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。
The risks can be so complex that banks hire mathematicians to assess them.
数学家们几乎都为这一成就自鸣得意。
The mathematicians were almost smug about this accomplishment.
数学家们转而去挑选周期解。
但是数学家们仍然学要他们的门捷列夫。
But mathematicians are still to have their Mendeleev moment.
数学家们需要列出三位空间中所有可能的图形方案。
It challenges mathematicians to list the possible shapes into which three-dimensional space can be wrapped up.
数学家们能想象出不止一种无穷大的数。
Mathematicians can imagine more than one kind of infinite number.
那么，数学家们的思想又要危险多少倍呢？
顶级的数学家们将毫无疑问继续扮演重要的角色。
物理界过去和现在都是从不关心数学家们的分类的。
The physical world was and still is indifferent to the mathematicians' classification.
奇怪的是，数学家们坚持说11“严格地说不是一个回文数字”。
Strangely, mathematicians insist 11 is a “strictly non-palindromic number”.
数学家们思考的许多难题之一，就是一种新的打结方法。
Of the many puzzles mathematicians ponder, one is new ways to tie knots.
物理学家们说我是数学家，数学家们又把我归为物理工作者。
Physicists say that I am a mathematician, and the mathematicians refer to me as a physicist.
物理学家们说我是数学家，数学家们又把我归为物理工作者。
The physicists say that I am a mathematician, and the mathematicians say that I am a physicist.
谜底是由那些像孩子们一样一直在思虑瓷砖外形的数学家们供给的。
The answer came from mathematicians who, like children, had been thinking about patterns of tiles.
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’。
Mathematicians write this number as 1015: the superscript tells you how many zeros there are after the one.
E8是一个包含248维的怪物，数学家们花了120年的时间才把它的结构摸透。
E8 is a monster. It has 248 dimensions and its structure took 120 years to solve.
澳洲数学家们发明出一条”未婚妻公式”，能让男士们算出自己多大时求婚最合适。
Mathematicians from Australia came up with a "fiancée formula" which allows a man to work out his optimal proposal age.
数学家们的同胞手足中有孤独症的比例较高，说明数学与孤独症的关联确有遗传学的因素在内。
Siblings of mathematicians also have a higher risk of autism, suggesting the link between maths and autism is genetically mediated.
数学家们经常讲你要理解某事就要先去读它，然后用自己的语言写下来，再去向别人传授。
Mathematicians often say that to understand something you must first read it, then write it down in your own words, then teach it to someone else.
里维斯表示：“起初，数学家们认为可能需要15分钟才能算出结果。所以他们很高兴。”
"At first, the mathematicians thought it was going to take about 15 minutes to run, " Levis said. "They were pleased. "
通常，数学家们都觉得这种题目有内在的复杂性，也就是说没有什么聪明的方式能找到解决方法。
The general feeling among mathematicians is that problems of this sort have an inbuilt complexity, which means that there won't be any clever way of finding the solution.
那些对希腊数学造诣很深的、关于批评的数学家们，怎么能满足于在启发性的基础上进行工作呢？
How could critical mathematicians, well versed in Greek mathematics, have been content to operate on a heuristic basis?
本周，来自巴西到比利时的女性科学家、技术师、工程师以及数学家们都在庆祝她的伟大的一生。
This week, women scientists, technologists, engineers and mathematicians from Brazil to Belgian have been celebrating her life.
数学家们用了很难懂的话，来证明这些，这里我就不多说了，如果你学分析的话，还会看到这些的，还有问题吗？
I mean mathematicians have more complicated words to justify this statement. I will spare them for now, and you will see them when you take analysis if you go in that direction Any questions so far?
但这里我要纠正一种误解，有人认为纯数学家们以他们工作的无用性为荣，并自夸其没有实际的用途。
But here I must deal with a misconception. It is sometimes suggested that pure mathematicians glory in the uselessness of their work, and make it a boast that it has no practical applications.
大自然之所以如此浪费，是因为对付那些数学家们所说的完全探索的“潜力空间”的最好的办法，就是无目的战略。
Nature is so wasteful because scattershot strategies are the best way to do what mathematicians refer to as fully exploring "the potential space."
但直到19世纪数学家们才发现隐藏在数学方程解法中的对称性，其中包括郁郁寡欢的法国数学天才艾瓦里斯特·伽罗瓦。
But it was not until the 19th century that mathematicians such as Evariste Galois, an unhappy French genius, discovered symmetries hidden in the solutions to mathematical equations.
但直到19世纪数学家们才发现隐藏在数学方程解法中的对称性，其中包括郁郁寡欢的法国数学天才艾瓦里斯特·伽罗瓦。
But it was not until the 19th century that mathematicians such as Evariste Galois, an unhappy French genius, discovered symmetries hidden in the solutions to mathematical equations.
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