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Oxford Mathematician Heather Harrington has been awarded a Royal Society University Research Fellowship. The fellowships recognise outstanding scientists in the UK who are in the early stages of their research career and have the potential to become leaders in their field. Heather's work covers a range of topics in applied mathematics, including algebraic systems biology, inverse problems, computational biology, and information processing in biological and chemical systems.

The Fourier transform is that rarest of things: a mathematical method from over 200 years ago which not only remains an active area of research in its own right, but is also an invaluable tool in nearly every branch of mathematics. Though originally developed by Fourier in 1807 to help solve certain partial differential equations, the transform is a living example of a remarkable feature of mathematics, that a tool created in one sub-discipline can break through these artificial classifications and become vital in another. Find out more about a method that has attracted the attention of mathematicians from Hardy and Littlewood to John Nash.

The Fourier Trasform is the latest in our Oxford Mathematics Alphabet, a sequence of 26 letters explaining key concepts and our latest research. 

Professor Nigel Hitchin FRS, Savilian Professor of Geometry in the Mathematical Institute, University of Oxford has won the prestigious Shaw Prize in Mathematical Sciences for, in the words of the Prize Foundation "his far-reaching contributions to geometry, representation theory and theoretical physics. The fundamental and elegant concepts and techniques that he has introduced have had wide impact and are of lasting importance."

Professor Frances Kirwan FRS, a colleague in Oxford, paid tribute: "Nigel Hitchin has made fundamental contributions to the fields of differential and algebraic geometry and richly deserves the award of the Shaw Prize. His work has influenced a wide range of areas in geometry and mathematical physics, including symplectic and hyperkähler geometry, the theory of instanton and monopole equations, twistor theory, integrable systems, Higgs bundles, Einstein metrics and mirror symmetry."

Professor Martin Bridson FRS, Head of the Mathematical Institute in Oxford, said: "'it is a real joy to see Nigel Hitchin's profound and influential work recognised by the award of the 2016 Shaw Prize. His inspiring intellectual leadership in geometry has been matched throughout his career by many services to the mathematical community in the UK and across the world, for which we are all deeply grateful. Oxford has been extremely fortunate to have Nigel with us for so much of his career, and we are very proud of him."

Nigel said on news of the award: "I am delighted and honoured to be awarded this prize. Since most of my working life has been spent in Oxford, it is also a recognition of the support I have received here. I was pleased to note that my “twin” in New College, the Savilian Professor of Astronomy, won the Shaw prize a few years ago.”

The Shaw Prize is an annual award first presented by the Shaw Prize Foundation in 2004. Established in 2002 in Hong Kong it honours living individuals who are currently active in their respective fields and who have recently achieved distinguished and significant advances, who have made outstanding contributions in academic and scientific research or applications, or who in other domains have achieved excellence. The 2016 prize is worth US$1.2m to each winner.

Congratulations to Oxford Mathematics' Zubin Siganporia who has won the award for Outstanding Tutor for the Mathematical, Physical and Life Sciences Division in the 2016 Oxford University Student Union Student Led Teaching Awards.

The work of Oxford University Professor Sir Andrew Wiles was celebrated as having 'heralded a new era in number theory' as he received the top international prize for mathematics. 

Sir Andrew received the 2016 Abel Prize from Crown Prince Hakon of Norway at the prize ceremony in Oslo on 24 May. He was awarded the prize 'for his stunning proof of Fermat's Last Theorem by way of the modularity conjecture for semistable elliptic curves, opening a new era in number theory'.

The ceremony at the University Aula was attended by more than 400 guests, from members of the international mathematics community to local residents. 

Professor Ole Sejersted, President of the Norwegian Academy of Science and Letters, which presents the Abel Prize, said: 'Mathematicians have tried to prove Fermat's Last Theorem for 350 years, without success, indicating that mathematicians regard this as one of the great mathematical puzzles.

'The Abel Committee says that Sir Andrew's work has heralded a new era in number theory. To me, this indicates that the work on the theorem required the development of an entirely new mathematical foundation, the significance of which goes far beyond the actual proving of the theorem.'

Accepting the prize, Sir Andrew Wiles said: 'As a ten-year-old eager to explore mathematics I rummaged in the popular mathematics section of my local public library and found a copy of a book called The Last Problem by E.T. Bell. I did not even have to open the book. On the bright yellow front cover it told the story of the 1907 Wolfskehl prize offered for the solution of a famous mathematical problem. The problem itself was on the back cover. I was hooked.

