How students perceive "What is mathematics?" directly affected how they learn mathematics and how they solve mathematics problems.
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。
Milnor says that what he loves most about mathematics is “a feeling of miracles.
米尔诺尔说数学让他最喜爱的地方是那种“奇迹的感觉”。
The aim is to discover not what pupils know but how well they can manipulate what they have learned in reading, mathematics and science.
考察的目的主要是发现学生的知识面以及他们对已学到的阅读素养、数学素养和科学素养。
So what does Hardy mean when he says there is no permanent place for ugly mathematics?
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？
The question remains, to what degree is the absence of women in science, mathematics and engineering caused by innate, immutable ability?
还是那个问题，到底多大程度上女性在科学、数学领域的缺位是由先天的，不可改变的能力决定的？
The mathematics of fractals – very complex geometric shapes – is just what the doctor ordered, helping to capture the difference between the shape of a healthy cell and a cancerous one.
数学上的分形（fractals）是一种非常复杂的几何形状，这正是医生所要关注的，它是协助医生区分健康的细胞形态和癌变的一个重要特征。
By this children can work out problems quickly but what they have learned is just typing skill not mathematics skill, so I think computer should be banned in class.
这样孩子们可以很快地解决问题，但是他们学到的只是打字技巧而不是数学技巧；因此，我认为在课堂上应禁止使用计算机。
What sort of brain is it that can compose the propositions and systems of mathematics?
哪种类型的大脑能够创造数学的定理和系统？
Like the Goldbach conjecture in mathematics, what is law is one of the most famous still unsolved problems in jurisprudence.
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。
So literary can sometimes be very abstract like mathematics, and therefore, if someone says make me a movie, showing me what the square of minus two means that is going to be a challenge.
文学有时候也可以很抽象，像数学，因此如果有人说，给我做一部电影吧，给我展示一下负二的平方，那将是一个挑战。
This paper briefly reviewed the discussions about "what is the mathematics essence" in recent years.
回顾了近年来国内几位知名学者对数学本质的一些讨论。
Mathematics on the corner there is an obtuse, straight Angle, acute Angle, right Angle, the students, what Angle ah?
数学上的角有钝角，平角，锐角，直角，同学们，还有什么角啊？
In this section I advance the notion that present school mathematics reflects an inappropriate perspective of what mathematics is.
这节我要提出一种看法，认为学校数学反映了数学一个不适当的方面。
An important problem arises from the subjects itself: How can I —— of anyone who is not a mathematician —— talk about this? What right has a philosopher to talk about mathematics?
这一个问题，若是换做康德来问，则可能会变成：「（由哲学家主导的）数学哲学是如何可能的?。
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.
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。
In fact, what we ought to do is take a page from their playbook, because the initiatives and programs that have been set in place for women in science and engineering and mathematics are fantastic.
事实上，我们要做的是站在男孩的立场来思考解决问题，因为在学校已设置的初级教学和课程计划适合女孩在科学，工程学和数学方面有杰出表现。
What he is really working on, he says, is a new mathematics of perpetual novelty .
他真正在从事的，用他的话说，是一种新的恒新的算术。
What is certain is that few people in history have created a greater impact than Newton on the development of both science and mathematics.
可以肯定的是，历史上鲜有人能同时在科学和数学领域的成就比牛顿更突出。
However, what we're finding is about half of our students are not prepared for mathematics at the college level.
然而，我们发现，大约一半的学生没有为大学的数学水平做好准备。
This is what Marcus du Sautoy, professor of mathematics, wants to explore.
这是马库斯杜sautoy，数学教授，希望去探索。
It is impossible and dispensable to make an answer to satisfy everybody completely about What Mathematics is.
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。
At present, the elementary school mathematics classroom teaching attaches great importance to the construction of "high-efficient class", then what is efficient?
当前，小学数学课堂教学非常重视“高效课堂”的建设，那么何谓高效？
At present, the elementary school mathematics classroom teaching attaches great importance to the construction of "high-efficient class", then what is efficient?
当前，小学数学课堂教学非常重视“高效课堂”的建设，那么何谓高效？
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