One of the most exciting places in the mathematical world is the Isaac Newton Institute for Mathematical Sciences (INI), an international research centre and our neighbour here on the University of Cambridge's maths campus.

The INI attracts leading mathematical scientists from all over the world, and is open to all. We are proud to be collaborating with the INI to bring the cutting edge mathematics that is being done there to the general public. The following content is part of this collaboration.

Shining a light on gold

People have been using gold particles dispersed in water — gold hydrosols — for medical purposes for over 1000 years. Recently, hydrosols containing gold nanoparticles have become particularly popular because they have exciting potential in cancer therapies, pregnancy tests and blood sugar monitoring.

Saving lives: the mathematics of tomographyNot so long ago, if you had a medical complaint, doctors had to open you up to see what it was. These days they have a range of sophisticated imaging techniques at their disposal, saving you the risk and pain of an operation. **Chris Budd and Cathryn Mitchell** look at the maths that isn't only responsible for these medical techniques, but also for much of the digital revolution.

Fermat's last theorem and Andrew Wiles**Neil Pieprzak** tells the fascinating story of Andrew Wiles who, with intense devotion and in secret, proved a deceptively simple-looking conjecture that had defeated mathematicians for almost 400 years.

String theory: From Newton to Einstein and beyondOver the last few years the words *string theory* have nudged their way into public consciousness. It's a theory of everything in which everything's made of strings — or something like that. But why strings? What do they do? Where did the idea come from and why do we need such a theory? **David Berman** has an equation-free introduction for beginners.

An enormous theorem: the classification of finite simple groups**Winner of the general public category**. Enormous is the right word: this theorem's proof spans over 10,000 pages in 500 journal articles and no-one today understands all its details. So what does the theorem say? **Richard Elwes** has a short and sweet introduction.

The power of groupsGroups are some of the most fundamental objects in maths. Take a system of interacting objects and strip it to the bone to see what makes it tick, and very often you're faced with a group. **Colva Roney-Dougal** takes us into their abstract world and puzzles over a game of Solitaire.

How maths can make you rich and famous: Part IIOne million dollars is waiting to be won by anyone who can solve one of the grand mathematical challenges of the 21st century. In the second of two articles, Chris Budd looks at the well-posedness of the **Navier-Stokes equations**.

Model behaviourTo study a system, mathematicians begin by identifying its most crucial elements, and try to describe them in simple mathematical terms. As Phil Wilson tells us, this simplification is the essence of **mathematical modelling**.

Beyond reasonable doubtIn 1999 solicitor Sally Clark was found guilty of murdering her two baby sons. Highly flawed statistical arguments may have been crucial in securing her conviction. As her second appeal approaches, *Plus* looks at the case and finds out how courts deal with statistics.