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。
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。
His conjecture, made in 1904, was that in this four-dimensional world, all closed three-dimensional surfaces that are simply connected could be transformed to look like a three-dimensional sphere.
他在1904年就提出猜想：在四维空间，所有单连通的封闭三维面都能转化为一个三维球体。
Whether Aquarius is right or wrong in his conjecture is an issue that continues to rage in every country of the world. But from the viewpoint of this idealistic sign, there is always hope.
无论水瓶座的臆说孰对孰错，重要的是他将持续在这世界上的个个国家风行不灭。然而从这个理想主义星座的观点出发…希望永存。
Whether Aquarius is right or wrong in his conjecture is an issue that continues to rage in every country of the world. But from the viewpoint of this idealistic sign, there is always hope.
无论水瓶座的臆说孰对孰错，重要的是他将持续在这世界上的个个国家风行不灭。然而从这个理想主义星座的观点出发…希望永存。
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