A reclusive Russian won the math world's highest honor Tuesday for solving a problem that has stumped some of the discipline's greatest minds for a century — but he refused the award.
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Grigory Perelman, a 40-year-old native of St. Petersburg, won a Fields Medal — often described as math's equivalent of the Nobel prize — for a breakthrough in the study of shapes that experts say might help scientists figure out the shape of the universe.
John Ball, president of the International Mathematical Union, said that he had urged Perelman to accept the medal, but Perelman said he felt isolated from the mathematics community and "does not want to be seen as its figurehead." Ball offered no further details of the conversation.
Besides shunning the award for his work in topology, Perelman also seems uninterested, according to colleagues, in a separate $1 million prize he could win for proving the Poincare conjecture, a theorem about the nature of multidimensional space.
The award, given out every four years, was announced at the mathematical union's International Congress of Mathematicians. Three other mathematicians — Russian Andrei Okounkov, Frenchman Wendelin Werner and Australian Terence Tao — won Fields medals in other areas of mathematics.
They received their awards from King Juan Carlos to loud applause from delegates to the conference. But Perelman was not present.
"I regret that Dr. Perelman has declined to accept the medal," Ball said.
Perelman's work is still under review, but no one has found any serious flaw in it, the math union said in a statement.
The Fields medal was founded in 1936 and named after Canadian mathematician John Charles Fields. It come with a $13,400 stipend.
Perelman is eligible for far more money from a private foundation called The Clay Mathematics Institute in Cambridge, Mass.
In 2000, the institute announced bounties for seven historic, unsolved math problems, including the Poincare conjecture.
If his proof stands the test of time, Perelman will win all or part of the $1 million prize money. That prize should be announced in about two years.
The Poincare conjecture 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.
Proving the conjecture — an exercise in acrobatics with mindboggling imaginary doughnuts and balls — is anything but trivial. Colleagues say Perelman's work gives mathematical descriptions of what the universe might look like and promises exciting applications in physics and other fields.
"It is very important indeed because it really gives us an insight into geometry and in particular the geometry of the space we live in," said Oxford University math professor Marcus du Sautoy. "It does not say what the shape (of the universe) is. It just says, 'look, these are the things it could be.'"
Academics have been studying Perelman's proof since he left the first of three papers on it on a math Web site in Nov. 2002. Normal procedure would have been to seek publication in a peer-approved journal.
Three separate teams have presented papers or books explaining the details of Perelman's work, which draws heavily from a technique developed by another mathematician, Richard Hamilton of Columbia University. The Clay Mathematics Institute says the two men could conceivably share the Poincare money.
Ball said he asked Perelman if he would accept that money. Perelman said that if he won, he would talk to the Clay institute.
Perelman is believed to live with his mother in St. Petersburg. Repeated calls over many days to a telephone number listed as Perelman's went unanswered. Acquaintances refused to give out his address or the number they use to contact him, saying he did not want to talk to the media.
By DANIEL WOOLLS, Associated Press Writer
Wednesday, August 23, 2006
Saturday, August 12, 2006
Happy 25th Birthday to the PC
August 12, 1981. If you were ready to plunk down about $1,600, you could have owned a piece of history: The original IBM 5150 PC, generally considered to be the "first" PC.
At 25 years old, it's fun to look back on how far we've come. At 21 pounds (without drives), the 5150 wasn't much fatter than the PCs of today. Under the hood, things looked a bit different: 40KB of read-only memory and 16KB of RAM (upgradable to 256KB). You could configure the machine with one or two 160KB floppy drives, but a jack for a cassette player was included. Users certainly loved the "power-on automatic self-test of system components" and "built-in speaker for musical programming." And the keyboard (included) weighed six pounds. The 11.5-inch monochrome monitor, capable of displaying 25 lines of text, weighed in at 17 lbs. and supported both upper- and lowercase characters. Whoa.
