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December 22, 2012

Today would have been the 125th birthday of the legendary Indian mathematician Srinivasa Ramanujan. This self-taught genius formed a remarkable working relationship with the mathematician G.H. Hardy which served as inspiration for the 2008 play A disappearing number by Complicite. Read our article on the play and some of the maths behind it, our interview with an actor/mathematician involved in the play, and an article featuring one of Ramanujan's contribution to number theory.


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December 21, 2012

Quick, quick, before the world ends get your head around Schrödinger's equation. This central equation of quantum mechanics is the origin of weird phenomena like quantum entanglement, also known as spooky action at a distance, and quantum superposition, being in several apparently mutually exclusive states at once. A possible consequence of the equation is the idea that the universe is constantly splitting into many parallel branches. So while one copy of you sitting in one of these branches might witness a spectacular end to the world today, another can rest assured that it will survive.

Schrödinger's equation — what is it?

In the 1920s the Austrian physicist Erwin Schrödinger came up with what has become the central equation of quantum mechanics. It tells you all there is to know about a quantum physical system and it also predicts famous quantum weirdnesses such as superposition and quantum entanglement. In this, the first article of a three-part series, we introduce Schrödinger's equation and put it in its historical context.


Schrödinger's equation — in action

Now it's time to see the equation in action, using a very simple physical system as an example. We'll also look at another weird phenomenon called quantum tunneling.


Schrödinger's equation — what does it mean?

Here comes the crazy bit. How should we interpret the solution to Schrödinger's equation, the wave function? What does it tell us about the physical world? Or indeed many worlds?

You can also read other articles on quantum physics and quantum mechanics on Plus.


December 20, 2012

On the 23rd of June this year Alan Turing would have celebrated his 100th birthday. During his short and tragic life he revolutionised the scientific world and so 2012 was declared Turing Year. We're sad to see that an official pardon for his 1952 conviction for homosexuality, which was then illegal, still hasn't been granted. But that hasn't stopped us from celebrating his life and scientific achievements. See all our articles related to his work below.

If you're a secondary school student then you can join the Alan Turing Cryptography Competition run by the School of Mathematics at the University of Manchester. It involves a story of six chapters, following the exploits of two children, Mike and Ellie, who get involved in a cryptographic adventure involving a mysterious ancient artifact — the Egyptian Enigma! Every two weeks, starting on Monday 7th January, a new chapter of the story will be released on the website. Each of the six chapters contains a code to be solved. Teams of at most four students have to solve these codes as fast as they can and submit their answers on the competition website.

There are some great prizes for the three top-placed teams at the end of the competition. There will also be a prize for the first team to solve each chapter and a number of spot prizes awarded throughout the competition. See the competition website for details.

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.


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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.


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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.


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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?


December 19, 2012

Space is three-dimensional ... or is it? When we spoke to theoretical physicist David Berman in October this year we found out that in fact, we are all used to living in a curved, multidimensional universe. And a mathematical argument might just explain how those higher dimensions are hidden from view.



Kaluza, Klein and their story of a fifth dimension — David Berman explains the concept of dimension and how a mathematical idea suggests that we might well live in five of them.


The ten dimensions of string theory — String theory has one very unique consequence that no other theory of physics before has had: it predicts the number of dimensions of space-time. David Berman explains where these other dimensions might be hiding and how we might observe them.


How many dimensions are there? – the podcast — You can listen to an interview with David Berman as he tells us how Kaluza, Klein and their fifth dimension might help us understand the ten dimensions of string theory.



December 18, 2012

The maths of growth is one of the many topics explored on STEM NRICH.

Want to stop your brain from rusting this Christmas? Then visit our sister project NRICH which received a major make-over this year and now has a beautiful new website. NRICH is aimed at students and teachers of maths of all ages and backgrounds. It offers challenging and engaging activities that develop mathematical thinking and problem-solving skills and show rich mathematics in meaningful contexts.

To train your brain have a look at the NRICH advent calendar, which has an activity for every day up to Christmas, or the regular weekly challenge. If you're interested in real-life applications of maths, then visit STEM NRICH which explores the ways in which mathematics, science and technology are linked. And if you're stuck on a problem or have a general maths question you can ask the team at the Ask NRICH forum.

Because life is too short for long division!


December 17, 2012
Daffodils outside the Isaac Newton Institute in Cambridge.

Daffodils and mathematical art outside the Isaac Newton Institute in Cambridge.

Time, coffee, something to scribble on and others to chat to — these are the key ingredients necessary for producing first rate mathematics. And they are exactly what the Isaac Newton Institute in Cambridge provides. The Institute runs research programmes on selected themes in the mathematical sciences, with applications in a wide range of science and technology. It's a place where leading mathematicians from around the world can come together for weeks or months at a time to indulge in what they like doing best: thinking about maths and exchanging ideas without the distractions and duties that come with their normal working lives.

The Institute celebrates its 20th birthday this year, having opened in July 1992. We celebrated with a selection of articles exploring some of the research programmes that have been held there. The Institute asked us to produce these articles in 2010 and we were honoured by being afforded this rare glimpse behind its venerable doors. And as you'll see, what starts out as abstract mathematics scribbled on the back of a napkin can have a major impact in the real world.

Happy birthday, Newton Institute!


Building bridges from mathematics to the city — Many people's impression of mathematics is that it is an ancient edifice built on centuries of research. However, modern quantitative finance, an area of mathematics with such a great impact on all our lives, is just a few decades old. The Isaac Newton Institute quickly recognised its importance and has already run two seminal programmes, in 1995 and 2005, supporting research in the field of mathematical finance.


Renewable energy and telecommunications — When the mathematician AK Erlang first used probability theory to model telephone networks in the early twentieth century, he could hardly have imagined that the science he founded would one day help solve a most pressing global problem: how to wean ourselves off fossil fuels and switch to renewable energy sources.


Taming water waves — Few things in nature are as dramatic, and potentially dangerous, as ocean waves. The impact they have on our daily lives extends from shipping to the role they play in driving the global climate. From a theoretical viewpoint water waves pose rich challenges: solutions to the equations that describe fluid motion are elusive, and whether they even exist in the most general case is one of the hardest unanswered questions in mathematics.


Strings, particles and the early Universe — The Strong Fields, Integrability and Strings programme, which took place at the Isaac Newton Institute in 2007, explored an area that would have been close to Isaac Newton's heart: how to unify Einstein's theory of gravity, a continuation of Newton's own work on gravitation, with quantum field theory, which describes the atomic and sub-atomic world, but cannot account for the force of gravity.


From neurobiology to online gaming — Artificial neural networks grew out of researchers' attempts to mimick the human brain. In 1997 the Isaac Newton Institute hosted a landmark research programme in the area. Today, neural networks are able to learn how to perform complex tasks and are crucial in many areas of life, from medicine to the Xbox.


The shape of things to come — Progress in pure mathematics has its own tempo. Major questions may remain open for decades, even centuries, and once an answer has been found, it can take a collaborative effort of many mathematicians in the field to check that it is correct. The New Contexts for Stable Homotopy Theory programme, held at the Institute in 2002, is a prime example of how its research programmes can benefit researchers and its lead to landmark results.


Back to the 2012 Plus Advent Calendar

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