## Plus Blog

February 27, 2014
We've read the book. We've bought the T-shirt. And now, finally, here it is: the movie of one of our favourite maths problems, the bridges of Königsberg. Though admittedly, we made it ourselves. We learnt several interesting lessons in the process. For example that a bin doesn't make a good supporting character and that people who shouldn't be in the frame should get out of it. But other than that, we're well on course for an Oscar this weekend! You can read more about the bridges of Königsberg here. |

February 25, 2014
There was a brief pause in research at the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge (DAMTP, also the home of Stephen Hawking experiencing zero gravity (Image: NASA) "When I arrived at DAMTP in 1962 cosmology was a speculative science and we didn't know if the Universe had a beginning or had existed forever in a steady state," Hawking said. He went on to say that the new Professorship recognised the role of the department in taking cosmology from this speculative start to the remarkably successful field it is today. We'd like to congratulate Hawking on his new post (and thank him for the cake and champagne!) and look forward to the next exciting discovery from our cosmologist neighbours.
You can read more about Hawking's life and work in his articles 60 years in a nutshell and A brief history of mine, and in our coverage of his 60th and 70th birthday symposia. And of course, there's much more about cosmology on |

February 25, 2014
Georg Cantor Are there more irrational numbers than rational numbers, or more rational numbers than irrational numbers? Well, there are infinitely many of both, so the question doesn't make sense. It turns out, however, that the set of rational numbers is infinite in a very different way from the set of irrational numbers. As we saw here, the rational numbers (those that can be written as fractions) can be lined up one by one and labelled 1, 2, 3, 4, etc. They form what mathematicians call a So let’s suppose the real numbers are countable, so that we can make a list of them, for example 1. 2. 3. 4. 5. and so on, with every real number occurring somewhere in the infinite list. Now take the first digit after the decimal point of the first number, the second digit after the decimal point of the second number, the third digit after the decimal point of the third number, and so on, to get a new number . Now change each digit of this new number, for example by adding . This gives the new number . This new number is not the same as the first number on the list, because their first decimal digits are different. Neither is it the same as the second number on the list, because their second decimal digits are different. Carrying on like this shows that the new number is different from every single number on the list, and so it cannot appear anywhere in the list. But we started with the assumption that every real number was on the list! The only way to avoid this contradiction is to admit that the assumption that the real numbers are countable is false. And this then also implies that the irrational numbers are uncountable. It's easy to see that an uncountable infinity is "bigger" than a countable one. An uncountable infinity can form a continuum, such as the number line, in a way that a countable infinity can't. Cantor went on to define all sorts of other infinities too, one bigger than the other, with the countable infinity at the bottom of the hierarchy. When he first published these ideas, Cantor faced strong opposition from some of his colleagues. One of them, Henri Poincaré, described Cantor's ideas as a "grave disease" and another, Leopold Kronecker, went so far as to denounce Cantor as a "scientific charlatan" and "corrupter of youth". Cantor suffered severe mental health problems which may have resulted in part from the rejection his work had met with. But we now know that his work had simply come too soon: 150 years on, Cantor's ideas form a central pillar of mathematics and many of his results can be found in standard textbooks. See our infinity page to find out more about this and other things to do with infinity. |

February 20, 2014
With spring (hopefully) on its way, it looks increasingly less likely that we will be blessed with the cold, white, fluffy stuff this year. But if the winter Olympics leave you yearning for snow and ice, here are some related maths stories for you.
Maths solves frozen mystery
A molecule's eye view of water Maths and climate change: the melting Arctic
Teacher package: On thin ice - maths and climate change in the Arctic You can also read more about the expedition in the news stories On thin ice and Further evidence for Arctic meltdown. Career interview: Avalanche researcher And if you want to learn more about maths and sport in general, visit our sporty sister site. |

February 14, 2014
Climate change threatens the world's glaciers, which is why scientists simulate them on computers. Based on mathematical models, these computer simulations help predict how glaciers are likely to change in the future, depending on environmental factors. The Aletsch glacier in Switzerland. But you can also run these simulations backwards in time, to see how a glacier behaved in the past. This is what a mathematician and a glaciologist have just done, not in order to understand glaciers, but in order to solve a mystery. In March 1926 four young men, three of whom were brothers, set off on a tour from the Aletsch glacier in Switzerland, the longest glacier in the Alps. They never returned. It's likely they got caught up in a blizzard that raged in the mountains for several days. Despite an extensive search their bodies could not be found and nobody knew where on their trip they met their end. Eighty-six years later, in the summer of 2012, two English alpinists found the remains of the three brothers and some of their equipment. The mathematician Guillaume Jouvet of Freie Universität Berlin and the glaciologist Martin Funk of the ETH in Zürich realised that they could use a computer model of glaciers, which Jouvet had developed during his PhD in 2012, to find out where the men had met their death. The model was the first to represent the three-dimensional flow of a glacier, including the velocity of the flow beneath its surface. Starting from the place the men's bones were found, the scientists simulated the evolution of the glacier backwards in time. They found that the bodies probably moved by around 10.5km in the 86 years since they had been swallowed by the ice, at an average speed of 122 meters per year. In 1980 they were buried some 250m below the surface of the ice. And the place of the men's demise could be narrowed down to an area of 1600m by 300m. Jouvet and Funk hope that they can solve other glacial mysteries using their method. For example, in 1964 a plane carrying US military crashed on the Gauli glacier in Switzerland. Crew and passengers could be rescued, but the plane disappeared in the ice without a trace. Using their model, Juvet and Funk hope to predict when and where it will be released from the ice. And who knows what other icy stories their model will reveal in the future. Jouvet and Funk's work on the young men who died in 1926 has been published in the Journal of Glaciology. Thanks to our friend Thomas Vogt of the German Mathematical Association for bringing this story to our attention. You can read more about maths, ice and snow here on |

January 29, 2014
It might be grey and raining outside, but inside the Museum of London and Barnard's Inn Hall, Gresham College have some fascinating lectures planned to brighten the darkest day! First up Caroline Crawford will explore the lives of stars on Wednesday 5 February at 1pm at the Museum of London, how they are born, evolve over billions of years and dramatically burn, revealing clues to our own origins. It seems Hollywood isn't the only place where the stars crash and burn. Prince Charming? Or just a slimy toad? And surely the best way to cheer up a dreary day is to fall in love. Tony Mann will explain the mechanics of computer dating and how maths can help us find our heart's desire (or at least a charming dinner companion) in Finding stable matches: the mathematics of computer dating on Monday 17 February at 6pm, at Barnard's Inn Hall. And if you are using a coin to decide whether to get out of bed or stay under the duvet, you need to hear what Raymond Flood has to say about Probability and its limits on Tuesday 18 February at 1pm at the Museum of London. He'll explain why we know a coin will come up heads roughly half the time over many tosses, but we can't tell you whether yours will land heads or tails tomorrow morning. If it lands heads and you make it to his lecture, you'll find out much more!
There's no need to register for these free public events, just come a bit early to get a seat. You can find out about all the other fascinating talks on the Gresham College website and you can get in the mood by reading about astronomy, dating and probability on |