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1·It was even announced you have finally proved the poincare Conjecture.

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？

2·Microcosmic space is the hollow ball that has limit, it is not the ball of Poincare conjecture.

选择大型篮或妨碍为此，一个有很多空洞空间。

3·To understand the poincare conjecture, start by thinking of any object existing in a three-dimensional world.

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。

4·Then by using Poincare-Bendixson theorem sufficient conditions for the existence of limit cycles are obtained.

在此基础上，利用微分方程的环域定理获得了所述系统存在极限环的条件。

5·FOR the past century mathematicians have struggled to prove the conjecture of a late-19th-century French polymath, Henri poincare.

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。

6·In the third chapter we start with the Poincare group and construct various unitary representations in suitable Hilbert spaces.

第三章我们从庞加莱群着手构造合适的希尔伯特空间的多种幺正表象。

7·Given that we live in a world with three spatial dimensions, the poincare conjecture tells us ultimately what shape our universe could be.

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。

8·With the help of Poincare mapping, the stability problem of periodic orbits was changed to that of the fixed points on the mapping plane.

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。

9·But the recent solution of another challenging problem, the poincare conjecture, gives us hope that even the most elusive problems can be conquered.

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。

10·It's 1908. Henri Poincare - another scientist - decides to make it his business to research how others come up with their creative breakthrough ideas.

1908年，另外一位科学家彭加勒决定开始研究人类的创造性思维是如何激发而产生的。