学生对“数学是什么”的认知直接影响他们学习数学和解数学题的方式。
How students perceive "What is mathematics?" directly affected how they learn mathematics and how they solve mathematics problems.
不可能也没有必要对“数学是什么”做出一个令所有人都完全满意的回答。
It is impossible and dispensable to make an answer to satisfy everybody completely about What Mathematics is.
在高等数学界，多样性是个问题，这已经不是什么秘密了。
It's no secret in the advanced-math community that diversity is a problem.
数学作业是什么？
对于所有不喜欢数学的我们来说，我们都不得不做的事情就是为了知道生活是什么体验而生活下去。
For all of us who do not like math all we have to do is live life in order to get a taste of what it is all about.
他们想知道这些家长是怎样教出这么多的数学天才和音乐神童，这些家庭内部到底是什么样，他们自己是否也能做到。
They wonder what these parents do to produce so many math whizzes and music prodigies, what it's like inside the family, and whether they could do it too.
那哈代说“世上没有永久的地方容纳丑陋的数学”是什么意思呢？
So what does Hardy mean when he says there is no permanent place for ugly mathematics?
接线员：你需要人帮忙的是什么样的数学题？
Operator: What kind of math do you have that you need help with?
说，通过表明不确定性始终存在在数学中，，这个新成果是建立在这个基础上，而不管涉及的是什么材料。
The new work, says Szymczak, builds on that foundation by showing that the instability always exists in the math, no matter what materials are involved.
Szymczak说，通过表明不确定性始终存在在数学中，，这个新成果是建立在这个基础上，而不管涉及的是什么材料。
The new work says Szymczak builds on that foundation by showing that the instability always exists in the math no matter what materials are involved.
没提需要的是什么方面的数学，也没提这个数学的适用性或是它所产生的模型的健壮性，而仅仅是“我们需要更多的数学”这么一句话。
No mention of what sort of maths, no mention of the relevance of the maths or the robustness of the resulting models. Just "we need more maths."
是什么使女性在数学的高成就方面欠缺?。
What does make female lacking in the high achievement of mathematics?
正确学习数学的方法是广度优先，而非深度优先。你需要生存在空间里，学习事物的名字，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.
听并圈出。陈小姐是一个数学/英语老师。格雷先生是一个音乐/语文老师。 再听一次并回答。 陈小姐是什么样的？ 格雷先生是什么样的？
Miss Chen is a maths / an English teacher. Mr Grey is a music / Chinese teacher. Listen again and answer. What is Miss Chen like? What is Mr Grey like?
关于“数学的灵魂是什么?。
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.
一如数学领域中的歌德巴赫猜想，“法律是什么”这个问题是法学中最著名的、尚未得到解决的问题之一。
Like the Goldbach conjecture in mathematics, what is law is one of the most famous still unsolved problems in jurisprudence.
学习数学的最好方法是什么？
那么，到底是什么原因导致大多数学习者在口语课堂上消极参与、不肯开口?我们有必要研究是哪些因素阻碍或促进了口语学习。
What cause learners' inactive participation or silence in the oral class?It is of necessity to investigate factors which may obstruct or enhance oral English acquisition.
那么，我们所谓的数学美和优雅，并且可以引起我们的美的情感的主体究竟是什么？
Now, what are the mathematic entities to which we attribute this character of beauty and elegance, and which are capable of developing in us a sort of esthetic emotion?
是什么让数学时，以便有效地进入科学是一个神秘的谜，本书要达到不超过阐明有多深这个奥秘的。
What makes mathematics so effective when it enters science is a mystery of mysteries, and the present book wants to achieve no more than to explicate how deep this mystery is.
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.
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