HotmailCentury-old brain-twister now solved
Conjecture named for Henri Poincare, who proposed it in 1904
 |
 Kid chef cooks holiday treats Nov. 27: A 13-year-old cook teaches the TODAY hosts how to whip up a turkey risotto that is perfect for the holidays. |
 | Special feature |
 | 10 tips to be a better coupon sleuth Want to save now? 10 Tips columnist Laura T. Coffey offers advice to help you upgrade your electronic and paper coupon skills. |
| FirstPerson |
 | Gallery: Your latest splurges Despite tough economic times, readers share photos of recent big-ticket purchases. |
|
 Family ditches home for RV Nov. 27: With the high rate of foreclosures, many families are going to extremes to survive. NBC's Michelle Franzen has the story of one family who is spending their days on the road. |
MADRID, Spain - The Poincare conjecture involves topology, a branch of math that studies shapes. It essentially says that in three dimensions you cannot transform a doughnut shape into a sphere without ripping it, although any shape without a hole can be stretched or shrunk into a sphere.
There is a catch: the space has to be finite. Imagine an ant crawling on an apple in a straight line. It can only walk so far before it's back where it started.
That surface is two-dimensional. In three dimensions, shapes are harder to determine because people cannot directly 'see' them and there are many more possible types of holes.
The conjecture is named for French mathematician and physicist Henri Poincare, who proposed it in 1904.
An analogous conjecture was proved for spaces of more than three dimensions over 20 years ago. But the specific 3-D case flummoxed mathematicians for years.
In 1982, Columbia University's Richard Hamilton developed a technique called Ricci flow that mathematically ironed out wrinkles in 3-D surfaces and provided a blueprint for cracking the Poincare conundrum.
A problem was posed by puzzling, dense spots called singularities, which exhibited sudden, uncontrolled change.
Grigory Perelman's breakthrough was to understand how to analyze these singularities, essentially neutralizing them for a while and allowing the Ricci flow to proceed smoothly and show what a given space is really like, topologically speaking.
- Discuss Story On Newsvine
-
Rate Story:
View popularLowHigh - Instant Message
MORE FROM TECHNOLOGY & MONEY |
 Technology & Money Section Front |
| Add Technology & Money headlines to your news reader: |
Sponsored links
Resource guide