News from the world of maths

Random, but not by chance

noreply@blogger.com (Plus) — Tue, 20 Apr 2010 15:51:00 +0000

Researchers from the University of Maryland have devised a new kind of random number generator that is cryptographically secure, inherently private and — most importantly — certified random by the laws of physics. Randomness is important, particularly in the age of the Internet, because it guarantees security. Valuable data and messages can be encrypted using long strings of random numbers to act as "keys", which encode and decode the information. Randomness implies unpredictability, so if the key is truly random, it's next to impossible for an outsider to guess it.

Electoral impossibilities

noreply@blogger.com (Plus) — Fri, 09 Apr 2010 12:22:00 +0000

One advantage of the UK voting system is that nobody could possibly fail to understand how it works. However, the disadvantages are well-known. Differently sized constituencies mean that the party in government doesn't necessarily have the largest share of the vote. The first-past-the-post system turns the election into a two-horse race, which leaves swathes of the population un-represented, forces tactical voting, and turns election campaigns into mud-slinging contests.

There are many alternative voting systems, but is there a perfect one? The answer, in a mathematical sense, is no.

Get ready for May 6 with some election maths

noreply@blogger.com (Plus) — Tue, 06 Apr 2010 13:09:00 +0000

Official campaigning for the UK general election may only just have started, but most of us already suffer from election fatigue. So why not divert your mind from the political mud-slinging fest with a look at some of the maths that makes democracy work? Here's a list of Plus articles exploring voting systems and voting paradoxes:

Medical research plagued by bad reporting

noreply@blogger.com (Plus) — Fri, 26 Mar 2010 15:37:00 +0000

A study of 1,000 randomised clinical trials used to test medical treatments has shown that the way in which these trials are reported in medical journals still doesn't come up to scratch. According to Sally Hopewell, of the University of Oxford, and her colleagues, important information, like the size of the sample a treatment was tested, on still aren't reported in published papers. "Without complete and transparent reporting of how a trial was designed and conducted, it is difficult for readers to assess its conduct and validity or to differentiate trials with unbiased results from those with questionable results,” they write in the British Medical Journal.

Abel Prize 2010 goes to John T. Tate

noreply@blogger.com (Plus) — Wed, 24 Mar 2010 12:14:00 +0000

The Abel Prize 2010 has been awarded to John T. Tate from the University of Texas at Austin "for his vast and lasting impact on the theory of numbers". The honour puts Tate on a par with a Nobel Prize winner. In fact, the Abel Prize was established to make up for the fact that there is no Nobel Prize in mathematics.

Perelman awarded Millennium Prize for proof of Poincaré Conjecture

noreply@blogger.com (Plus) — Wed, 24 Mar 2010 09:26:00 +0000

Last week the Clay Mathematics Institute announced that Grigoriy Perelman has won the Millennium Prize for his proof of the century old Poincaré Conjecture. And almost as soon as it was announced the speculation began as to whether Perelman would accept the prize, and the $US 1,000,000 of prize money.

The Poincaré Conjecture is a question essentially about the nature of shapes in space. Mathematicians have long understood the nature of every possible 2D surface in 3D space. For example the surface of a sphere, such as the outside of a ball, is completely characterised by being simply connected — it has no edge, and any loop on the surface can be slid off without being cut or torn. And these two properties are true not matter how much a sphere is squashed or stretched out of shape. However they aren't true for any other kind of 2D surface, for example the surface of a doughnut: a loop through the centre hole of a donut can't be removed without being cut. That is because a doughnut is not the same, topologically speaking, as a sphere.

Poincaré proposed that all 3D spheres can be characterised by the same two properties. However for over a century the result remained unproven despite the efforts of some of the best mathematical minds. The problem was seen as so important that it was included in the list of seven Millennium Problems chosen by the Clay Institute in 2000. The solution to any of these Millennium Problems would be a monumental advancement in mathematics, and the Clay Institute offered a prize of $US 1,000,000 for the solution for each.

In 2003 Perelman surpised the mathematical world by posting a proof of a much wider conjecture online. He claimed to have proved Thurston's Geometrisation Conjecture, that characterised every 3D surface. The Poincaré Conjecture would be proven true as a consequence of this wider result.

After much examination, discussion and exposition, the mathematical community accepted that Perelman had proved the Poincaré conjecture and he was awarded the Fields Medal in 2006, the highest prize in mathematics. Controversially Perelman declined to accept the prize, the first person to ever do so. He withdrew from mathematics and now lives a reclusive life in the outskirts of St Petersburg.

