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Breakthrough of the Year!

PoincarecoverFrom Devlin's Angle: "The image says it all. When SCIENCE magazine declares that the proof of a theorem in mathematics is the breakthrough of the year in all of science, you know that something special has occurred.

We've had a double wait for this breakthrough. Henri Poincare first formulated his now famous conjecture just over 100 years ago, in 1904, and despite several heroic attempts to prove it, the puzzle remained unsolved until late 2002 and through into 2003, when the somewhat reclusive Russian mathematician Grigori Perelman posted a series of three papers on the Internet that claimed to outline a proof of the Thurston Geometrization Conjecture, which was known to yield the Poincare Conjecture as a consequence.

That was the first wait. But another was in store. Such was the intricacy of Perelman's argument, compounded by the highly compressed manner in which he presented it, that is took over three years of effort by various groups around the world before the consensus agreement came in: he had indeed proved the Poincare Conjecture. (The experts are still unsure about Perelman's proof of the Geometrization Conjecture.)"  More...

Messiness Rules: In high dimensions, disorder packs tightest

Prime Should you find yourself with a 60-dimensional suitcase, the best way to pack it may be the easiest: Throw in everything in a jumble. That's the way to fit the most high-dimensional spheres into a fixed space, new research suggests.

The finding may be useful even to people without extra-dimensional luggage. It may improve the design of mathematical procedures called error-correcting codes used in computers to interpret noisy data. More...

Math genius declines top prize

Grigory Perelman, the Russian who seems to have solved one of the hardest problems in mathematics, has declined one of the top prizes in maths. The Fields Medals are among the most important prizes for mathematics, and Perelman was to have picked up the award at a ceremony in Madrid. However, the organisers told the BBC that Perelman had declined the prize.  More...

The Goat Problem

Imagine that the set of Monty Hall's game show Let's Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does.

The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn't hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors.

After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the car if she stays with her first choice? What if she decides to switch?  More...

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