The work of a reclusive Russian mathematician who solved a 100-year-old mystery has been voted Breakthrough of the Year by Science, one of the world's leading scientific journals.
Grigori Perelman published three articles on the internet more than three years ago claiming to have solved Poincare's conjecture, a mathematical puzzle first identified in 1904 by the French mathematicican Henri Poincaré.
This year Dr Perelman won the ultimate accolade in mathematics - the Fields Medal - but refused to accept it, along with a separate prize of $1m (£530m) offered by the Clay Mathematics Institute in Massachussets, preferring to retreat to his mother's flat in St Petersburg.
His proposed solutions to the conjecture, published in 2002 and 2003, were validated by other mathematicians in the field of topology - the science of surfaces.
"While bringing new results to topology, Perelman's work brought new techniques to geometry," said Science. "It cemented the central role of geometric evolution equations, powerful machinery for transforming hard-to-work-with spaces into more-manageable ones."
Topology is sometimes known as "rubber-sheet geometry" because it deals with properties of surfaces that can undergo any amount of arbitary stretching or squeezing - but not tearing or, the opposite, sewing. Poincaré's conjecture has foxed the best mathematical minds for decades, and even a lay explanation is difficult to comprehend.
The simplest explanation involves imagining the surface of a football. Its surface remains essentially the same whether the ball is inflated or deflated - and in this respect the ball's surface is said to be two-dimensional.
A rubber band stretched over the ball can be squeezed into a single point anywhere on the surface without breaking or tearing the band, or the ball. This is not the case if the ball has a hole in it to make it into a torus, a doughnut-like shape.
This means that the football is the only two-dimensional shape with this property. Poincaré recognised there was a three-dimensional space for which it was also true and asked whether it was the only such three-dimensional space. Dr Perelman effectively demonstrated that this was indeed true.
Three separate teams of mathematicians took two years to work through Dr Perelman's proof and concluded he had solved the famous conjecture.
Dr Perelman has resigned from the Steklov Institute of Mathematics in St Petersburg and still lives in his mother's flat.
Breakthroughs of 2006
Two teams of scientists announced in 2006 that they had decoded the sequence of long stretches of DNA extracted from the bone of Neanderthal man. This close cousin diverged from our ancestral line about 450,000 years ago.
The world's two biggest ice sheets, on Greenland and Antarctica, are melting at an accelerating pace according to pioneering studies involving airborne laser measurements and space radar mapping.
A fossil dating back 375 million years was described as a creature that was half-fish, half-amphibian. It appears to be a "missing link" in the water-to-land transition of the vertebrates. Tiktaalik's fin-like front limbs had a wrist and elbow.
Physicists claimed to have invented a camouflage jacket that makes people disappear. It only works when viewed in microwaves, which veer round the jacket, producing a bizarre "see-through" effect.
A study published in October showed that a drug called ranibizumab improves the vision of about a third of patients with the more serious form of age-related macular degeneration and stabilises the condition of the rest. The drug received approval in the US this year.
Charles Darwin puzzled over speciation - how two species evolve from one. Now scientists have shown just one genetic mutation can do this. Beach mice in Florida and the cactus finch are two species where small changes can result in big physical differences between two related species.
Biologists gained insights into the internal workings of cells and proteins this year with microscopic techniques that side-stepped the limits of conventional optical instruments. The scientists overcame the barrier of the physical limit to light's wavelength.
Several 2006 studies claim memories form by a process that strengths the connections between individual nerve cells. The process - long-term potentiation - is the basis of how we remember past events years later.
Research supports the idea that genes are controlled by small molecules of RNA - a close cousin of DNA. A new class of RNA molecules which can interfere with genes were found in the testes of mammals - probably to maintain sperm development.Reuse content