Now that Perelman's work has survived several years of critical review and has been accepted by the mathematical world the Clay Institute has awarded him the Millennium Prize for his proof of the Poincaré Conjecture, the first of the Millennium Problems to be solved. However most people in the mathematical community expect that, like the Fields medal, Perelman will not accept this prize or the prize money. Despite some reports in the media, the Clay Institute told Plus that they had been in contact with Perelman and that "he said he would think about it".

Whether or not Perelman's decides to accept the Millennium Prize at a ceremony in June, his enormous contributions to mathematics will be celebrated for many years, and we hope that he is able to live his life happily in whatever way he chooses. It might seem hard for most of us to understand how someone could refuse such wealth and fame but, as Marcus du Sautoy explained to BBC Radio 4's The World Tonight, for some people other things are more important:

"I think there is something noble in that he values solving a mathematical problem above the glory of being in the limelight and winning prizes and getting vast sums of money. There is something rather nice about Perelman's choice to just enjoy the mathematics."

You can read more about the Poincaré Conjecture and the Clay Millennium Problems on Plus, and you can read more about his award, including his original papers at the Clay Mathematics Institute.

Further evidence of Arctic melt-down

noreply@blogger.com (Plus) — Tue, 16 Mar 2010 10:56:00 +0000

The worrying decline of Arctic sea ice as a result of global warming is continuing. Last month the results of the Catlin Arctic Survey, an expedition to measure the thickness of Arctic sea ice, were presented at a press conference called by the World Wildlife Fund. On their 434km trek across the Arctic the explorers measured an average ice thickness of 1.77m. This confirms that the ice is getting thinner, but also means that they encountered mainly young ice, rather than the older and thicker multi-year ice they had expected.

Do you know what's good for you - what's the best medicine?

noreply@blogger.com (Plus) — Wed, 03 Mar 2010 13:36:00 +0000

How do you judge the risks and benefits of new medical treatments, or of lifestyle choices? With a finite health care budget, how do you decide which treatments should be made freely available on the NHS? Historically, decisions like these have been made on the basis of doctors' individual experiences with how these treatments perform, but over recent decades the approach to answering these questions has become increasingly rational. Statistics and maths are used not just to test new treatments, but also to measure such fuzzy terms as quality of life, and to figure out which treatments provide most "health for money".

While the decisions of health authorities affect all our lives, the underlying calculations are rarely discussed in the media. To explore these difficult decisions and the role of maths in evidence-based medicine, we have put together a package of six articles, three podcasts, a career interview and a classroom activity.

The Plus podcast: Evaluating a medical treatment

noreply@blogger.com (Plus) — Wed, 03 Mar 2010 12:02:00 +0000

New treatments and drugs are tested extensively before they come on the market using randomised controlled trials (RCTs). We talk to David Spiegelhalter (Winton Professor of the Public Understanding of Risk), Sheila Bird (Professor at the Medical Research Council Biostatistics Unit), and Nigel Hawkes (journalist and director of Straight Statistics) about why RCTs are used and how they test if a new treatment works. You can also read an accompanying article.

Listen to the podcast.

Mathematical mind reading on pi day

noreply@blogger.com (Plus) — Wed, 03 Mar 2010 10:00:00 +0000

To celebrate pi day on the 14th of March 2010, a mathematician and a magician will attempt to pull off what promises to be the world's largest live online magic trick — and you can join in via Twitter!

The mathematician James Grime and the magician Brian Brushwood will exploit the magical power of mathematics to read your mind over the internet. Visit the pi day magic website for instructions on how to join up to this record-breaking attempt, and watch this space for an explanation of how it's done to be published after the event.

The trick will be part of the Cambridge Science Festival, which runs from the 8th to the 21st of March 2001.

Calling all algebraic artists!

noreply@blogger.com (Plus) — Tue, 02 Mar 2010 17:32:00 +0000

Everyone has the chance to create mathematical beauty as part of a competition during the Cambridge Science Festival. As part of the Imaginary exhibition of beautiful mathematical images and artwork taken from algebraic geometry and differential geometry, visitors (both real and virtual) can create their own mathematical art.

By downloading the SURFER program, anyone can create images of algebraic surfaces by simple equations using the three spatial coordinates of x, y and z. For example, the equation x² + y² + z² = 1 results in a sphere.

The competition requires creativity, intuition and mathematical skill in order to create equations yourself or to change given equations to produce beautiful images. The images are easily generated with the SURFER programme, and you can then upload your artwork to the competition gallery by 20 March. Everybody is invited to take part, including group entries from classes and families. The entries will be judged by a distinguished panel including Sir Christopher Frayling (Royal College of Art and Arts Council England) and Conrad Shawcross (sculptor and artist-in-residence at the Science Museum, London).

