If mathematics is the perception of this realm of pure ideas, then doing mathematics requires our brains to somehow reach beyond the physical world.
如果数学是对纯理念王国的感知的话，那么研究数学就需要让自己的大脑以某种方式抵达现实世界之外的某地。
When something so fundamental to life as food is priced beyond the reach of the poor, we know that something in our world has gone terribly wrong.
对生命至关重要的食品的价格上涨到穷人难以问津的地步，我们知道大事不妙，情况实在过于离谱了。
These are the things I want for you-to grow up in a world with no limits on your dreams and no achievements beyond your reach.
这些是我想要让你们得到的东西：在一个梦想不受限制、无事不能成就的世界中长大。
Because they can aspire to a world beyond the village, even if they never reach it, young Mexicans have an added reason to stay in school beyond a ninth year, the authors show.
由于这里的学生迫切渴望到他们从未曾接触过的大千世界去看看。因此，他们会选择在完成九年级学习之后，继续学业。
Because they can aspire to a world beyond the village, even if they never reach it, young Mexicans have an added reason to stay in school beyond a ninth year, the authors show.
由于这里的学生迫切渴望到他们从未曾接触过的大千世界去看看。因此，他们会选择在完成九年级学习之后，继续学业。
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