Two Chinese mathematicians have put the final pieces together in
the solution to a puzzle that has perplexed scientists around the
globe for more than a century.
The two scientists have published a paper in the latest US-based
Asian Journal of Mathematics, providing complete proof of
the Poincar Conjecture promulgated by Frenchman Henri Poincar in
1904.
Professor Cao Huaidong, of Lehigh University in Pennsylvania,
and Professor Zhu Xiping, of Zhongshan (Sun Yat-sen) University in
south China's Guangdong Province, co-authored the paper, "A
Complete Proof of the Poincar and Geometrization Conjectures --
application of the Hamilton-Perelman theory of the Ricci flow",
published in the June issue of the journal.
Cao and Zhu put the finishing touches to the complete proof of
the Poincar Conjecture, which had puzzled mathematicians around the
world, said Professor Shing-Tung Yau, a mathematician at Harvard
University and one of the journal's editors-in-chief.
The conjecture was rated as one of the major mathematical
puzzles of the 20th Century, said Yau.
"The conjecture is that if in a closed three-dimensional space,
any closed curves can shrink to a point continuously, this space
can be deformed to a sphere," he explained.
By the end of the 1970s, US mathematician William P. Thurston
had produced partial proof of Poincar's Conjecture on geometric
structure, and was awarded the Fields Prize for the achievement.
Fellow American Richard Hamilton completed the majority of the
program and the geometrization conjecture. In 2003, Russian
mathematician Grigory Perelman made key new contributions.
Based on those major developments, the paper by Cao and Zhu,
which ran to more than 300 pages, provided complete proof, said
Yau, adding the findings would help scientists to further
understand three-dimensional space and heavily influence the
development of physics and engineering.
(Xinhua News Agency June 4, 2006)