Breakthrough of the Year

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Science  22 Dec 2006:
Vol. 314, Issue 5807, pp. 1841
DOI: 10.1126/science.1138510

Last year, evolution was the breakthrough of the year; We found it full of new developments in understanding how new species originate. But we did get a complaint or two that perhaps we were just paying extra attention to the lively political/religious debate that was taking place over the issue, particularly in the United States.

Perish the thought! Our readers can relax this year: Religion and politics are off the table, and n-dimensional geometry is on instead. This year's Breakthrough salutes the work of a lone, publicity-shy Russian mathematician named Grigori Perelman, who was at the Steklov Institute of Mathematics of the Russian Academy of Sciences until 2005. The work is very technical but has received unusual public attention because Perelman appears to have proven the Poincaré Conjecture, a problem in topology whose solution will earn a $1 million prize from the Clay Mathematics Institute. That's only if Perelman survives what's left of a 2-year gauntlet of critical attack required by the Clay rules, but most mathematicians think he will.

CREDIT: CAMERON SLAYDEN/WWW.COSMOCYTE.COM

The analysis supplied by Dana Mackenzie on p. 1848 struck me as a fascinating exploration, full of metaphors suggesting a multidisciplinary dimension in Perelman's analysis. He first got interested in Ricci flow, a process by which topological regions of high curvature flow into regions of lower curvature. He also identified a quantity, which he called “entropy,” that increased during the flow, providing a gradient. Tight spots in spatial connections block the application of these rules to dimensions higher than two, so Perelman dealt with these through “surgical intervention.” This story is rich with borrowings: from fluid mechanics, thermodynamics, and even surgery! It's hard to deal with a three-dimensional object in four-dimensional space. Perelman's solution is a stunning triumph of intellect. Alas, it has led to bitter controversy, involving others but not Perelman.

Of course, in any Breakthrough year we are obliged to have a Breakdown. This time around, we had to blow the whistle on ourselves. In recognizing this as a year in which scientific fraud took center stage, it was clear that we had to lead with the story involving the retraction of two of our own papers, an event that drew worldwide press attention and required us to ask for an outside evaluation of how we had handled the papers. That brought us some tough news about how competitive the scientific enterprise has become, and the consequential incentive to push (or shred) the ethical envelope.

On the positive side, it was a rich year for important experimental studies. My favorites include some new explanations for how species originate, one of the daunting post-Darwinian puzzles. Among other examples, there is a clear case for speciation through hybridization, an exception to the more general rule that hybrids either don't make it or are reproductively incompetent. Because I like coastlines, when I see new evidence about sea-level rise, I pay attention. This year we got new measures of rates of glacial melting at both ends of the globe: in Greenland, where rates are in hundreds of gigatons a year, and in Antarctica, where drainage by ice streams is accelerating. I also follow the Neanderthal story, because it's interesting to ponder how different human species—now thought from archaeological evidence to have overlapped for perhaps 10,000 years—might have interacted. New sequencing of the Neanderthal genome indicates that the point of divergence is nearly half a million years old and opens up a wealth of comparisons with the human genome sequence. The question everyone asks—“Did they have sex?”—is still open, though barely.

All in all, it's not been a bad year. The predictions we made in 2005 of “Areas to Watch” turned out pretty well. We said RNA interference would be an active sector—good call. Cosmic-ray capture didn't work out, but there was the predicted level of activity on the “small worlds” of microbial communities. We predicted lots of activity on high-temperature superconductivity, and there were more applications, although less new theory. The worst miss was the prediction that the ivory-billed woodpecker would be re-found. Come on, birders, give us some help out there; a good photo, please, not the skin.

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