In 2006, researchers closed a major chapter in mathematics, reaching a consensus that the elusive Poincaré Conjecture, which deals with abstract shapes in three-dimensional space, had finally been solved. Science and its publisher AAAS, the nonprofit society, now salute this development as the Breakthrough of the Year and also give props to nine other of the year's most significant scientific accomplishments.
Science's Top Ten list appears in the journal's 22 December 2006 issue.
The Poincaré Conjecture is part of a branch of mathematics called topology, informally known as "rubber sheet geometry" because it involves surfaces that can undergo arbitrary amounts of stretching. The conjecture, proposed in 1904 by Henri Poincaré, describes a test for showing that a space is equivalent to a "hypersphere," the three-dimensional surface of a four-dimensional ball.
A century later, researchers were still trying to prove the conjecture. In 2000, the Clay Mathematics Institute named the Poincaré Conjecture as one of its million-dollar "Millennium Prize" problems.
In 2002, Russian mathematician Grigori Perelman, who had been working mostly incommunicado for seven years, posted on the Internet the first of three papers that outlined a proof of Poincaré's conjecture as part of an even more ambitious result.
The work set experts abuzz. Though there were still many gaps to be filled in, it looked as if Perelman had scored a historic coup. But, after a visit to the United States in 2003, the reclusive mathematician returned to Russia and stopped replying to phone calls and emails. Other mathematicians were left on their own to determine whether Perelman had truly solved the Poincaré Conjecture.
By 2006, the others finally caught up. Three separate teams wrote papers that filled in key missing details of Perelman's proof, and there was little doubt among his colleagues that he had solved the famous problem. This summer, the International mathematics Union decided to award Perelman the Fields Medal, the "Nobel prize of mathematics," though Perelman declined the award.
Unfortunately, the year has ended on a note of discord, with claims of plagiarism by some of the researchers who worked on the follow-up papers to Perelman's proof and other mathematicians crying foul over how they were quoted in a prominent New Yorker article. Still, other researchers are ready to celebrate this landmark achievement in their field.
The other achievements on the Science's Top Ten list are as follows, in no particular order.
Pulling DNA out of Fossils: Using new techniques for decoding and analyzing DNA, researchers captured genetic information from Neanderthal and mammoth fossils.
Shrinking Ice Sheets: Researchers documented a disturbing trend this year. The Antarctic and Greenland ice sheets are losing ice, at an ever faster rate, to the oceans.
Fishy First Steps: The discovery of a fossil fish with sturdy, jointed fins made a big splash in 2006. The fish is the closest known kin to limbed vertebrates and provides a window into how life left the oceans and ventured onto terra firma.
The Science of Invisibility: Though it looks nothing like Harry Potter's magical cape, the invisibility "cloak" that scientists developed this year is the first rudimentary device for shielding objects from view. The device guides incoming microwaves in such a way that they produce neither a reflection nor a shadow.
Hope for Macular Degeneration Patients: Researchers who study the form of vision loss known as age-related macular degeneration showed that the drug ranibizumab improves vision in some patient and identifying several genes that influence a person's susceptibility to the disease.
How Biodiversity Happens: From beach mice, to fruit flies, to butterflies, a variety of animals helped scientists uncover genetic changes that lead to the evolution of a new species.
New Frontiers in Microscopy: This year, biologists used new microscopy techniques that enabled them to see details smaller than about 200 nanometers, giving them a clearer view of the fine structure of cells and proteins.
Making Memories: Several discoveries in 2006 brought neuroscientists closer to understanding how the brain records new memories. The so-called "long-term potentiation" process that strengthens connections between neurons now seems even more likely to be the basis for remembering.
New Class of Small RNAs: Scientists discovered a new class of small RNA molecules that shut down gene expression, called "Piwi-interacting RNAs."
Breakdown of the Year - Scientific Fraud: The extent of the fraud committed by stem cell researcher Woo Suk Hwang and his colleagues, who published two key papers in Science, came to light in 2006, as did several other incidents.
Areas to Watch: This year, Science's predictions for hot fields and topics in the upcoming year include whole-genome association studies, optical lattices, the search for Earthlike planets around other stars, and comparisons of primate genomes.
The American Association for the Advancement of Science (AAAS) is the world's largest general scientific society, and publisher of the journal Science (www.sciencemag.org). AAAS was founded in 1848, and serves some 262 affiliated societies and academies of science, serving 10 million individuals. Science has the largest paid circulation of any peer-reviewed general science journal in the world, with an estimated total readership of one million. The nonprofit AAAS (www.aaas.org) is open to all and fulfills its mission to "advance science and serve society" through initiatives in science policy; international programs; science education; and more. For the latest research news, log onto EurekAlert!, www.eurekalert.org, the premier science-news Web site, a service of AAAS.