Plus Blog

July 17, 2012

Henri Poincaré died 100 years ago today.

Henri Poincaré died 100 years ago today. He is most famous for the conjecture (now theorem) which carries his name and which remained open for almost 100 years, until Grigori Perelman announced a proof in 2003. But the conjecture isn't all there was to Poincaré. One of his teachers reportedly described him as a "monster of maths" who, perhaps because of his poor eyesight, developed immense powers of visualisation, which must have helped him particularly in his work on geometry and topology. He has been hailed one of the last people whose understanding of maths was truly universal. And he also thought about the philosophy of mathematics. He believed that intuition has an important role to play in maths, and anticipated the work of Kurt Gödel, who proved that maths cannot ever be completely formalised. Finally, and extremely pleasingly for us here at Plus, Poincaré was one of the few scientists of his time to share his knowledge by writing numerous popular science articles.

You can find out more about the Poincaré conjecture and related maths in these Plus articles:

And there is more on Poincaré's life and work on the MacTutor history of maths archive.

July 3, 2012

So results just released from the Tevatron experiment in the US strongly support last December's announcement from the LHC – it's looking promising that the Higgs boson exists and that it has a mass around 125GeV. But as we explained in our previous news story, Countdown to the Higgs, the level of evidence produced so far doesn't count as a discovery. Physicists will only declare they have discovered the Higgs boson if they are 99.99995% confident of their result – the elusive five-sigma level.

And we might not have to wait much longer. Excitement is mounting about tomorrow's announcement of the latest results from the LHC. You can watch the seminar at 8am and press conference at 10am BST live from CERN. And to whet your appetite here are some new articles explaining exactly what the Higg's particle is, does and how they are hunting for it. We're just off to put some champagne on ice...


Particle hunting at the LHC

Our favourite particle physicist, Ben Allanach, explains exactly what they are looking for at the LHC. Welcome to the world of quantum jelly....


Secret symmetry and the Higgs boson: Part I and Part II

The notorious Higgs boson, also termed the god particle, is said to have given other particles their mass. But how did it do that? In this two-part article we explore the so-called Higgs mechanism, starting with the humble bar magnet and ending with a dramatic transformation of the early Universe.


Countdown to the Higgs?

What does all this talk about sigma levels mean? It turns out that finding the Higgs is not so much a matter of catching the beast itself, but keeping a careful count of the evidence it leaves behind.


Hooray for Higgs!

The LHC gave particle physicists an early Christmas present last year – the first glimpses of the Higgs boson.

July 3, 2012

The European Congress of Mathematics. The logo is an infinity-shaped pretzel!

Greetings from the beautiful city of Krakow, where the 6th European Congress of Mathematics opened yesterday! Around 1,000 mathematicians, donning straw hats and flip-flops to resist the incredibly hot weather, have come together here to chat, share and listen to lectures, and Plus will be reporting from the congress all week.

The day started with the Oscars of European mathematics: at the opening ceremony the European Mathematical Society awarded prizes to twelve young mathematicians for their excellent contributions to maths, their subjects ranging from geometry and group theory to chaos theory, quantum chemistry and the history of maths.

After that it was a conference lunch including infinity-shaped pretzels, and then the auditorium filled once more to hear Adrian Constantin's fascinating talk on water waves — it's not the water that moves with the wave, but the wave moving through the water. And when a wave breaks the maths that describes it seizes to work. I'll be talking to Constantin about his maths tomorrow and you'll be able to read an article on Plus soon. I'll also be interviewing Marta Sanz-Solé, the President of the European Mathematical Society.

Sara Santos

Sara Santos and her maths buskers on the streets of Krakow. The challenge here was to turn the waistcoat inside out while being handcuffed.

But the congress isn't just about mathematicians talking to each other. After the lecture I went in search of Sara Santos, who has taken her mathematical buskers to the streets of Krakow, handcuffing innocent Krakowians (a punishment for dividing by zero), constructing emergency pentagons, and reading minds. But as Sara says, it's not about magic tricks but about the magical fact that the world we live in is written in the language of maths. You can hear from some maths buskers in our podcast to be published soon and if you'd like to become a maths busker yourself, visit the maths busking website.

Krakow really is as beautiful as everyone says. It's the oldest city of Poland with an amazing medieval market square, the largest in Europe. And the town has picked up the mathematical theme with no less than three art galleries showing mathematical art — if I find the time between lectures, interviews, and wine-and-canapé receptions, I'll go and visit. But now I'm off for the last task of today: investigate the specific gravity of Polish beer.


Krakow's Market Square.

June 25, 2012

On Saturday Alan Turing would have celebrated his 100th birthday. In his short life he revolutionised the scientific world and so 2012 has been declared Turing Year to celebrate his life and scientific achievements. You can join the celebrations by visiting the special exhibition at the Science Museum or attending the Turing Educational Day at Bletchley Park. Turing is also being honoured in this year's Manchester Pride Parade and the LGBT History Month. And here at Plus, apart from getting to work on building our own Turing machine out of LEGO, we're also celebrating with these favourites:

Alan Turing: ahead of his time

Alan Turing is the father of computer science and contributed significantly to the WW2 effort, but his life came to a tragic end. This article explores his story.

What computers can't do

Another look at Turing's life and work. Find out what types of numbers we can't count and why there are limits on what can be achieved with Turing machines.