Mock it if you must, but remember that the 5150 was unlike anything anyone had ever seen. The Apple II, released a few years earlier, came close, but it was more of a hacker toy and game-playing machine than something that would be at home in a business. The 5150 had built-in BASIC and Pascal support for writing programs, and it included a ton of business software: VisiCalc, Peachtree accounting software, and the EasyWriter word processor. And yes, Microsoft Adventure, a text-based adventure game, was available for diversions.
So that was 25 years ago. Looking ahead 25 years is almost impossible (and the further we get from the birth of the PC, the harder and harder it gets), but let's imagine. Magnetic storage will still be around, and your average hard drive will hold something in the vicinity of 30 terabytes (30,000GB) and cost $50 or less. CPU architecture will be vastly different. If we're still using silicon wafers, you could have a 32-core CPU with dedicated encryption and graphics components. In 25 years, graphics will have evolved to the point where Toy Story will seem quaint. You'll be able to compose a production like that in real time, and it'll look perfect on your wall-sized display. And dare we dream of something in true 3-D? Memo to Silicon Valley: Better get busy!
For another walk down memory lane (or rather, a walk down a lane filled with computers that predate the PC most of which you have probably never heard of), check out this page of personal computer milestones, dating back to 1950. And let's hear your memories of the early days of the personal computer. What was your first machine, and how did it change your life? The comments are open!
By Christopher Null
At 25 years old, it's fun to look back on how far we've come. At 21 pounds (without drives), the 5150 wasn't much fatter than the PCs of today. Under the hood, things looked a bit different: 40KB of read-only memory and 16KB of RAM (upgradable to 256KB). You could configure the machine with one or two 160KB floppy drives, but a jack for a cassette player was included. Users certainly loved the "power-on automatic self-test of system components" and "built-in speaker for musical programming." And the keyboard (included) weighed six pounds. The 11.5-inch monochrome monitor, capable of displaying 25 lines of text, weighed in at 17 lbs. and supported both upper- and lowercase characters. Whoa.
Mock it if you must, but remember that the 5150 was unlike anything anyone had ever seen. The Apple II, released a few years earlier, came close, but it was more of a hacker toy and game-playing machine than something that would be at home in a business. The 5150 had built-in BASIC and Pascal support for writing programs, and it included a ton of business software: VisiCalc, Peachtree accounting software, and the EasyWriter word processor. And yes, Microsoft Adventure, a text-based adventure game, was available for diversions.
So that was 25 years ago. Looking ahead 25 years is almost impossible (and the further we get from the birth of the PC, the harder and harder it gets), but let's imagine. Magnetic storage will still be around, and your average hard drive will hold something in the vicinity of 30 terabytes (30,000GB) and cost $50 or less. CPU architecture will be vastly different. If we're still using silicon wafers, you could have a 32-core CPU with dedicated encryption and graphics components. In 25 years, graphics will have evolved to the point where Toy Story will seem quaint. You'll be able to compose a production like that in real time, and it'll look perfect on your wall-sized display. And dare we dream of something in true 3-D? Memo to Silicon Valley: Better get busy!
For another walk down memory lane (or rather, a walk down a lane filled with computers that predate the PC most of which you have probably never heard of), check out this page of personal computer milestones, dating back to 1950. And let's hear your memories of the early days of the personal computer. What was your first machine, and how did it change your life? The comments are open!
By Christopher Null
Monday, August 07, 2006
Beams reveal Archimedes' hidden writings
Previously hidden writings of the ancient Greek mathematician Archimedes are being uncovered with powerful X-ray beams nearly 800 years after a Christian monk scrubbed off the text and wrote over it with prayers.
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Over the past week, researchers at Stanford University's Linear Accelerator Center in Menlo Park have been using X-rays to decipher a fragile 10th century manuscript that contains the only copies of some of Archimedes' most important works.
The X-rays, generated by a particle accelerator, cause tiny amounts of iron left by the original ink to glow without harming the delicate goatskin parchment.
"We are gaining new insights into one of the founding fathers of western science," said William Noel, curator of manuscripts at Baltimore's Walters Art Museum, which organized the effort. "It is the most difficult imaging challenge on any medieval document because the book is in such terrible condition."
