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.
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.
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.
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.
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.
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.
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.
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.
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.
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.