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 pair have published a paper in the latest U.S.-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, U.S. 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.