一般认为莫扎特音乐会增强数学思考的神经联系。
It is believed that Mozart strengthens neural connections that underlie mathematical thinking.
从十七世纪开始，人们对幻方的构造与性质展开比较严肃的数学思考。
People started to do some mathematical analysis on the structure and the character of magic square from seventeen century.
大部分数学教育，对数学思考的本质和数学创造的过程而言，是一种讽刺。
Most mathematics instruction is a kind of satire on the nature of mathematical thinking and the process of creating mathematics.
戴明发现，同时需要社交和思考能力(特别是数学思考)的职业，在工作岗位和工资方面的处境是最好的。
Jobs that require both socializing and thinking, especially mathematically, have fared best in employment and pay, Mr. Deming found.
但在用数学的方式进行思考时，我们都倾向于变成柏拉图主义者。
But in thinking about math, most of us are inclined to be Platonists.
就这样，这对可爱而大智若愚的父子激发学生们对他们所受训练作更富创造性的思考，也向大众展示数学其实并非如此令人难以接近。
Along the way, the lively and often goofy duo have inspired students to think more creatively about their discipline, and have shown the public that math doesn't have to feel inaccessible.
另一个哲学家，笛卡尔在思考上帝万能的时候觉得，如果万能的上帝无法改变数学，那么便不能称为万能。
And another philosopher, Descartes, in thinking about God's omnipotence, thought that it wouldn't be good enough if God as omnipotent couldn't change the facts of mathematics.
尽管这看起来与计算机系统的数学分析没有太大关系，但是对于思考这些问题来说，这是非常有用的一种方法，而且也是到目前为止最好的一种方法。
While this may seem tangential to a mathematical analysis of computer systems, it is a useful way to think about them and is done haphazardly today at best.
思考清楚你应该采取什么行动的概率后会相对容易些，但给答案时却依然反直觉行之——甚至对那些数学领悟力超强的人而言也是如此。
It's relatively easy to run through the probabilities that show which action you should take, but the answer remains counterintuitive-even for those with an exceptional grasp of math.
从量子理论的数学说到人类思考的本质似乎有些荒唐。
It may sound preposterous to imagine that the mathematics of quantum theory has something to say about the nature of human thinking.
“当我们思考古代数学的时候，我首先想到的是毕达哥拉斯和欧几里德，”她说，但“这不应该是这样。”
"When we think of ancient mathematics, the first names that come to mind are Pythagoras and Euclid," she said, but that "this shouldn't be the case."
研究论文，通过思考一些复杂和支离破碎的细节，用涉及希尔伯特系统和熵的数学来支持论证。
The research paper, thought a bit esoteric and lacking in detail, supports its argument with math involving Hilbert systems and entropy.
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.
他大把的岁月都是在剑桥大学宿舍里独自思考数学问题度过的。
He spent many months more or less alone in his Cambridge University dormitory working on exciting new mathematical ideas.
我很喜欢计算机专家的思考方式，因为他们将数学，工程学和自然科学中一些最好的特征结合在一起。
I like the way computer scientists think because they combine some of the best features of Mathematics, Engineering, and Natural Science.
理解曼德布洛特的观察的最佳方式是思考这个让数学家们在年轻时非常着迷的极其简单的问题的答案：“英国的海岸线有多长？”
The best way to approach Mandelbrot's observation is to ponder the answer to the very simple question that intrigued the mathematician as a young man: "How long is the coast of England?"
这并非Nowak第一次通过电脑模拟和数学计算迫使大家对复杂的现象重新进行思考了。
It wasn't the first time Nowak's computer simulations and mathematics forced a rethinking of a complex phenomenon.
假如别人和一样深刻和持续地思考数学真理，他们会作出同样的发现的。
If someone as deeply and constantly thinking and mathematical truth, they will make the same discovery.
数学的最终目的是不需要智能的思考。
The ultimate goal of mathematics is not to need to smart thinking.
如果解一道数学难题算“思考”的话，电脑也会，而且比人脑快很多。
If solving a mathematical problem is "thinking", then computer can and does so much faster than a man.
Nowak一直在忙着思考如何简化生命出现的过程，直至他有可能用数学描述这个最简单的化学系统。
Nowak has been busy working on how to whittle down the emergence of life into the simplest possible chemical system that he can describe mathematically.
我喜欢思考…在初中，我的数学成绩较佳，每次考试都在全级前三名内。
I like to think... in junior high school, my mathematics result better, every time the exam within the top three in the grade.
有时我会花整个周末来读数学书，有时会数周都不再思考它。
Sometimes I'll spend a whole weekend reading a math book, and sometimes I'll go for weeks without thinking about it even once.
然而不是每个人都能够领会数学分析思维，即使反复解释也不能——仔细思考这一点就让人感到惊异了。
But that not every one can understand mathematical reasoning when explained appears very surprising when we think of it.
然而不是每个人都能够领会数学分析思维，即使反复解释也不能——仔细思考这一点就让人感到惊异了。
But that not every one can understand mathematical reasoning when explained appears very surprising when we think of it.
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