Following a successful trial run last year, Stanford researchers invited X-ray scientists, rare document collectors and classics scholars to take part in the 11-day project.
It takes about 12 hours to scan one page using an X-ray beam about the size of a human hair, and researchers expect to decipher up to 15 pages that resisted modern imaging techniques. After each new page is decoded, it is posted online for the public to see.
On Friday, members of the public watched the decoding process via a live Web cast arranged by the San Francisco Exploratorium.
"We are focusing on the most difficult pages where the scholars haven't been able to read the texts," said Uwe Bergmann, the Stanford physicist heading the project.
Born in the 3rd century B.C., Archimedes is considered one of ancient Greece's greatest mathematicians, perhaps best known for discovering the principle of buoyancy while taking a bath.
The 174-page manuscript, known as the Archimedes Palimpsest, contains the only copies of treatises on flotation, gravity and mathematics. Scholars believe a scribe copied them onto the goatskin parchment from the original Greek scrolls.
Three centuries later, a monk scrubbed off the Archimedes text and used the parchment to write prayers at a time when the Greek mathematician's work was less appreciated. In the early 20th century, forgers tried to boost the manuscript's value by painting religious imagery on some of the pages.
In 1998, an anonymous private collector paid $2 million for the manuscript at an auction, then loaned it to the Walter Arts Museum for safekeeping and study.
Over the past eight years, researchers have used ultraviolet and infrared filters, as well as digital cameras and processing techniques, to reveal most of the buried text, but some pages were still unreadable.
"We will never recover all of it," Noel said. "We are just getting as much as we can, and we are going to the ends of the earth to get it."
By TERENCE CHEA, Associated Press Writer
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Over the past week, researchers at Stanford University's Linear Accelerator Center in Menlo Park have been using X-rays to decipher a fragile 10th century manuscript that contains the only copies of some of Archimedes' most important works.
The X-rays, generated by a particle accelerator, cause tiny amounts of iron left by the original ink to glow without harming the delicate goatskin parchment.
"We are gaining new insights into one of the founding fathers of western science," said William Noel, curator of manuscripts at Baltimore's Walters Art Museum, which organized the effort. "It is the most difficult imaging challenge on any medieval document because the book is in such terrible condition."
Following a successful trial run last year, Stanford researchers invited X-ray scientists, rare document collectors and classics scholars to take part in the 11-day project.
It takes about 12 hours to scan one page using an X-ray beam about the size of a human hair, and researchers expect to decipher up to 15 pages that resisted modern imaging techniques. After each new page is decoded, it is posted online for the public to see.
On Friday, members of the public watched the decoding process via a live Web cast arranged by the San Francisco Exploratorium.
"We are focusing on the most difficult pages where the scholars haven't been able to read the texts," said Uwe Bergmann, the Stanford physicist heading the project.
Born in the 3rd century B.C., Archimedes is considered one of ancient Greece's greatest mathematicians, perhaps best known for discovering the principle of buoyancy while taking a bath.
The 174-page manuscript, known as the Archimedes Palimpsest, contains the only copies of treatises on flotation, gravity and mathematics. Scholars believe a scribe copied them onto the goatskin parchment from the original Greek scrolls.
Three centuries later, a monk scrubbed off the Archimedes text and used the parchment to write prayers at a time when the Greek mathematician's work was less appreciated. In the early 20th century, forgers tried to boost the manuscript's value by painting religious imagery on some of the pages.
In 1998, an anonymous private collector paid $2 million for the manuscript at an auction, then loaned it to the Walter Arts Museum for safekeeping and study.
Over the past eight years, researchers have used ultraviolet and infrared filters, as well as digital cameras and processing techniques, to reveal most of the buried text, but some pages were still unreadable.
"We will never recover all of it," Noel said. "We are just getting as much as we can, and we are going to the ends of the earth to get it."
By TERENCE CHEA, Associated Press Writer
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