So good luck to all aspiring artists, and if you need some inspiration why not browse through the Plus articles on maths and art.

What does mathematics feel like?

noreply@blogger.com (Plus) — Tue, 02 Mar 2010 16:39:00 +0000

If you have ever wondered what it feels like to do mathematics, take a look at the series of beautiful short films produced by the mathematics department at the University of Bristol. Chrystal Cherniwchan, Azita Ghassemi and Jon Keating interviewed over 60 mathematicians, asking them to describe the emotional aspects of maths research. The discussions range from the role of creativity and beauty in maths, to what it feels like to pursue the wrong research path, and the eureka moment of discovering mathematical truth. You can view them all on the Mathematical Ethnographies site.

You can also read more about beauty in mathematics, in Plus, as well as the mathematical lives of John Conway, Stephen Hawking and Gerardus 't Hooft and many others in our careers with maths library.

Einstein right on time

noreply@blogger.com (Plus) — Wed, 17 Feb 2010 12:27:00 +0000

A central prediction of Albert Einstein's general theory of relativity is that gravity makes clocks tick more slowly — time passes slower when you're close to a massive body like the Earth, compared to when you're further away from it where its gravitational pull is weaker. This prediction has already been confirmed in experiments using airplanes and rockets, but a new experiment in an atom interferometer measures the slowdown 10,000 times more accurately than before — and finds it to be exactly what Einstein predicted.

Browse with Plus: Symmetry, reality's riddle

noreply@blogger.com (Plus) — Wed, 17 Feb 2010 12:23:00 +0000

Marcus du Sautoy is a mathematician and Charles Simonyi Professor for the Public Understanding of Science. In this TED talk he explores how the world turns on symmetry — from the spin of subatomic particles to the dizzying beauty of an arabesque — complete with an introduction to groups.

Marcus du Sautoy has also written several articles for Plus:

Maths in a minute — Achilles and the tortoise

noreply@blogger.com (Plus) — Wed, 17 Feb 2010 12:10:00 +0000

Achilles and a tortoise are competing in a 100m sprint. Confident in his victory, Archilles lets the tortoise start 10m ahead of him. The race starts, Achilles zooms off and the tortoise starts bumbling along. When Achilles has reached the point A from where the tortoise started, it has crawled along by a small distance to point B. In a flash Achilles reaches B, but the tortoise is already at point C. When he reaches C, the tortoise is at D. When he's at D, the tortoise is at E. And so on. He's never going to catch up with the tortoise, so he has no chance of winning the race.

Something's wrong here, but what? Let's assume that Achilles is ten times faster than the tortoise and that both are moving at constant speed. In the times it takes Achilles to travel the first 10m to point A, the tortoise, being ten times slower, has only moved by 1m to point B. By the time Achilles has travelled 1m to point B, the tortoise has crawled along by 0.1m to point C. And so on. After n such steps the tortoise has travelled

1+1/10+1/100+1/1000+ .... +1/10^(n-1) metres.

And this is where the flaw of the argument lies. The tortoise will never cover the 90m it has to run using steps like these, no matter how many of them it takes. In fact, the distance covered in this way will never exceed 10/9=1.111... metres. This is because the geometric progression

1+1/10+1/100+1/1000+...

converges to 10/9. Since the tortoise is travelling at constant speed, it covers this distance in a finite time, and it's precisely when it's done that that Achilles overtakes it.

This problem is known as one of Zeno's paradoxes, after the ancient Greek philosopher Zeno, who used paradoxes like this one to argue that motion is just an illusion.

Find out more about Zeno's paradoxes in the Plus article
Mathematical mysteries: Zeno's Paradoxes,
and about convergent series in the Plus articles
An infinite series of surprises,
Outer space: Series, and
In perfect harmony.

Maths at the Cambridge Science Festival

noreply@blogger.com (Plus) — Fri, 12 Feb 2010 13:01:00 +0000

If you're wondering how to feed your maths habit between the 8th and 21st of March, then why not head to Cambridge for the 2010 Cambridge Science Festival? There'll be plenty of free maths events, including:

