Author: the Plus team

When we arrived at the The New Diorama Theatre in London we didn't know what to expect. The universal machine is a musical about the life of mathematician and WWII code breaker Alan Turing. I have only seen one musical in my whole life, Cats, and it made me feel ill, so I really could not fathom how this was going to work. But as it turned out, we loved it.

Superposition, an audio-visual performance written by Ryoji Ikeda, is not for the faint hearted. We certainly wouldn't ever be tempted to listen to the sound track on its own. But despite its challenging nature, it is a wonderful experience which evoked a sense of beauty from chaos, mathematics, and physics, carried across by visual art and music.

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 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.

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.

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.

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.

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.
Will we ever be able to make computers that think and feel? If not, why not? And what has all this got to do with tiles? Plus talks to Sir Roger Penrose about all this and more.
Astronomer Royal Sir Martin Rees gives Plus a whistlestop tour of some of the more extraordinary features of our cosmos, and explains how lucky we are that the universe is the way it is.