Science has developed sophisticated models of the atmosphere and instruments can help make detailed weather forecasts but to truly understand global climate change, scientists need more than just a one-day forecast or a seven-day guess. They need a deeper understanding of the complex and interrelated forces that shape climate.

They need applied mathematics, says Brad Marston, professor of physics at Brown University. He is working on sets of equations that he says can be used to more accurately explain climate patterns.

“Climate is a statement about the statistics of weather, not the day-to-day or minute-by-minute fluctuations,” Marston said. “That’s really the driving concept. We know we can’t predict the weather more than a couple of weeks out.

A problem which has defeated mathematicians for almost 140 years has been solved by a researcher at Imperial College London.

Professor Darren Crowdy, Chair in Applied Mathematics, has made the breakthrough in an area of mathematics known as conformal mapping, a key theoretical tool used by mathematicians, engineers and scientists to translate information from a complicated shape to a simpler circular shape so that it is easier to analyze.

This theoretical tool has a long history and has uses in a large number of fields including modelling airflow patterns over intricate wing shapes in aeronautics.

A new way of looking at cities has emerged during the last 20 years that could revolutionise planning and ultimately benefit city dwellers.

‘The Size, Scale and Shape of Cities’ in Science advocates an integrated approach to the theory of how cities evolve by linking urban economics and transportation behaviour with developments in network science, allometric growth and fractal geometry.

Professor Batty argues that planning’s reliance on the imposition of idealised geometric plans upon cities is rooted in the nineteenth century attitude which viewed cities as chaotic, sprawling and dirty.

A straight line may be the shortest distance between two points, but it isn’t necessarily the fastest or easiest path to follow.

That’s particularly true when terrain is not level, and now researchers have developed a mathematical model showing that a zigzag course provides the most efficient way for humans to go up or down steep slopes.

An international team of cosmologists, leaded by a researcher from Paris Observatory, has improved the theoretical pertinence of the Poincaré Dodecahedral Space (PDS) topology to explain some observations of the Cosmic Microwave Background (CMB). In parallel, another international team has analyzed with new techniques the last data obtained by the WMAP satellite and found a topological signal characteristic of the PDS geometry.

The last fifteen years have shown considerable growth in attempts to determine the global shape of the universe, i.e. not only the curvature of space but also its topology. The « concordance » cosmological model which now prevails describes the universe as a « flat » (zero-curvature) infinite space in eternal, accelerated expansion.

Forty years ago, mathematician Mark Kac asked the theoretical question, "Can one hear the shape of a drum?"

If drums of different shapes always produce their own unique sound spectrum, then it should be possible to identify the shape of a specific drum merely by studying its spectrum, thus "hearing" the drum's shape (a procedure analogous to spectroscopy, the way scientists detect the composition of a faraway star by studying its light spectrum).

But what if two drums of different shapes could emit exactly the same sound?

Sports pundits across the country have been comparing the so-far unbeaten 2007 New England Patriots to the perfect 1972 Dolphins all year. A New York cardiologist has used the scientific statistics used in large-scale medical trials to determine which of the two teams is superior.

Using a format and approach typically reserved for the cardiovascular therapy studies he writes and reviews, Dr.

Three-dimensional snowflakes can now be grown in a computer using a program developed by mathematicians at UC Davis and the University of Wisconsin-Madison.

No two snowflakes are truly alike, but they can be very similar to each other, said Janko Gravner, a mathematics professor at UC Davis. Why they are not more different from each other is a mystery, Gravner said.

Who needs a computer? Two theoretical physicists at Rensselaer Polytechnic Institute grabbed a piece of paper and described the motion of interstellar shock waves — violent events associated with the birth of stars and planets.

The mathematical solution developed by Wayne Roberge, lead author and professor of physics, applied physics, and astronomy at Rensselaer and his colleague, adjunct professor Glenn Ciolek, reveals the force and movement of shock waves in plasma, the neutral and charged matter that makes up the dilute “air” of space. Unlike many previous studies of its kind, the researchers focused specifically on shock waves in plasma, which move matter in very different ways than the uncharged air on Earth.

For centuries, human beings have been entranced by the captivating glimmer of the diamond. What accounts for the stunning beauty of this most precious gem?

As mathematician Toshikazu Sunada explains in an article in the Notices of the American Mathematical Society, some secrets of the diamond's beauty can be uncovered by a mathematical analysis of its microscopic crystal structure. It turns out that this structure has some very special, and especially symmetric, properties. In fact, as Sunada discovered, out of an infinite universe of mathematical crystals, only one other shares these properties with the diamond, a crystal that he calls the "K_4 crystal".