How the leopard got its spots

How does the uniform ball of cells that make up an embryo differentiate to create the dramatic patterns of a zebra or leopard? How come there are spotty animals with stripy tails, but no stripy animals with spotty tails? The answer comes from an ingenious mathematical model developed by Alan Turing.

Omega and why maths has no TOEs

Is there a Theory of Everything for mathematics? Gregory Chaitin thinks there isn't and Turing's famous halting problem plays an important part in his work.

Exploring the Enigma

Turing is most famous for his work as a WWII code breaker. This article looks at the efforts of all the code breakers at Bletchley Park, which historians believe shortened the war by two years.


CAPTCHA if they can

A version of Turing's famous test – the "Completely automated public Turing test to tell computers and humans apart", or CAPTCHA for short – helps in the fight against the everyday evil of spam email.


Building a bio computer

Turing's scientific legacy is going stronger than ever. An example is an announcement from February this year that scientists have devised a biological computer, based on an idea first described by Turing in the 1930s.


Did a philosopher kill WALL-E?

AI has become big business in Hollywood, but will we ever see the computers reliably pass the Turing test? Or is it philosophically impossible?

June 14, 2012
Mathematics of Planet Earth

Our planet is shaped by the oceans, the dynamic geology and the changing climate. It teems with life and we, in particular, have a massive impact as we build homes, grow food, travel and feed our ever-hungry need for energy. Mathematics is vital in understanding all of these, which is why 2013 has been declared as the year for the Mathematics of Planet Earth.

As well as encouraging research into fundamental questions about the Earth and how to meet the challenges it faces, there will also be many opportunities during 2013 for everyone to get involved including public lectures and workshops, competitions and exhibitions. The first such competition is now underway: the MPE 2013 competition to design an exhibit about the mathematics of Planet Earth.

Everyone is invited to design an interactive or physical exhibit, images or videos that explain how mathematics helps to understand our world and solve its problems. MPE 2013 has come up with a list of possible topics to get you started and there are several examples of what an exhibit might look like, from fractal coasts to crystal flights and subway scheduling.

The competition is open for submissions until 20 December 2012. The winning entries, as well as winning cash prizes, will be exhibited in institutions around the world, including the UNESCO headquarters in Paris in the inaugural exhibition in March 2013. All exhibitions will be open source and hosted by IMAGINARY, where anyone can download and reproduce the exhibits in their own museums or galleries.

Have you got an idea of how to explain the maths of planet Earth? Perhaps after reading about climate change and the Arctic or why we should all be nicer to one another? Then why not develop your ideas into an exhibit and share your mathematical ideas with all of us on planet Earth!

For more information visit the competition website or

May 9, 2012
knit that torus

If you've never heard of cubic Hamiltonian graphs before then take a look at Christopher Manning's wonderful cubic Hamiltonian graph builder. No, really, do! We too had never heard of them and now we think they are the bee's knees!

But what is a cubic Hamiltonian graph, you ask? A graph, of course, is just a bunch of points (vertices) connected by lines (edges). A cubic graph is a graph where every vertex has 3 edges – that is, each vertex is connected to exactly three others in the graph. And a Hamiltonian graph is a graph which has a closed loop of edges (a cycle) that visits each vertex in the graph once and only once, (this is called a Hamiltonian cycle). So a cubic Hamiltonian graph is a graph where each vertex is joined to exactly three others and the graph has a cycle visiting each vertex exactly once.

What has made us so excited about cubic Hamiltonian graphs is watching Manning's cubic Hamiltonian graph builder in action. The builder starts from the Hamiltonian cycle in the graph. This loop of edges accounts for two out of the three edges for every vertex in the graph. The builder then starts adding in the third edge for each vertex, knitting the graph together before your eyes. The creation of a torus is particularly beautiful to watch.

Manning uses something called the LCF notation to build the graphs. This ingenious notation succinctly describes the structure of cubic Hamiltonian graphs by describing how you add the extra edge to each vertex by counting backwards or forwards around the Hamiltonian cycle. For example our torus has the LCF notation [10]150. This means that every vertex is joined to another 10 edges along the cycle, and this process is repeated 150 times, once for each vertex, to complete the graph. (The 1st vertex is joined to the 11th, the 2nd to the 12th, the 3rd to the 13th, and so on...)

A graph represented by the LCF notation [10,7,4,-4,-7,10,-4,7,-7,4]2 starts with a cycle of 20 vertices – inside the square brackets is a list of instructions for 10 edges, and these are repeated twice, giving the total number of extra edges, and therefore vertices, as 20. In this graph the 1st vertex is joined to the 11th (a distance of 10 edges), the 2nd to the 9th (a distance of 7), the 3rd to the 7th (a distance of 4), the 4th to the 20th (a distance of -4, or counting backwards 4 edges), the 5th to the 18th (distance of -7), and so on. This graph is knitted into a dodecahedron.

Watching Manning's program knit together these graphs is beautiful to watch. But this mathematics has many important uses as well. Not only are Hamiltonian cycles important mathematically, they also have many useful applications. You can read more about graphs on Plus, and about the role Hamiltonian cycles play in bell ringing and DNA analysis. And you can read more about Christopher Manning's work on his blog.

Syndicate content