这一结果唯一合理的数学解释就是哈代悖论。
The only mathematically consistent explanation known for this result is therefore Hardy's.
阐述了数学解释的定义，分类及其功能。
The definition, the classification and the function of mathematical explanation are expounded.
如果用数学解释，给它一个数字，给它一个零。
That's going to presumably be given — mathematically if we gave it a number, we'd slap a zero on that.
牛顿和开普勒关于行星运动的数学解释是科学史上极其重要的两大成就。
The mathematical explanations about planets′ motion given by Newton and Kepler are two of the most important achievements in science history.
但是这个例子这说明了，为什么得到的具体答案是数学解释而不是物理解释。
But the explanation is to why it comes up with that particular answer is a mathematical explanation not a physical one.
论文主要包括引言、中学生数学解释的实证研究、中学生数学解释的理论研究以及实现理解的数学教学建议四个部分。
The dissertation consists of four parts, including the introduction, the empirical study, the theoretical study, Suggestions to realize teaching mathematics for understanding.
所谓数学解释，就是以某种方法对数学某一分支或者构成它的成分，诸如概念、命题、公式、符号等所赋予的各种意义的总和。
The so called maths summary is to summarize, by a certain way, the various meanings of a branch of its structural element such as conception, proposition, formula and sign etc.
我们想让数学老师再解释一遍这个难题，但他拒绝了。
We requested that the math teacher explain the puzzle again, but he refused.
这是因为，对能解释所有自然力量的统一理论的追求已经把目前的数学推到了极限。
That's because the quest for a unified theory that would account for all the forces of nature has pushed current mathematics to its limits.
其他科学家也曾著书向非科学家们解释他们的研究领域，但却不得不忽略数学运算以使得书籍简单易懂，尽管数学运算为他们的理论提供了基础。
Other scientists have written books to explain their fields to non-scientists, but have necessarily had to omit the mathematics, although it provides the foundation of their theories.
他在1915年11月4日发表了第一次演讲，演讲解释了他的新方法，尽管他承认他还没有精确的数学公式。
His first lecture was delivered on Nov 4, 1915, and it explained his new approach, though he admitted he did not yet have the precise mathematical formulation of it.
凯文惊讶于约翰如何把通常很难的数学作业解释得如此简单。
Kevin was amazed how John explained the usually very difficult math homework and made it look so easy.
哈利法克斯新举办的一个展览用日常活动来解释我们经常使用、但不易察觉的数学原理。
A new exhibition in Halifax uses everyday activities to explain the hidden math principles we all use on a regular basis.
现存的数学理论无法解释它。
我相信这可以帮助解释为什么我高中毕业时，我对数学的兴趣开始与做一些对社会有用的事打架。
I believe this does help explain why by the time I finished high school, my interest in mathematics was beginning to compete with a desire to do something useful for society.
关于为什么计算器能如实地反映数学事实，可以进行物理解释。
You can give a physical explanation for why my calculator faithfully reproduces mathematical facts.
不过，他应付有方，已经研究出一套数学模型来解释第二位数的分布，将统计上的疑异置于更充裕的分析基础上。
However, he has managed to develop a mathematical model that explains the distribution of the second digits, putting what might appear to be a statistical oddity on a more solid footing.
阿齐兹·伊南解释说，当一个人详细地来观察这个日期时，它还有一些有趣的数学特点。
Inan explained that when one looks closely at the date, it too has some interesting mathematical properties.
制造是如此容易，这就解释了为什么在软件开发中没有那么高的数学严密性。
Ease of manufacturing explains why we don't have much mathematical rigor in software development.
这也许会被视为无聊的消遣，然而已有学者提出数学方程序解释人们的拖延症。
It might seem an idle pastime but academics have come up with a mathematical equation for why people procrastinate.
你的计算机的处理器把你执行一切指令当做一系列的数学问题来解释。
Your computer's processor interprets any command you execute as a series of math problems.
即使你只有六七个，你还可以-根据数学，而我在书中有介绍-这是相当简单的问题，但很明显，我不能在收音机里解释。
Even if you've only got half a dozen, you've still got a - according to the mathematics, which I've got in the book - it's fairly simple, but I can't obviously explain on radio.
然而，威斯康星医学院的著名色视觉专家杰·奈茨说，单从数学上解释，其差别会令人震惊。
But mathematics alone suggests the difference would be astounding, said Jay Neitz, a renowned color vision researcher at the Medical College of Wisconsin.
他承认，挑战在于如何解释数学陈述的真假与口味或者一时兴起无关。
The challenge, he admits, is to explain why it is that mathematical statements can be definitively true or false, not subject to taste or whim.
这个发现有助于解释为何一个人精通数学却不通音律，或者擅长于空间导航技术而不善于学习语言。
This could help explain what makes one person good at math but bad at music, or good at spatial navigation but bad at language
Nowak 解释说，“数学帮助我们看到了什么才是最重要而最有趣的实验。
Math helps us to see what the most crucial and interesting experiment is.
例如，比利时布鲁塞尔自由大学的物理学家DiederikAerts实际上已经用基于量子数学理论的更广泛逻辑来解释这些错误。
Physicist Diederik Aerts of the Free University of Brussels, Belgium, has shown that these errors actually make sense within a wider logic based on quantum mathematics.
学者创造数学方程序解释人们的拖延症。
Academics invent a mathematical equation for why people procrastinate.
书里面没有数学公式(也许是因为受到137页的篇幅的限制，不能完全解释爱因斯坦的等式)。
There are no mathematical equations in the book (possibly because the 137 pages don't quite allow enough room to fully explain Einstein's equations).
“我在那教数学”，我解释说。
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