IMAGINARY: through the eyes of mathematics — A travelling exhibition of beautiful mathematical images and artwork taken from algebraic geometry and differential geometry in which visitors are able to create their own mathematical art. Age range: 12+.
Conversations across science and art — A talk and discussion event centred on the relationship between science and art, including the presentation Every picture tells a story by Professor John D Barrow and a talk by Professor Gerry Gilmore exploring the relationship between art and astronomy. Age range: 14+.
Enigma: codes and codebreaking — The Enigma cipher was one of the most powerful weapons of the Second World War. An apparently unbreakable code. How did a small group of mathematicians crack it? Come and see a demonstration of a genuine Enigma machine, and try your hand at breaking different codes used through 2500 years of history! Age range: 8+.
Who Wants To Be a Mathionaire? — Explore the maths of probability, chance and uncertainty in this exciting and highly interactive game-show style quiz, using hand-held voting technology to answer against the clock! Age range: 14+.
The Maths and Physics of Sport — Professor John D Barrow looks at some applications of physics and simple mathematics to a variety of sports, including weightlifting, rowing, throwing, jumping, drag car racing, balance sports, and track athletics, as well as some of the paradoxical systems of judging used in ice skating, and the effects of latitude and air resistance on some performances. Age range: 14+.
What's the risk of getting out of bed? — We are constantly being exhorted to change our behaviour to reduce the chances that things will turn out badly for us, and government is continually intervening to make our society safer. But are we being too cautious? In this lecture, Professor David Spiegelhalter will look at attempts to measure and communicate the benefits, and possible harms, of risk reduction in a range of areas, from swine flu to climate change, heroin to hang-gliding. Age range: 14+.
The hands on maths fair — Games and puzzles for all ages from the University's Millennium Mathematics Project. Pit your wits against the SOMA cube, tangrams, Auntie's Tea Cups or giant dominoes, and sharpen your strategic reasoning skills! Age range: 5+.

To find out about all the Cambridge Science Festival events go to the festival website.

Unintended consequences of mathematics

noreply@blogger.com (Rachel) — Wed, 10 Feb 2010 14:09:00 +0000

Mathematicians (and Plus authors) John Barrow, Colva Roney-Dougal and Marcus du Sautoy will be discussing unintended consequences in mathematics with Melvyn Bragg on his BBC Radio 4 programme In Our Time tomorrow morning at 9am.

Image courtesy NASA

Many of the most exciting developments in science is is when knowledge from one area such as pure mathematics unexpectedly crosses boundaries to provide deeper understanding of a previously unconnected problem in another area. The programme will explore many such unintended consequences, including how the ancient purely geometric study of conic sections turned out to be vital in understanding the orbits of the planets, how Einstein used the theoretical concepts from non-Euclidean geometry for his groundbreaking work on special relativity, and how the number theory provided the security necessary for our digital age.

You can read more from John, Colva and Marcus on Plus, as well as articles on conic sections and planetary orbits, non-euclidean geometry and special relativity, and number theory and chryptography.

Putting the magic back into classroom maths

noreply@blogger.com (Rachel) — Thu, 04 Feb 2010 14:28:00 +0000

Mathematics and magic may seem a strange combination, but Queen Mary's Matt Parker and Peter McOwan want to show students otherwise. They have produced many of the The Manual of Mathematical Magic, a unique kit of magical miracles, to show that the most powerful magical effects performed today have a mathematical basis.

Freely available to any school in England, the Manual exposes the secrets behind street magic, close-up and stage tricks, revealing the varied and exciting everyday uses for the mathematics powering your magic. It gives young mathematicians the chance to be creative, finding new ways to solve problems and discovering the key to the perfect magic trick. Along the journey they will also uncover the skills of a good mathematician, one with the useful employment skills you get from being good at mathematics.

Both McOwen and Parker regularly visit secondary schools to do Mathematical Magic shows for students. “Our goal is to help more students engage with Mathematics," reveals Parker, who is also involved with the More Maths Grads programme. "Magic tricks get the students excited and then we show them the mathematical principles that make the whole trick hang together. We also reveal how the same Mathematics underpins everything from medical scans to sending text messages.”

As well as The Manual of Mathematical Magic, the kit also contains a pack of cards, notebook and pencil – all of which have hidden Mathematical Magic. Teachers can use the tricks in the book in their lessons and then explain the Mathematics and its applications.

“Maths is magic. But too often school maths is a dull diet which sucks the joy out of what should be a thrilling and beautiful subject," said Paul McGarr, Deputy leader Maths Faculty at Langdon Park School where Parker gave a magical lesson to Year 10 pupils this week. "This new pack, quite literally, helps put the magic back into classroom maths. My pupils really loved it, they were engaged, excited and happy – not bad for last period of a long day! The 'wow' was audible when they saw some of the tricks demonstrated, and you could almost taste their intense curiosity to find out how it was done using maths. I would strongly recommend teachers to get hold of this pack and use it.”

For more information and to conjure up a kit for your school, visit http://www.mathematicalmagic.com.

And for more on maths and magic you can read 1089 and all that and Maths and magic on Plus, and learn mathematical magic tricks at the Magic of Computer Science.

