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.
"Eights" by George Hart, featured in this issue of Eureka
Looking for some great Christmas reading? Good news! The annual magazine Eureka has just published its first ever digital issue and to celebrate they have reprinted some of the best articles from past issues featuring authors such as Stephen Hawking, Roger Penrose, John Conway, Stephen Wolfram, Paul Dirac and many others.
This summer, while at a conference in Poland, we were lucky enough to watch Sara Santos and her maths buskers perform on the streets of Krakow, handcuffing innocent Krakowians (a punishment for dividing by zero), constructing emergency pentagons, and reading minds. Maths busking is about showing the public the surprising and fascinating side of mathematics through the medium of street performance. Sara Santos is co-founder of Maths Busking, which is both a network of performers and a business delivering training, school and entertainment services. The training sessions are particularly popular amongst teachers, science communicators, and researchers in mathematics and sciences.
If you're interested in maths busking performances or becoming a maths busker yourself, visit the Maths Busking website or listen to our interviews with Sara and other maths buskers in our podcast.
Here at Plus we were completely taken by surprise with just how exciting London 2012 Olympic and Paralympic games were! Whether it was marvelling at the architecture, developing new strategies or equipment or keeping score, there was an application of maths providing those precious incremental advances that made all the difference. Here are our favourite moments from our Olympic and Paralympic calendars.
Gearing up for gold — Inspired by Sara Storey's phenomenal gold medal we calculate whether we, and our bikes, have what it takes to triumph in our newfound quest for speed!
Racing for new records — Wheelchair racing is one of the most exciting disciplines in the Paralympics. And it's not just a wheel-based equivalent of Olympic racing: John D. Barrow, mathematician, cosmologist and prolific popular science writer, has spotted an important difference.
No limits for Usain — Usain Bolt is determined to beat his record and run the 100m in 9.4 seconds. But what does mathematics have to say about this quest? Is there an ultimate limit which no runner can possibly surpass? If there is one, where would such a limit lie? For instance, is there a sub 9 second record in the offing?
Horses for courses — It's a great day for individual dressage today with the Grand Prix freestyle test taking place in Greenwich Park. It's amazing how those horses can perform elegant and complicated movements without getting their legs in a muddle. Coming to think of it, it's amazing that they can even go through their innate gaits without getting their legs in a muddle, given that there's four of them and they are very long. And what about animals who've got even more legs?
Rowing has its moments — The men's lightweight fours and the women's eights are going to compete for medals today, but are they sitting in the right place? Usually you expect to find rowers positioned in a symmetrical fashion, alternately right-left, right-left as you go from one end of the boat to the other. However, the regularity of the rower's positions hides a significant asymmetry that affects the way the boat will move through the water.
You can find lots more excellent material on the maths behind sports in the MMP Sportal!
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. There's been a call for daily bloggers, inviting you to take part in a public conversation about Earth maths, whether you are an old hand at blogging or a newcomer to social media.
The MPE 2013 competition to design an exhibit about the mathematics of planet Earth is also underway, inviting you to design an interactive or physical exhibit, images or videos that explain how mathematics helps to understand our world and solve its problems. 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. But hurry, you only have another week to submit your entry: the deadline is 20th December 2012.
It's a prize for achievements in physics, but as we all know, physics is written in the language of maths. And this wasn't the only prize celebrating maths this year...
The Abel Prize 2012 — When did you first realise that you like numbers? Was it when you were first learning your times tables and saw all those number patterns and rhythms unfold in front of your eyes? If yes, then you'll be happy to hear that this year's Abel Prize, one of the highest honours in mathematics, has been awarded to a man whose most famous result answers a simple question related to those humble number sequences.
Prizes from the European Congress of Mathematics — At the beginning of July Plus went to the European Congress of Mathematics in Krakow! Around 1,000 mathematicians came together there for a week-long programme of talks and seminars. In this podcast we talked to Tom Sanders and Alessio Figalli, who were awarded prizes for their excellent contributions to maths, Arieh Iserles, a distinguished mathematician from the University of Cambridge, and a group of PhD students visiting their first big conference.
A Nobel Prize for quantum optics — The 2012 Nobel Prize for Physics has been awarded to Serge Haroche and David J. Wineland for ground-breaking work in quantum optics. By probing the world at the smallest scales they've shed light on some of the biggest mysteries of physics and paved the way for quantum computers and super accurate clocks.
How to make a marriage stable — How do you best allocate students to universities, doctors to hospitals, or kidneys to transplant patients? It's a tough problem that has earned this year's Memorial Prize in Economics.
String Theory, Duality and Art: how the Higgs boson and Turner Prize collide — On the face of it, an artist and a theoretical physicist might seem an unlikely pairing. But Turner Prize-winning sculptor Grenville Davey and string theorist David Berman's collaboration is producing beautiful, thought-provoking work inspired by the fundamental structure of the Universe. Julia Hawkins interviewed them to find out more about how the Higgs boson and T-duality are giving rise to art.