A few years ago, I was surprised to see an announcement in Mathworld stating (again) that the Poincare conjecture has been proved. “This time for real” they said. Being skeptical, I waited for more independent confirmation of this result… which never came.
The author of the proof was a respected professor (Dr. Grigori Perelman).
Today, however, I found more news about Perelman and his work. Turns out that the earlier proof was more a set of guidelines on hwo to find the real proof of Poincare’s conjecture. In the meantime, the proof has apparently been completed by two Chinese mathematicians.
A Columbia professor Richard Hamilton and a Russian mathematician Grigori Perelman have laid foundation on the latest endeavors made by the two Chinese. Prof. Hamilton completed the majority of the program and the geometrization conjecture.
Yang, member of the Chinese Academy of Sciences, said in an interview with Xinhua, “All the American, Russian and Chinese mathematicians have made indispensable contribution to the complete proof.”
Prof. Zhu at Guangzhou-based Zhongshan University and Prof. Cao at Lehigh University in Pennsylvania co-authored the 300-page paper, “The Hamilton-Perelman Thoery of Ricci Flow-The Poincare and Geometization Conjecture,” which was published in the June issue of the journal.
Indeed, the article confirms Dr. Perelman’s work, but it gives more clarity on what is proof and what isn’t.
“The total length of Perelman’s work on the conjecture by the end of 2002 was about 70 pages,” said Yang, citing that Perelman raised guidelines for proving the conjecture but not specifically pointed out how to unravel the puzzle.
“Guidelines are totally different to complete proof of theories,” Yang said.
As a side note, this mathematical conjecture got a undeserved publicity. The Clay Mathematics Institute says that, if you solve it, you get one million dollars!