The Heroes of Sir Michael Atiyah

In the final part of my interview with Sir Michael Atiyah – one of his last ever before he passed away – he talks about some of his mathematical heroes, from Einstein and Newton to Brouwer and Michelangelo, including the most beautiful description of the ceiling of the Sistine Chapel I’ve ever heard. A true giant of Mathematics, who is sorely missed.

With thanks to the Heidelberg Laureate Forum.

Eureka Magazine

The first 3 articles from my Millennium Problems series have been published in Cambridge University’s Eureka Magazine – one of the oldest recreational mathematics magazines in the world, with authors including: Nobel Laureate Paul Dirac, Fields Medallist Timothy Gowers, as well as Martin Gardner, Stephen Hawking, Paul Erdös, John Conway, Roger Penrose and Ian Stewart. To say I’m excited would be an understatement… (pages 82-84 in case you’re interested).

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Carnival of Mathematics 167

You know you’ve made it as a maths communicator when you have the honour of hosting the Carnival of Mathematics (if you have no idea who I am or what I do then check out this interview for St Hugh’s College Oxford). But, before we get to the Carnival proper, as the creator of ‘Funbers’ I can’t help but kick things off with 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 the name of a periodic comet in our solar system
  • The M167 Vulcan is a towed short-range air defence gun
  • 167 is the London bus route from Ilford to Loughton

Now that we all have a new-found appreciation for the number 167, I present to you the 167th Carnival of Mathematics…

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Reddit’s infamous theydidthemath page tackles ‘fake news’ on Instagram with a quite brilliant response to a post claiming that avoiding eating 1 beef burger will save enough water for you to shower for 3.5 years. Whilst the claim is hugely exaggerated we should still probably stop eating beef…

Next up, Singapore Maths Plus take a light-hearted look at the definition of ‘Singapore Math’ on Urban Dictionary – which is apparently the world’s number one online dictionary (sounds like more ‘fake news’ to me).

Math off the grid jumps in ahead of hosting next month’s Carnival to discuss the book ‘Geometry Revisited’ with a re-examination of the sine function as a tool for proving many fundamental geometric results. Scott Farrar also has the sine bug as he encourages us not to reject imprecise sine waves, but instead to consider the circle that they would form (warning contains a fantastic GIF).

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John D Cook introduces what is now my new favourite game with his explanation of the ‘Soviet Licence Plate Game’. Have a go at the one to the right – can you make the four numbers 6 0 6 9 into a correct mathematical statement by only adding mathematical symbols such as +, -, *, /, ! etc. ? Send your answers to me @tomrocksmaths on Social Media or using the contact form on my website.

If by this point, you’ve had enough of numbers (which apparently happens to some people?!), then here’s a lovely discussion of ‘numberless word problems’ from Teaching to the beat of a different drummer. If that doesn’t take your fancy, how about some group theory combined with poetry via this ridiculous video of Spike Milligan on The Aperiodical

If like me you’re still not really sure what you’ve just watched, then let’s get back to more familiar surroundings with some intense factorial manipulation courtesy of bit-player. What happens when you divide instead of multiply in n factorial? The result is truly mind-blowing.

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Finding our way back to applications in the real world, have you ever wondered how the photo effect called ‘Tiny Planets’ works? Well, you’re in luck because Cor Mathematics has done the hard work for us and created some awesome mini-worlds in the process!

Sticking with the real world, Nautilus talks to Computer Scientist Craig Kaplan who discusses how the imperfections of the real world help him to overcome the limitations of mathematics when creating seemingly impossible shapes. They truly are a sight to behold.

With our feet now firmly planted in reality, let’s take a well-known mathematical curiosity – say the Birthday Problem – and apply it to the 23-man squad of the England men’s football team from the 2018 World Cup. Most of you probably know where this one is going, but it’s still fascinating to see it play out with such a nice example from Tom Rocks Maths intern Kai Laddiman.

The fun doesn’t stop there as we head over to Interactive Mathematics to play with space-filling curves, though Mathematical Enchantments take a more pensive approach as they mourn the death of the tenth Heegner Number.

Focusing on mathematicians, Katie Steckles talks all things Emmy Noether over at the Heidelberg Laureate Forum Blog, whilst I had the pleasure of interviewing recent Fields Medal winner Alessio Figalli about what it feels like to win the biggest prize of all…

And for the grand finale, here are some particularly February-themed posts…

The next Carnival of Mathematics will feature mathematical marvels posted online during the month of March, which of course means ‘Pi Day’ and all the madness that follows. Good luck to the next host ‘Math off the grid’ sorting through what will no doubt be an uncountably large number of fantastic submissions!

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 Fields Medal – the mathematical equivalent of the Nobel Prize.

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,_Grigori_(1966)

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.

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