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Scientists try to understand the world around us and modern sciencewould have got nowhere without careful, and often surprising,experimental observations. But all scientists are theorists as well,as they seek to understand their experiments, discovering the simplestpossible ``theory'' that explains all the known facts.Mathematics is the language of theory, certainly in the physicalsciences, and increasingly in biology. It is not just a descriptivelanguage --- it is a tool that allows the theories to be manipulated,improved, or even disproved. Equations are solved --- known quantitiesare used to discover the unknowns.With the advent of modern powerful computers theorists have gained anew tool. Not only can computers now do many mathematical tasks, suchas solving very complex equations, they can also manipulate theoriesthat would be very difficult or impossible for a traditionalmathematician to handle using a pencil and lots of paper.I am a theorist who is interested in understanding ``condensedmatter'' --- or most of the ``stuff'' in the universe that we, ashumans, are likely to be able to touch. This includes semiconductorcrystals and liquid crystals, metals and superconductors, mineralsthat might be found deep in the Earth or other planets, and evenmolecules that keep us alive.The fundamental theory that my research relies on was discovered inthe early 20th century --- Quantum Mechanics, a mechanics of the verysmall particles that most matter is made of: electrons, protons andneutrons. The equations that we still believe explain most of thephenomena that we can see around us were written down over fifty yearsago, but were impossible to solve!Using theoretical advances and enthusiastically making use ofcomputers and supercomputers, I actually solve these equations for avast range of realistic situations, from discovering what makesdiamond so strong, to understanding proteins. I have helped develop astate-of-the-art computer program: CASTEP, which can be used tocalculate the properties of very large collections of atoms.A feature of my research is that having concentrated on solving themost basic, and widely applicable quantum mechanical equations I amable to answer relevant questions in a wide range of scientificdisciplines. Much of my current (and proposed future) work aims at helpingscientist ``see'' the atomic structure of matter. When we seesomething with our naked eyes, light scatters from the object, isfocused by our eye's lens and falls onto the retina. This sends aflurry of signals to our brain, which somehow does the necessarycalculations to allow us to figure out what we are seeing. When peopletry to see atoms the situation is more complicated. Shorter wavelengthlight (or particles) have to be used, and quantum mechanics becomesimportant. The scattered light (eg. x-rays) is diffracted and we see apattern of spots which are not atoms. Our brains cannot directlyinterpret these patterns, but with the help of a quantitative theoryof diffraction from crystals we are able to sort out where the atomsare. The technique of Nuclear Magnetic Resonance (NMR) is not based onscattering and diffraction. A magnetic field applied to a sample setsup electric currents, which in turn produce magnetic fields. Thesecurrents depend of where the electrons are in the sample and what theyare doing, and can be measured by special atomic nuclei which behavelike tiny magnets. However, the relationship between where the atomsare and the measured magnetic field is not straightforward. In thecourse of my research I am developing a quantitative theory ofmagnetic resonance which has the potential to enable NMR to be asdirect a way to see atoms as x-ray crystallography --- without theneed to grow large perfect crystals.
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