You can listen 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. Graihagh Jackson spoke to Cambridge University’s Tom Crawford to find out what these problems are…

Tom – So, yeah. These are sort of a second reincarnation of the idea of important maths problems. So, in the year 1900, there was a mathematician called Hilbert who actually came up with 23 problems that he considered to be the most important in the year 1900. In fact, one of these is actually one of the millennium problems as well. And then the year 2000 came around, it’s a big event, lots of things happened, and maths thought, “Let’s get involved with this.”

Graihagh – Jump on the bandwagon.

Tom – Exactly. They sort of sat down and said, “Right. These are the biggest unsolved problems in mathematics at this time.

Graihagh – Did they say 7 because 7 is a prime number and an interesting maths number?

Tom – I’m not sure exactly why they chose 7, but that sounds like a good idea to me.

Graihagh – And you say ‘they’, these mathematicians, who are they and I assume, they’re the ones fitting the bill of a million dollars, right?

Tom – Yes. So, this is the Clay Institute. It’s an institute based in America. They had money left to them and thought, “Let’s use this as prize money as a sort of extra motivation.” But if you ask most mathematicians – I won’t say all – if you ask most mathematicians, they wouldn’t actually try and tackle these problems for the money. It’s more just for the fun of doing the maths in some sense.

Graihagh – So, can you give me a quick rundown of the final 7.

Tom – I’ll start with the one I’m doing my PhD on, this is the Navier-Stokes equations. This is fluid dynamics. This is a set of equations that model the flow of every fluid – so water, air, anything. Then we’ve got the Mass Gap Hypothesis. You can think of this one as asking the question “why do things have mass?”

Graihagh – Sounds interesting. So, you’ve mentioned 2 of them there. There’s 4 more by my count, by my math.

Tom – 5

Graihagh – 5? Oh no! Okay, what are the other 5?

Tom – We’ve got the Poincare Conjecture which is an interesting one as we’ll find out later. We’ve got the Riemann Hypothesis which looks at prime numbers. We have P versus NP – one of the more famous ones. So, this is basically looking at how computers work. And then the last two are quite abstract. So, you have the Birch and Swinnerton-Dyer Conjecture.

Graihagh – Wow! Great names.

Tom – And then finally, the Hodge Conjecture. So, the Hodge Conjecture is quite an interesting one because depending on which expert in the field you ask about this problem, they will give you a different definition of what this problem is.

Graihagh – So, no one can agree what the actual problem is in the first place?

Tom – Yeah. That’s how complex some of these problems are.

Graihagh – Wow! So, how are we ever going to go about solving them if we can’t even agree what they are in the first place?

Tom – Well, I mean some of them are a bit more approachable and there’s a bit more general consensus about what this problem is. But I think the main idea of these problems it’s not necessarily getting a solution, it’s understanding more. So, by trying to conquer this giant mountain of a problem, you’ll scale smaller peaks along the way and make new advances in other areas of maths.

Graihagh – A million pounds sounds like an awful lot, but I suppose if you spend your entire life doing this then actually, it’s not that much.

Tom – No. Sort of estimates of the amount of time it would take to solve one of these problems, it actually works out as being paid below minimum wage for the amount of time you would need to spend to solve one of these problems.

Graihagh – Wow! We’ve got some very dedicated mathematicians out there.

Tom – Yeah, most mathematicians I think actually do it for fun, if you can believe that.

Graihagh – I’m just thinking about my maths class back when I was 16 and maths certainly wasn’t my favourite subject but maybe I should revisit that.

Tom – Yes, sounds good.

 

If you want to find out more about the Millennium Problems check out my articles here.

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