On the afternoon of March 17, 2016, the famous Mathematician & Academician Tian Gang, at the 63rd session of SUSTech Lecture, gave a wonderful lecture entitled Poincare Conjecture & Geometry, which helped SUSTech students understand the importance and beauty of Poincare Conjecture & geometry. The lecture was chaired by SUSTech Vice President Tang Tao.
Academician Tian Gang was graduated from Nanjing University in 1982. Now he is the Academician in the Chinese Academy of Sciences, Dean of School of Mathematical Sciences in Peking University, and Chair Professor at Princeton University Mathematics Department. The Academician is known for his prominent achievements in the fields of geometry and mathematical physics. In particular, he is most credited for his pioneering efforts in Kahler-Einstein metric studies.
Proposed by French Mathematician Poincare in 1904 about 3-sphere topological characterization, Poincare Conjecture is of significant meaning for a series of geometrical development. In an escalating way, Academician Tian Gang introduced the development history of geometry, and shared his opinions on presentation and breakthrough of Poincare Conjecture.
History of geometry
According to the Academician, “In ancient Greece, learning geometry was deemed as the most effective route to find the truth”, showing the important position of geometry in mathematics. The Elements of Geometry composed by Euclid was the earliest paradigm of mathematical deduction system based on axiomatic approaches. Nevertheless, the 5th Axiom about parallel lines mentioned in the book could not be proved, which made space for development of Non-Euclidean geometry of János Bolyai, and Riemannian geometry, which raised concepts of Manifold and Metric, and found that curvature was the sole connotative invariant of metrics. And this was the instrument used by Einstein to explain the general relativity.
Prove Poincare Conjecture
Development of geometry also triggers that of topology. Poincare Conjecture is of vital importance for both geometry and topology. Poincare thought he had proved the conjecture. But he later found he was wrong. Academician Tian Gang said, none of the mathematicians succeeded though some of them claimed they had done it. Some mathematicians found they could solve the Poincare Conjecture from the perspective of high dimensionality, but no progress was made in terms of 3 dimensions. The world-class problem was not solved until the geometric conjecture was raised by Perelman.
Academician Tian Gang answers questions in Q&A session
