The risks can be so complex that banks hire mathematicians to assess them.
这类风险可以是如此复杂以至于银行雇佣数学家们去评估它们。
Only when each logical step has been checked by other mathematicians will the proof be accepted.
只有在每个逻辑步骤都由其他数学家验证之后，该证明才会被接受。
Some present the lives of colorful mathematicians.
其中一些展示了丰富多彩的数学家的生活。
Mathematicians, by contrast, tend historically towards solitude.
相比之下，数学家在历史上倾向于独处。
To mathematicians, a chair is equivalent to an apple; a mug—at least, one with a handle—is like a doughnut.
对于数学家而言，一把椅子相当于一个苹果；一个杯子——至少是有把手的——就像一个油炸圈饼。
Mathematicians describe his results as elegant and beautiful but they are much too complex to be appreciated by laymen.
数学家描述他的结果是优雅而美丽的，但是这些结果太复杂了，外行人无法欣赏。
In their groundbreaking work regarding complexity and the limitations of formal systems, mathematicians Gregory Chaitin and A.N. Kolmogorov force us to consider this last claim more closely.
数学家Gregory Chaitin和A.N.Kolmogorov在他们关于复杂性和形式系统的局限性的开创性工作中，迫使我们更仔细地考虑最后一个说法。
Zu Chongzhi was one of the greatest mathematicians in ancient China.
祖冲之是中国古代最伟大的数学家之一。
In order to remember Zu, some mathematicians suggest calling pi "Zu Lv".
为了纪念祖，一些数学家建议称圆周率为“祖率”。
About half of the mathematicians studied by Benjamin Bloom had little good to say about school.
本杰明·布卢姆研究过的数学家中，约有一半人对学校没有什么好感。
We are trained as engineers, not as mathematicians.
本质上，我们是工程师而不是数学家。
Right now, it seems to be focused on mathematicians.
现在的用户似乎以数学家为主。
Mathematicians and scientists call such graphs curves.
数学家和科学家称它们为图形曲线，尽管是直线。
Strangely, mathematicians insist 11 is a “strictly non-palindromic number”.
奇怪的是，数学家们坚持说11“严格地说不是一个回文数字”。
While both men are mathematicians and artists, they have clear specialties.
虽然父子俩都既是数学家又是艺术家，但他们各有特长。
Daniel Bernoulli (1700-82) was born into a family of distinguished mathematicians.
丹尼尔·伯努利(Daniel Bernoulli)(1700- 1782)生于一个杰出的数学世家。
Mathematicians have studied the golden ratio because of its unique and interesting properties.
而数学家研究这个比例是因为其独特而有趣的性能。
As mathematicians say, “Every simply connected closed 3-manifold is homeomorphic to a 3-sphere.”
用数学语言表达就是“每个单连通3重（3-manifold）封闭体与一个三维球体同胚（homeomorphic）。”
But at my school there was no future in that. No international mathematicians came out of my school.
我数学一直很好，但是在我的学校那是没有前途的，没有一个世界级的数学家在我们学校诞生。
To mathematicians, a chair is equivalent to an apple; a mug-at least, one with a handle-is like a doughnut.
对于数学家而言，一把椅子就相当于一个苹果，一个带柄的杯子就像一个油炸圈饼。
Mathematicians write this number as 1015: the superscript tells you how many zeros there are after the one.
数学家们将这个数字写成1015：右上角的数字告诉你‘1’之后有多少个‘0’。
It challenges mathematicians to list the possible shapes into which three-dimensional space can be wrapped up.
数学家们需要列出三位空间中所有可能的图形方案。
The group includes accredited journalists, software programmers, network engineers, mathematicians and others.
这一组织包括被任命的新闻记者，软件工程师，网络工程师，数学家和其他人。
WHEN people talk about Singapore's education miracle, they normally think of rows of clever young mathematicians.
谈起新加坡非凡的教育时，浮现在人们脑海里的是成堆聪明年轻的数学家。
No wonder it is sometimes said that Mr Gardner made mathematicians out of children and children out of mathematicians.
难怪时常有人说，加德纳先生使黄口小儿成为日后的数学巨匠，使数学巨匠的作品走入黄口小儿的世界。
However, in the mid-90s a group of mathematicians devised a technique for reducing the dimensionality of complex data sets.
然而，上世纪90年代中期有一组数学家设计出了一种方法，能够对复杂的数据集进行降维。
Kids right out of school have the greatest potential, just like young mathematicians, but they do need how to work for a living.
从学校毕业的孩子们拥有最大的潜力，就像年轻的数学家一样，但是他们更需要知道如何为了生活而工作。
Spend a moment thinking about the typical traits of a professor, scientists, or mathematicians to increase problem solving ability.
花几分钟思考专业人士、科学家、教授或数学家提高解决问题能力的典型特征。
Spend a moment thinking about the typical traits of a professor, scientists, or mathematicians to increase problem solving ability.
花几分钟思考专业人士、科学家、教授或数学家提高解决问题能力的典型特征。
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