要理解庞加莱猜想，当始于对三维世界存在的一切物体的认识。
To understand the poincare conjecture, start by thinking of any object existing in a three-dimensional world.
甚至有报道说你们最终证明了庞加莱猜想。你是怎么熬过来的？
It was even announced you have finally proved the poincare Conjecture.
这就是庞加莱和瑟斯顿所说的三维流形：没有除了已发现的之外的任何流形存在。
This is what Poincaré and Thurston say about the world of 3-manifolds: there are no manifolds besides those which has been already discovered.
然后基于不变流形理论和庞加莱截面方法，设计了不同拉格朗日点间转移轨道。
Then on the basis of invariant manifold theory and Poincaré section, a transfer trajetory between L1 and L2 of the Earth-Moon system was given.
给出我们生活的这个世界的三维空间，庞加莱猜想能够告诉我们我们的宇宙的形状。
Given that we live in a world with three spatial dimensions, the poincare conjecture tells us ultimately what shape our universe could be.
利用庞加莱映射将周期轨道的稳定性分析转化为映射平面上不动点的稳定性分析。
With the help of Poincare mapping, the stability problem of periodic orbits was changed to that of the fixed points on the mapping plane.
庞加莱认为：“如果我们希望预知数学的将来，适当的途径是研究这门学科的历史和现状”。
Pioncare says: if we should predict the future of math, the proper way is to know the history and development of the subject.
庞加莱猜想最先由法国数学家亨利?庞加莱于1904年提出，是一个关于三维空间形状的问题。
The Poincaré Conjecture was first posed by the French mathematician, Jules Henri Poincaré, in 1904, and seeks to understand the shape of the universe by linking shapes, spaces and surfaces.
庞加莱猜想的重要不仅在于它的实际应用性，还因为巨量的数学工作是基于假定庞加莱猜想是正确的。
Poincare's conjecture is important not for its practical applications, but because a vast quantity of mathematical work assumes that it is true.
所有中国人都应该为中国数学家在微分几何领域所取得的成就，和对庞加莱猜测的贡献而感到骄傲。
All Chinese can be proud of the achievements of their mathematicians in differential geometry and their contributions to the completion of the proof of Poincare conjecture.
佩雷尔曼博士利用广为人知的“瑞奇流（Ricci flow）”这样一个热方程来证明了庞加莱猜想。
Dr Perelman proved Poincaré's conjecture by taking an equation normally used to model heat dissipation in three-dimensional objects, known as Ricci flow.
庞加莱是法国著名的数学家、天文学家、理论物理学家和科学哲学家，是横跨19、20世纪的科学大师。
A renowned French mathematician, astronomer, theoretical physicist and scientific philosopher, Poincare saw his remarkable scientific life spanning the 19th and 20th centuries.
一旦证明猜想是伪命题，那将使人们对现代数学的许多部分产生质疑——当然也包括基于庞加莱猜想的一切。
Proving the conjecture false would have cast doubt on much of modern mathematics-and everything that depends on it.
方法利用庞加莱截面、李雅普·诺夫指数、关联维等工具分别对抛物方程和椭圆方程的非线性动力学行为进行描述。
Methods Nonlinear dynamical behavior of both parabolic equation and elliptic equation were investigated by several tools such as Poincare section, Lyapunov exponent, and correlation dimension.
19世纪晚期的法国博学家亨利·庞加莱(Henri poincare)提出了一个猜想，结果数学家们为之奋斗了整整一个世纪。
FOR the past century mathematicians have struggled to prove the conjecture of a late-19th-century French polymath, Henri poincare.
但最近，我们解决了庞加莱猜想这一难题，对于这一具有挑战性的问题的解决方式则给了我们希望，让我们有希望解决甚至是难以琢磨的问题。
But the recent solution of another challenging problem, the poincare conjecture, gives us hope that even the most elusive problems can be conquered.
曹怀东与朱熹平的文章中充分肯定了佩雷尔曼的工作对于证明庞加莱猜测所起的重要作用，同样，佩雷尔曼在文章中也明确指出他的工作是建构于前人的众多贡献基础上的。
They fully acknowledge Perelman's role in the completion of the proof of Poincare conjecture and likewise Perelman has acknowledged the work of previous researchers on which it's based.
8月22日的国际数学家大会（the InternationalCongressof Mathematicians）上，授予了佩雷尔曼博士最高荣誉——菲尔兹奖（theFieldsmedal），以表彰他对解决庞加莱猜想做出的贡献。 时过三年以后，佩雷尔曼对庞加莱猜想的证明已被证实了正确性。
On August 22nd the International Congress of Mathematicians awarded Dr Perelman its highest honour, the Fields medal, for his solution which, having stood for three years, is now taken as correct.
8月22日的国际数学家大会（the InternationalCongressof Mathematicians）上，授予了佩雷尔曼博士最高荣誉——菲尔兹奖（theFieldsmedal），以表彰他对解决庞加莱猜想做出的贡献。 时过三年以后，佩雷尔曼对庞加莱猜想的证明已被证实了正确性。
On August 22nd the International Congress of Mathematicians awarded Dr Perelman its highest honour, the Fields medal, for his solution which, having stood for three years, is now taken as correct.
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