<看看欧几里德:穿过奇妙数学世界的惊奇之行>.
Here’s Looking at Euclid: A Surprising Excursion Through the Astonishing World of Math.
数学世界很精彩，它与现实世界、与人们的生活息息相关。
The mathematics world is perfect wonderful, it is closed to the realistic world and human life.
极限的思想是人们认识数学世界解决数学问题的重要武器。
Summary: the limit is one of the extremely important concept in mathematics. limit mathematical solving mathematical problems in the world of thought is the awareness of the important weapons.
有时看着两个孩子我就会想到你，在数学世界里，他们就像两个完全平方数。
I thought of you sometimes as I raised my boys, perfect squares in their rational world.
在这些例子中，类的对象与现实世界(或者至少是数学世界)中的一些实体都有显著的对应关系。
In each case there is an obvious correspondence between the object and some entity in the real world (or at least a mathematical world).
正确学习数学的方法是广度优先，而非深度优先。你要考察的是整个数学世界，学习每个概念的名字，区分出什么是什么。
The right way to learn math is breadth-first not depth-first. You need to survey the space learn the names of things figure out what's what.
正确学习数学的方法是广度优先，而非深度优先。你要考察的是整个数学世界，学习每个概念的名字，区分出什么是什么。
The right way to learn math is breadth-first, not depth-first. You need to survey the space, learn the names of things, figure out what's what.
正确学习数学的方法是广度优先，而非深度优先。你要考察的是整个数学世界，学习每个概念的名字，区分出什么是什么。
The right way to learn math is breadth -first, not depth-first. You need to survey the space, learn the names of things, figure out what's what.
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。
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.
在世界各地的学校里，女孩在“语言科目”上往往比男孩更好，而男孩在数学和物理上表现更好。
In schools throughout the world girls tend to be better than boys at "language subjects" and boys better at maths and physics.
尽管科学理论的大致框架能被直观地勾勒出来，但当物质世界的一部分最终被理解时，它的描述看起来通常就像数学课本中的一页内容。
Though the broad outline of a scientific theory can be sketched intuitively, when a part of the physical universe is finally understood, its description often looks like a page in a mathematics text.
一项全球教育成就调查显示，全世界在数学和科学方面最聪明的青少年是新加坡的。
The world's smartest adolescence in mathematics and science are Singapore, according to a global survery of educational achievement.
由四名学生组成的小组制作一个视频，说明一个数学问题及其在现实世界中的应用。
Teams of four students make a video illustrating a math problem and its real-world application.
在最新的国际学生评估项目中，在全世界近50万名学生里，美国在科学方面的分数排名第二，阅读方面排名第三，数学方面排名第六。
In the latest PISA scores, the nation came second in science, third in reading and sixth in math among nearly half a million students worldwide.
数学和英语当然很重要，但在当今世界，他们还需要其他技能来帮助他们。
Maths and English are important, of course, but they need other skills too to help them in today's world.
但是每一位热衷于使用数学对现实世界建模的工程师都知道，模型只是模型。
But every engineer, enthusiastically using mathematical models of the real world, knows the model is just that, the model.
这就是他们学习、感受、实践、创造、表达情感、练习社交、提高语言和数学能力的方式，也是他们看待世界的新方法。
It's how they learn, experiment, tinker, express creativity, work through feelings, practice socialization, develop language and math skills, and see the world in new ways.
几个世纪以来，数学一直是科学和技术的主要动力，其结果已经改变了我们的世界。
For centuries, maths has been the main driver of science and technology, and the results have transformed our world.
数学工作站的商业使用群体非常庞大：从基础工程到设计创意，从基因治疗到天体导航，数学统治着整个世界。
Commercial USES for mathematical workstations are vast: from basic engineering to designer drugs and from gene therapy to celestial navigation, mathematics rules the world.
世界也不是最后的定论，你们记住，哲学问题不像数学问题，因此没有答案。
The world is not the last word. You remember, it's not like a mathematical problem so there's no solution.
由于头脑愚笨并遭现实物质世界打击，孤独症患儿的头脑常常更乐于接受数学、符号和代码等虚拟领域。
Clumsy and overwhelmed by the physical world, autistic minds are often far more comfortable with the virtual realms of maths, symbols and code.
直至500多年前，我们的祖先还在冶炼、经济、数学、航海、陶瓷、丝织等诸多方面引领着这个世界。
Up till 500 years ago, our ancestors still led advancements in fields of metallurgy, economics, mathematics, nautical navigation, ceramics and silk.
一个基于“世界上最美数学定理”的离奇怪圈出现在威尔特郡一架风车旁边的田里。
An extraordinary crop circle based on the 'world's most beautiful maths theorem' has appeared in a field next to a windmill in Wiltshire.
数学模型有别于其他模型的重要一点就是：数学通过定义公理来创造属于自己的世界。
Mathematical models differ in an important aspect from other models: mathematics create, by defining axioms, a universe of their own.
世界经济论坛最新发布的《全球竞争力指标》中，南非的数学和科学教育(在133个国家中)垫底。
In the World Economic Forum's latest Global Competitive Index it ranks bottom (out of 133 countries) in both maths and science education.
相反，他们的两家BASIS学校，一家在图森市，一家在菲尼克斯郊区，明确要跟世界上最好的学校竞争，比如韩国的数学教育或芬兰的古典学教育。
Instead, their two BASIS schools, one in Tucson and this one in suburban Phoenix, explicitly compete with the best schools in the world-south Korea's in maths, say, or Finland's in classics.
这表明了世界上不存在能够证明或证伪所有命题的终极数学体系。
This is thought to indicate that there is no grand mathematical system capable of proving or disproving all statements.
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。
If mathematics is the perception of this realm of pure ideas, then doing mathematics requires our brains to somehow reach beyond the physical world.
这是一个大量数据和应用数学取代其他工具的世界。
This is a world where massive amounts of data and applied mathematics replace every other tool that might be brought to bear.
这是一个大量数据和应用数学取代其他工具的世界。
This is a world where massive amounts of data and applied mathematics replace every other tool that might be brought to bear.
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