'It was a wonderful find for me. Apparently inside mathematics there was hidden treasure! A little over 300 years previously a Frenchman by the name of Pierre de Fermat had solved a beautiful sounding problem, but he had buried the proof and now there was a prize for finding it!

'Fermat did not leave any clues because he did not have a solution, but nature itself leaves clues. I just had to find them. There was never going to be a one-line proof. Nor do proofs come just because one has been born with mathematical perfect pitch. There is no such thing. One has to spend years mastering the problem so that it becomes second nature. Then, and only then, after years of preparation is one's intuition so strong that the answer can come in a flash.

'These eureka moments are what a mathematician lives for; the bursts of creativity that are all the more precious for the years of hard work that go into them. The moment in the morning of September 1994 when I resolved my last problem is a moment I will never forget.'

Fermat's Last Theorem had been widely regarded by many mathematicians as seemingly intractable. First formulated by the French mathematician Pierre de Fermat in 1637, it states:

There are no whole number solutions to the equation xⁿ + yⁿ = zⁿ  when n is greater than 2, unless xyz=0.

Fermat himself claimed to have found a proof for the theorem but said that the margin of the text he was making notes on was not wide enough to contain it. After seven years of intense study in private at Princeton University, Sir Andrew announced he had found a proof in 1993, combining three complex mathematical fields – modular forms, elliptic curves and Galois representations.

Sir Andrew not only solved the long-standing puzzle of the theorem, but in doing so he created entirely new directions in mathematics, which have proved invaluable to other scientists in the years since his discovery. The Norwegian Academy of Science and Letters said in its citation: 'Few results have as rich a mathematical history and as dramatic a proof as Fermat's Last Theorem.'

The Abel Prize is named after the Norwegian mathematician Niels Henrik Abel (1802-29) and was established in 2001 to recognize pioneering scientific achievements in mathematics. Abel himself did some of the early work on the properties of elliptical functions. Previous winners of the Prize include Britain's Sir Michael Atiyah and the late US mathematician John Nash.

Accompanying the prize-giving ceremony is a series of 'Abel week' activities aimed particularly at young people, including the awarding of the Holcombe Memorial Prize for an outstanding teacher of mathematics and the UngeAbel contest for teams of secondary pupils. This year's winning teacher and young winners were in the audience for the Abel Prize ceremony. 

The rolling of dice in a casino, Heisenberg's uncertainty, the meaning of consciousness. All are explored as Marcus takes us on a personal journey into the realms of the scientific unknown. Are we forever incapable of understanding all of the world around us or is it perhaps just a question of language, not having the right words to describe what we see?

What is a network and how can you use mathematics to unravel the relationships between a variety of different things? How can this understanding then be applied to a range of different settings?

In this Oxford Sparks podcast Oxford Mathematician Mason Porter studies how things are connected using mathematics. He builds up models of these connections to represent them as networks. But what are the basic components of a network? In the podcast Mason describes how from social networks to transport systems to locating a lost umbrella, the mathematics of networks can be used to address a range of apparently unconnected problems and how organisations around the world are using them to penetrate their ever-growing mass of data.

Congratulations to Oxford Mathematicians Martin Bridson, Marcus du Sautoy and Artur Ekert who have been elected Fellows of the Royal Society. Martin is Whitehead Professor of Pure Mathematics, a Fellow of Magdalen College and Head of the Mathematical Institute in Oxford. He has been elected for his many distinguished contributions to group theory and topology. Marcus is Charles Simonyi Professor for the Public Understanding of Science and a Fellow of New College and has been elected for his outstanding achievements in promoting the understanding of science and mathematics to a global audience and for eminent research that has completely transformed the study of zeta functions of groups. Artur is Professor of Quantum Physics at the Mathematical Institute and a Fellow of Merton College.  Artur has been elected FRS for his work on quantum physics, quantum computation and cryptography.

Appearing everywhere from state-of-the-art cryptosystems to the proof of Fermat's Last Theorem, elliptic curves play an important role in modern society and are the subject of much research in number theory today. Jennifer Balakrishnan, a researcher working in number theory, explains more in the latest in our Oxford Mathematics Alphabet.

Oxford Mathematician Rob Style has been awarded the 2016 Adhesion Society Young Scientist Award, sponsored by the Adhesion and Sealant Council, for his fundamental contributions to our understanding of the coupling of surfaces tension to elastic deformation.  Rob researches the mechanics of very soft solids like gels and rubber, in particular investigating why they don’t obey the same rules as hard materials that are more traditionally used by engineers.