Those innovations, upon which virtually all aspects of contemporary society now depend, were possible because the United States then led the world in mathematics and science education.

当代社会几乎所有方面都依赖这些创新，这些创新之所以成为可能，是因为于当时美国在数学和科学教育方面处于世界领先地位。

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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。

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Thanks to mathematics lots of real world problems are solved.

正是由于它，使得大量的现实世界问题得以解决。

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In terms of mathematics and science scores for school-leavers, these countries rank among the highest in the world.

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