有些程序可以证明数学定理。
但现在这个结果同时也帮助证明了一个新的数学定理。
But now it has also helped prove a new mathematical theorem as well.
理论上说，存在排除某些人使用某句诗歌或某个数学定理的可能。
It is theoretically possible to exclude some from the use of a poem, or a mathematical theorem, but exclusion is generally quite difficult.
就是在那里，他们一次又一次地努力弄懂那些棘手的数学定理。
It was there when they tried and tried to solve all those tricky 11.
从这种机器理论数学的角度上讲，就是有没有证明数学定理的算法。
In mathematical terms, they wanted to know whether there was an algorithm for proving the theorems of mathematics.
如果按这个意思的话，所有的数学定理都具有同等的和彻底的普遍性。
In this sense, which is quite easy to define, all mathematical theorems are equally and completely general.
一个基于“世界上最美数学定理”的离奇怪圈出现在威尔特郡一架风车旁边的田里。
An extraordinary crop circle based on the 'world's most beautiful maths theorem' has appeared in a field next to a windmill in Wiltshire.
本文利用数学定理和新的灵敏度定义给出特征值和特征向量导数的精确解。
The exact solution of derivatives of eigenvalue and eigenvector is presented by utilizing the mathematical theorem and new definitions of sensitivities.
本文以数学定理的形式指出该体系具有一类新的决定论的、物理内容明显的结果。
In this paper we point out in the form of mathematical theorem that the system possesses new and deterministic results with evident physical meanings.
我们在寻找另一种普遍性，可以将不同的数学定理区别开来，虽然在怀特黑德看来都是一样的。
We are looking for differences of generality between one mathematical theorem and another, and in Whitehead's sense all are equally general.
二十世纪七十年代，道格拉斯·莉娜的“自动数学家”程序自动生成数学定理，但是被证明基本上毫无用处。
In the 1970s, Douglas Lenat's Automated Mathematician automatically generated mathematical theorems, but they proved largely useless.
就是在那里，他们一次又一次地努力弄懂那些棘手的数学定理。当他们读到“穿越盐漠的爱”时，教室微笑了。
It was there when they tried and tried to solve all those tricky 11 theorems; it smiled as they read the "Love across salt desert".
本文根据的一个数学定理，对受多个物理白噪声激励的极一般的一个自由度系统导出了随机平均方程。
Based on a theorem due to Hasminskii, a stochastic averaging equation is derived for a general system with one degree of freedom subject to physical white noise excitations.
机器定理证明在数学定理证明、协议验证、软件和硬件的形式化验证等方面发挥出越来越重要的作用。
It has become more and more important that the application of theorem proving on mathematic theorem proving, protocol verification, hardware verification and software verification.
在数学定理的证明中我们并不需要太多的“变数”，“各种情况的列举”实际上是一种更无趣的数学论证方式。
We do not want many 'variations' in the proof of a mathematical theorem:' enumeration of cases', indeed, is one of the duller forms of mathematical argument.
对归结原理的基本概念与推理规则进行了讨论，并在此基础上通过实例探讨了归结推理方法在数学定理证明中的应用。
It discusses carefully the basic concepts and inference rule of the resolution principle. According to the discussion, resolution method is used to prove a mathematical theorem through a example.
高德的不完备定理更像是一组非常有趣的关于逻辑和哲学的数学定理，而不是严格意义上的科学。但是整体上，这些逻辑和哲学与科学密切相关。
It is not strictly science, but rather a very interesting set of mathematical theorems about logic and the philosophy that is definitely relevant to science as a whole.
信息论用数学精度捕获噪声影响的定理概括了这一思想。
Information theory generalises this idea via theorems that capture the effects of noise with mathematical precision.
我把我成功的大部分原因归结于学习数学的收获，尤其是分析复杂原则的那些定理。
I attribute much of my success there to having learned, through the study of mathematics, and, in particular, theorems, how to analyze complicated principles.
著名的定理决定数学的风景。
在数学里，一旦一个定理的证明被公布了，就不需要一个权利机构去认证这个定理是成立的。
In mathematics, once the proof of a theorem is published, there is no need for any authority to certify that the theorem is true.
那部分是数学的东西，即散度定理。
At that part is actually math, namely, the divergence theorem.
他说，专注于一个定理的感觉，就像“一个猎人，一个数学概念的收集者。”
The sensation of working on a theorem, he says, can be like being “a hunter and gatherer of mathematical concepts.”
虽然在数学领域也有一些新的进展，例如对著名的四色定理的证明，1但是基本的材料却保持不变。
Although there have been some new developments in mathematics, such as the proof of the famous four-color theorem, 1 the basic material has remained unchanged.
许多数学家只是把这些恼人的问题简单地弃置一旁，而忙于类似定理证明这样更有趣的事务。
Many mathematicians simply set nettlesome questions like these aside and get back to the more pleasant business of proving theorems.
中国剩余定理记载在一本由数学家孙子编写的书籍中（不要把他和与他同名的军事家孙子混淆了）。
This theorem is contained in a book writtenin the late third-century AD by a mathematician called Sun Tzu (not to beconfused with the military strategist of the same name).
其他的章节是关于巴赫的赋格曲和伟大的德国数学家Kurt Gordel的定理的。
Other chapters are focused on Bach's fugues and the theorems of great German mathematician Kurt Gordel.
哥德尔不完备性定理抽走了数学家的逻辑美信仰，数学界出现了信仰危机。
Godel theorem made mathematicians lose their belief of logic beauty, the crisis of belief appeared in mathematical field.
蕴涵在毕得哥拉斯的定理和及其概括中的观念非常深，但现在的数学家没人会觉得他们很难。
The ideas underlying Pythagoras's theorem and its generalization are quite deep, but no mathematicians now would find them difficult.
蕴涵在毕得哥拉斯的定理和及其概括中的观念非常深，但现在的数学家没人会觉得他们很难。
The ideas underlying Pythagoras's theorem and its generalization are quite deep, but no mathematicians now would find them difficult.
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