Controlling cockroach chaos

noreply@blogger.com (Rachel) — Thu, 04 Feb 2010 10:40:00 +0000

Catching sight of a cockroach tends to make us behave chaotically, what with the running and screaming and throwing of shoes. But it appears that chaos might actually explain how we, and the cockroach itself, behave.

An interdisciplinary team of scientists from Germany have created a robotic cockroach that autonomously behaves in a way reminiscent of a real cockraoch. The robot independently changes gait depending on the surface it is walking on, avoids obstacles and can even extricate its leg from a hole or run away from predators. Recreating lifelike behaviour is not new, but this robot reproduces a huge range of behaviours and quickly reacts to new situations and switch between them. And the secret to its success is controlled chaos in its robotic brain.

Beautiful symmetry provides glimpse into quantum world

noreply@blogger.com (Plus) — Fri, 22 Jan 2010 11:06:00 +0000

A complex symmetric structure known as the exceptional Lie group E8, which has so far only existed in the minds of mathematicians, seems to have turned up in real life for the first time. Physicists from the UK and Germany have conducted an experiment which involved cooling a crystal made of cobalt and niobium to near absolute zero and then applying a magnetic field. As they increased the strength of the magnetic field to a critical value, spontaneous patterns appeared in the configuration of electrons in the crystal, and these patterns carried the tell-tale signature of E8.

Maths for mums and dads

noreply@blogger.com (Plus) — Tue, 12 Jan 2010 15:40:00 +0000

In a survey published last week 79% of parents revealed that maths homework frequently leads to conflict and arguments in the household, and a third of those surveyed admitted that they avoid helping their children with their maths homework. Over 40% of parents proved unable to work out the answer to a question that a 10-year-old might be expected to solve in a national test. (Alex thinks of a number. He adds half of the number to a quarter of the number. The result is 60. What was the number Alex first thought of?) What's more, over 50% admitted to not being able to teach their kids basic maths techniques used in primary school, including division by chunking, the grid method, or number bonds?.

The survey questioned a random sample of 1000 parents who have children aged 6 -11 years. It was commissioned by Random House Group to coincide with the publication of a new book by Plus author Rob Eastaway and Mike Askew. Maths for Mums and Dads is designed to help parents come to grips with the techniques children are now taught at school and to give parents an insight into why children make mistakes. Look out for a review in the next issue of Plus or buy now from Amazon.

The speed of climate change

noreply@blogger.com (Plus) — Fri, 08 Jan 2010 12:23:00 +0000

How long will it be until climate change brings tropical butterflies, exotic birds, or malaria-infested mosquitoes to UK shores? A team of US scientists has come a step closer to an answer by estimating the speed of climate change: the distance animal and plant species would have to migrate every year to maintain a constant temperature in their surroundings. According to the team's study, recently published in the journal Nature, the global mean of this speed is 0.42 km per year, but the study also points to important differences between types of habitat. Mountain species will be able to move slower, a predicted 0.11 km a year, since temperature varies quickly as you move up and down a mountain slope. Ecosystems from flooded grass lands and savannas, however, may have to shift by as much as 1.26 km a year to keep their temperature constant.

Mysterious stocking filler for US physicists

noreply@blogger.com (Plus) — Tue, 22 Dec 2009 11:54:00 +0000

Researchers working on the Cryogenic Dark Matter Search experiment (CDMS) received an early Christmas gift last week when their detectors spotted evidence for the existence of dark matter, the mysterious substance that is believed to make up 25% of our Universe. The detectors, sitting half a mile underground in a disused mine in northern Minnesota, detected two events that may be results of dark matter particles bouncing off other atomic nuclei. It's the first time that such events were recorded by CDMS, and while they don't provide conclusive proof that dark matter exists, the detections have caused a stir in the scientific community.

Issue 53 of Plus is out now!

noreply@blogger.com (Plus) — Fri, 18 Dec 2009 15:55:00 +0000

If you are looking for something to while away the holiday, then this issue has plenty of ideas for you! We explore the power of origami to solve ancient (and very modern) problems, find the maths in fashion, and marvel at the complexities of church bell ringing. But it's not all fun and games, as we investigate the controversies surrounding breast screening and the maths behind drug-induced hallucinations, find out how to predict the impact of natural catastrophes, and answer some deep questions about the Universe.

Read issue 53 of Plus!

How long is a day?

noreply@blogger.com (Plus) — Fri, 18 Dec 2009 15:14:00 +0000

In our last online poll to find out what Plus readers would most like to know about the Universe you told us that you'd like to find out how long a day is. We took the question to the physicist Nicholas Mee and here is his answer — and it's not 24 hours!